Back Home Official Asymptote WEB Site
Asymptote Gallery in one page
List of pictures
Figure 0001
figure 0001
Figure 0002
figure 0002
Figure 0003
figure 0003
Figure 0004
figure 0004
Figure 0005
figure 0005
Figure 0006
figure 0006
Figure 0007
figure 0007
Figure 0008
figure 0008
Figure 0009
figure 0009
Figure 0010
figure 0010
Figure 0011
figure 0011
Figure 0012
figure 0012
Figure 0013
figure 0013
Figure 0014
figure 0014
Figure 0015
figure 0015
Figure 0016
figure 0016
Figure 0017
figure 0017
Figure 0018
figure 0018
Figure 0019
figure 0019
Figure 0020
figure 0020
Figure 0021
figure 0021
Figure 0022
figure 0022
Figure 0023
figure 0023
Figure 0024
figure 0024
Figure 0025
figure 0025
Figure 0026
figure 0026
Figure 0027
figure 0027
Figure 0028
figure 0028
Figure 0029
figure 0029
Figure 0030
figure 0030
Figure 0031
figure 0031
Figure 0032
figure 0032
Figure 0033
figure 0033
Figure 0034
figure 0034
Figure 0035
figure 0035
Figure 0036
figure 0036
Figure 0037
figure 0037
Figure 0038
figure 0038
Figure 0039
figure 0039
Figure 0040
figure 0040
Figure 0041
figure 0041
Figure 0042
figure 0042
Figure 0043
figure 0043
Figure 0044
figure 0044
Figure 0045
figure 0045
Figure 0046
figure 0046
Figure 0047
figure 0047
Figure 0048
figure 0048
Figure 0049
figure 0049
Figure 0050
figure 0050
Figure 0051
figure 0051
Figure 0052
figure 0052
Figure 0053
figure 0053
Figure 0054
figure 0054
Figure 0055
figure 0055
Figure 0056
figure 0056
Figure 0057
figure 0057
Figure 0058
figure 0058
Figure 0059
figure 0059
Figure 0060
figure 0060
Figure 0061
figure 0061
Figure 0062
figure 0062
Figure 0063
figure 0063
Figure 0064
figure 0064
Figure 0065
figure 0065
Figure 0066
figure 0066
Figure 0067
figure 0067
Figure 0068
figure 0068
Figure 0069
figure 0069
Figure 0070
figure 0070
Figure 0071
figure 0071
Figure 0072
figure 0072
Figure 0073
figure 0073
Figure 0074
figure 0074
Figure 0075
figure 0075
Figure 0076
figure 0076
Figure 0077
figure 0077
Figure 0078
figure 0078
Figure 0079
figure 0079
Figure 0080
figure 0080
Figure 0081
figure 0081
Figure 0082
figure 0082
Figure 0083
figure 0083
Figure 0084
figure 0084
Figure 0085
figure 0085
Figure 0086
figure 0086
Figure 0087
figure 0087
Figure 0088
figure 0088
Figure 0089
figure 0089
Figure 0090
figure 0090
Figure 0091
figure 0091
Figure 0092
figure 0092
Figure 0093
figure 0093
Figure 0094
figure 0094
Figure 0095
figure 0095
Figure 0096
figure 0096
Figure 0097
figure 0097
Figure 0098
figure 0098
Figure 0099
figure 0099
Figure 0100
figure 0100
Figure 0101
figure 0101
Figure 0102
figure 0102
Figure 0103
figure 0103
Figure 0104
figure 0104
Figure 0105
figure 0105
Figure 0106
figure 0106
Figure 0107
figure 0107
Figure 0108
figure 0108
Figure 0109
figure 0109
Figure 0110
figure 0110
Figure 0111
figure 0111
Figure 0112
figure 0112
Figure 0113
figure 0113
Figure 0114
figure 0114
Figure 0115
figure 0115
Figure 0116
figure 0116
Figure 0117
figure 0117
Figure 0118
figure 0118
Figure 0119
figure 0119
Figure 0120
figure 0120
Figure 0121
figure 0121
Figure 0122
figure 0122
Figure 0123
figure 0123
Figure 0124
figure 0124
Figure 0125
figure 0125
Figure 0126
figure 0126
Figure 0127
figure 0127
Figure 0128
figure 0128
Figure 0129
figure 0129
Figure 0130
figure 0130
Figure 0131
figure 0131
Figure 0132
figure 0132
Figure 0133
figure 0133
Figure 0134
figure 0134
Figure 0135
figure 0135
Figure 0136
figure 0136
Figure 0137
figure 0137
Figure 0138
figure 0138
Figure 0139
figure 0139
Figure 0140
figure 0140
Figure 0141
figure 0141
Figure 0142
figure 0142
Figure 0143
figure 0143
Figure 0144
figure 0144
Figure 0145
figure 0145
Figure 0146
figure 0146
Figure 0147
figure 0147
Figure 0148
figure 0148
Figure 0149
figure 0149
Figure 0150
figure 0150
Figure 0151
figure 0151
Figure 0152
figure 0152
Figure 0153
figure 0153
Figure 0154
figure 0154
Figure 0155
figure 0155
Figure 0156
figure 0156
Figure 0157
figure 0157
Figure 0158
figure 0158
Figure 0159
figure 0159
Figure 0160
figure 0160
Figure 0161
figure 0161
Figure 0162
figure 0162
Figure 0163
figure 0163
Figure 0164
figure 0164
Figure 0165
figure 0165
Figure 0166
figure 0166
Figure 0167
figure 0167
Figure 0168
figure 0168
Figure 0169
figure 0169
Figure 0170
figure 0170
Figure 0171
figure 0171
Figure 0172
figure 0172
Figure 0173
figure 0173
Figure 0174
figure 0174
Figure 0175
figure 0175
Figure 0176
figure 0176
Figure 0177
figure 0177
Figure 0178
figure 0178
Figure 0179
figure 0179
Figure 0180
figure 0180
Figure 0181
figure 0181
Figure 0182
figure 0182
Figure 0183
figure 0183
Figure 0184
figure 0184
Figure 0185
figure 0185
Figure 0186
figure 0186
Figure 0187
figure 0187
Figure 0188
figure 0188
Figure 0189
figure 0189
Figure 0190
figure 0190
Figure 0191
figure 0191
Figure 0192
figure 0192
Figure 0193
figure 0193
Figure 0194
figure 0194
Figure 0195
figure 0195
Figure 0196
figure 0196
Figure 0197
figure 0197
Figure 0198
figure 0198
Figure 0199
figure 0199
Figure 0200
figure 0200
Figure 0201
figure 0201
Figure 0202
figure 0202
Figure 0203
figure 0203
Figure 0204
figure 0204
Figure 0205
figure 0205
Figure 0206
figure 0206
Figure 0207
figure 0207
Figure 0208
figure 0208
Figure 0209
figure 0209
Figure 0210
figure 0210
Figure 0211
figure 0211
Figure 0212
figure 0212
Figure 0213
figure 0213
Figure 0214
figure 0214
Figure 0215
figure 0215
Figure 0216
figure 0216
Figure 0217
figure 0217
Figure 0218
figure 0218
Figure 0219
figure 0219
Figure 0220
figure 0220
Figure 0221
figure 0221
Figure 0222
figure 0222
Figure 0223
figure 0223
Figure 0224
figure 0224
Figure 0225
figure 0225
Figure 0226
figure 0226
Figure 0227
figure 0227
Figure 0228
figure 0228
Figure 0229
figure 0229
Figure 0230
figure 0230
Figure 0231
figure 0231
Figure 0232
figure 0232
Figure 0233
figure 0233
Figure 0234
figure 0234
Figure 0235
figure 0235
Figure 0236
figure 0236
Figure 0237
figure 0237
Figure 0238
figure 0238
Figure 0239
figure 0239
Figure 0240
figure 0240
Figure 0001
Figure 0001: BezierPatch.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

size(10cm);
currentlight=(0,0,1);

surface s=surface(patch(new triple[][] {
      {(0,0,0),(1,0,0),(1,0,0),(2,0,0)},
      {(0,1,0),(1,0,1),(1,0,1),(2,1,0)},
      {(0,1,0),(1,0,-1),(1,0,-1),(2,1,0)},
      {(0,2,0),(1,2,0),(1,2,0),(2,2,0)}}));

draw(s,yellow);
draw(s.s[0].vequals(0.5),squarecap+2bp+blue,currentlight);
draw(s.s[0].uequals(0.5),squarecap+2bp+red,currentlight);
Figure 0002
Figure 0002: BezierSurface.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

string viewpoint="{-24.132780075073242 7.2992024421691895 7.695427417755127}{0.8244762420654297 -0.563306450843811 0.0540805421769619}{35.62141440580922}{17.392748820528627}{}";

//viewpoint=getstring("viewpoint",viewpoint);
currentprojection=perspective(viewpoint);

currentlight=White;

triple[][][] P={{
    {(-1.6,0,1.875),(-1.6,-0.3,1.875),(-1.5,-0.3,2.1),(-1.5,0,2.1)},
    {(-2.3,0,1.875),(-2.3,-0.3,1.875),(-2.5,-0.3,2.1),(-2.5,0,2.1)},
    {(-2.7,0,1.875),(-2.7,-0.3,1.875),(-3,-0.3,2.1),(-3,0,2.1)},
    {(-2.7,0,1.65),(-2.7,-0.3,1.65),(-3,-0.3,1.65),(-3,0,1.65)}
  },{
    {(-2.7,0,1.65),(-2.7,-0.3,1.65),(-3,-0.3,1.65),(-3,0,1.65)},
    {(-2.7,0,1.425),(-2.7,-0.3,1.425),(-3,-0.3,1.2),(-3,0,1.2)},
    {(-2.5,0,0.975),(-2.5,-0.3,0.975),(-2.65,-0.3,0.7275),(-2.65,0,0.7275)},
    {(-2,0,0.75),(-2,-0.3,0.75),(-1.9,-0.3,0.45),(-1.9,0,0.45)}
  },{
    {(-2.7,0,1.65),(-2.7,0.3,1.65),(-3,0.3,1.65),(-3,0,1.65)},
    {(-2.7,0,1.875),(-2.7,0.3,1.875),(-3,0.3,2.1),(-3,0,2.1)},
    {(-2.3,0,1.875),(-2.3,0.3,1.875),(-2.5,0.3,2.1),(-2.5,0,2.1)},
    {(-1.6,0,1.875),(-1.6,0.3,1.875),(-1.5,0.3,2.1),(-1.5,0,2.1)}
  },{
    {(-2,0,0.75),(-2,0.3,0.75),(-1.9,0.3,0.45),(-1.9,0,0.45)},
    {(-2.5,0,0.975),(-2.5,0.3,0.975),(-2.65,0.3,0.7275),(-2.65,0,0.7275)},
    {(-2.7,0,1.425),(-2.7,0.3,1.425),(-3,0.3,1.2),(-3,0,1.2)},
    {(-2.7,0,1.65),(-2.7,0.3,1.65),(-3,0.3,1.65),(-3,0,1.65)}
  }};

picture pic;
size(pic,15cm);
size3(pic,10cm);
draw(pic,surface(P),blue);

add(embed("label",pic),(0,0),N);
label(cameralink("label"),(0,0),10S,fontsize(24pt));
Figure 0003
Figure 0003: Bode.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
texpreamble("\def\Arg{\mathop {\rm Arg}\nolimits}");

size(10cm,5cm,IgnoreAspect);

real ampl(real x) {return 2.5/(1+x^2);}
real phas(real x) {return -atan(x)/pi;}

scale(Log,Log);
draw(graph(ampl,0.01,10));
ylimits(0.001,100);

xaxis("$\omega\tau_0$",BottomTop,LeftTicks);
yaxis("$|G(\omega\tau_0)|$",Left,RightTicks);

picture q=secondaryY(new void(picture pic) {
    scale(pic,Log,Linear);
    draw(pic,graph(pic,phas,0.01,10),red);
    ylimits(pic,-1.0,1.5);
    yaxis(pic,"$\Arg G/\pi$",Right,red,
          LeftTicks("$% #.1f$",
                    begin=false,end=false));
    yequals(pic,1,Dotted);
  });
label(q,"(1,0)",Scale(q,(1,0)),red);
add(q);
Figure 0004
Figure 0004: CAD1.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import CAD;

sCAD cad=sCAD.Create();

// Freehand line
draw(g=cad.MakeFreehand(pFrom=(3,-1)*cm,(6,-1)*cm),
     p=cad.pFreehand);

// Standard measurement lines
draw(g=box((0,0)*cm,(1,1)*cm),p=cad.pVisibleEdge);
cad.MeasureParallel(L="$\sqrt{2}$",
                    pFrom=(0,1)*cm,
                    pTo=(1,0)*cm,
                    dblDistance=-15mm);

// Label inside,shifted to the right; arrows outside
draw(g=box((2,0)*cm,(3,1)*cm),p=cad.pVisibleEdge);
cad.MeasureParallel(L="1",
                    pFrom=(2,1)*cm,
                    pTo=(3,1)*cm,
                    dblDistance=5mm,
                    dblLeft=5mm,
                    dblRelPosition=0.75);

// Label and arrows outside
draw(g=box((5,0)*cm,(5.5,1)*cm),p=cad.pVisibleEdge);
cad.MeasureParallel(L="0.5",
                    pFrom=(5,1)*cm,
                    pTo=(5.5,1)*cm,
                    dblDistance=5mm,
                    dblLeft=10mm,
                    dblRelPosition=-1);

// Small bounds,asymmetric measurement line
draw(g=box((7,0)*cm,(7.5,1)*cm),p=cad.pVisibleEdge);
cad.MeasureParallel(L="0.5",
                    pFrom=(7,1)*cm,
                    pTo=(7.5,1)*cm,
                    dblDistance=5mm,
                    dblLeft=2*cad.GetMeasurementBoundSize(bSmallBound=true),
                    dblRight=10mm,
                    dblRelPosition=2,
                    bSmallBound=true);
Figure 0005
Figure 0005: CDlabel.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(11.7cm,11.7cm);
asy(nativeformat(),"logo");
fill(unitcircle^^(scale(2/11.7)*unitcircle),
     evenodd+rgb(124/255,205/255,124/255));
label(scale(1.1)*minipage(
"\centering\scriptsize \textbf{\LARGE {\tt Asymptote}\\
\smallskip
\small The Vector Graphics Language}\\
\smallskip
\textsc{Andy Hammerlindl, John Bowman, and Tom Prince}
http://asymptote.sourceforge.net\\
",8cm),(0,0.6));
label(graphic("logo."+nativeformat(),"height=7cm"),(0,-0.22));
clip(unitcircle^^(scale(2/11.7)*unitcircle),evenodd);
Figure 0006
Figure 0006: Coons.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);

pen[] p={red,green,blue,magenta};
path g=(0,0){dir(45)}..(1,0)..(1,1)..(0,1)..cycle;
tensorshade(g,p);
dot(g);
Figure 0007
Figure 0007: GaussianSurface.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size(200,0);

currentprojection=perspective(10,8,4);

real f(pair z) {return 0.5+exp(-abs(z)^2);}

draw((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle);

draw(arc(0.12Z,0.2,90,60,90,25),ArcArrow3);

surface s=surface(f,(-1,-1),(1,1),nx=5,Spline);

xaxis3(Label("$x$"),red,Arrow3);
yaxis3(Label("$y$"),red,Arrow3);
zaxis3(XYZero(extend=true),red,Arrow3);

draw(s,lightgray,meshpen=black+thick(),nolight);

label("$O$",O,-Z+Y,red);
Figure 0008
Figure 0008: Gouraud.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);

pen[] p={red,green,blue,magenta};
pair[] z={(-1,0),(0,0),(0,1),(1,0)};
int[] edges={0,0,0,1};
gouraudshade(z[0]--z[2]--z[3]--cycle,p,z,edges);

draw(z[0]--z[1]--z[2]--cycle);
draw(z[1]--z[3]--z[2],dashed);

dot(Label,z[0],W);
dot(Label,z[1],S);
dot(Label,z[2],N);
dot(Label,z[3],E);

label("0",z[0]--z[1],S,red);
label("1",z[1]--z[2],E,red);
label("2",z[2]--z[0],NW,red);
Figure 0009
Figure 0009: Gouraudcontour.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
import palette;
import contour;

size(200);

int n=100;

real[] x=new real[n];
real[] y=new real[n];
real[] f=new real[n];

real F(real a, real b) {return a^2+b^2;}

real r() {return 1.1*(rand()/randMax*2-1);}

for(int i=0; i < n; ++i) {
  x[i]=r();
  y[i]=r();
  f[i]=F(x[i],y[i]);
}

pen Tickpen=black;
pen tickpen=gray+0.5*linewidth(currentpen);
pen[] Palette=BWRainbow();

bounds range=image(x,y,f,Range(0,2),Palette);
draw(contour(pairs(x,y),f,new real[]{0.25,0.5,1},operator ..));

palette("$f(x,y)$",range,point(NW)+(0,0.5),point(NE)+(0,0.8),Top,Palette,
        PaletteTicks(Tickpen,tickpen));
Figure 0010
Figure 0010: HermiteSpline.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(140mm,70mm,IgnoreAspect); 
scale(false); 
real[] x={1,3,4,5,6};
real[] y={1,5,2,0,4}; 

marker mark=marker(scale(1mm)*cross(6,false,r=0.35),red,Fill); 

draw(graph(x,y,Hermite),"Hermite Spline",mark);
xaxis("$x$",Bottom,LeftTicks(x)); 
yaxis("$y$",Left,LeftTicks); 
attach(legend(),point(NW),40S+30E,UnFill);
Figure 0011
Figure 0011: Hobbycontrol.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);
pair z0=(0,0);
pair z1=(0.5,3);
pair z2=(2,1);

path g=z0..z1..z2;

pair d0=dir(g,0);
pair d1=dir(g,1);
draw(Label("$\omega_0$",1),z0-d0..z0+d0,blue+dashed,Arrow);
draw(Label("$\omega_1$",1),z1-d1..z1+1.5d1,blue+dashed,Arrow);
draw(z0--interp(z0,z1,1.5),dashed);
draw(subpath(g,0,1),blue);
draw("$\theta$",arc(z0,0.4,degrees(z1-z0),degrees(d0)),red,Arrow,
     EndPenMargin);
draw("$\phi$",arc(z1,1.05,degrees(z1-z0),degrees(d1)),red,Arrow,
     EndPenMargin);

dot("$z_0$",z0,SW,red);
dot("$z_1$",z1,SE,red);
Figure 0012
Figure 0012: Hobbydir.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);
pair z0=(0,0);
pair z1=(1,2);
pair z2=(2,1);

path g=z0..z1..z2;

label("$\ell_k$",z0--z1);
draw("$\ell_{k+1}$",z1--z2,dashed);
draw(z0--interp(z0,z1,1.5),dashed);
pair d1=dir(g,1);
draw(z1-d1..z1+d1,blue+dashed);
draw(g,blue);
draw(Label("$\theta_k$",0.4),arc(z1,0.4,degrees(z2-z1),degrees(d1)),blue,Arrow,
     EndPenMargin);
draw("$\phi_k$",arc(z1,0.4,degrees(d1),degrees(z1-z0),CCW),Arrow,
     EndPenMargin);

dot("$z_{k-1}$",z0,red);
dot("$z_k$",z1,NW,red);
dot("$z_{k+1}$",z2,red);
Figure 0013
Figure 0013: Klein.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size(469pt);

viewportmargin=0;

currentprojection=perspective(
camera=(25.0851928432063,-30.3337528952473,19.3728775115443),
up=Z,
target=(-0.590622314050054,0.692357205025578,-0.627122488455679),
zoom=1,
autoadjust=false);

triple f(pair t) {
  real u=t.x;
  real v=t.y;
  real r=2-cos(u);
  real x=3*cos(u)*(1+sin(u))+r*cos(v)*(u < pi ? cos(u) : -1);
  real y=8*sin(u)+(u < pi ? r*sin(u)*cos(v) : 0);
  real z=r*sin(v);
  return (x,y,z);
}

surface s=surface(f,(0,0),(2pi,2pi),8,8,Spline);
draw(s,lightolive+white);

string lo="$\displaystyle u\in[0,\pi]: \cases{x=3\cos u(1+\sin u)+(2-\cos u)\cos u\cos v,\cr
y=8\sin u+(2-\cos u)\sin u\cos v,\cr
z=(2-\cos u)\sin v.\cr}$";

string hi="$\displaystyle u\in[\pi,2\pi]:\\\cases{x=3\cos u(1+\sin u)-(2-\cos u)\cos v,\cr
y=8\sin u,\cr
z=(2-\cos u)\sin v.\cr}$";

real h=0.0125;

draw(surface(xscale(-0.38)*yscale(-0.18)*lo,s,0,1.7,h));
draw(surface(xscale(0.26)*yscale(0.1)*rotate(90)*hi,s,4.9,1.4,h));
draw(s.uequals(0),blue+dashed);
draw(s.uequals(pi),blue+dashed);

currentpicture.add(new void(frame f, transform3 t, picture pic, projection P) {
    draw(f,invert(box(min(f,P),max(f,P)),P));
  });
Figure 0014
Figure 0014: NURBSsurface.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

size(10cm);

currentprojection=perspective(40,40,50);

// Nonrational surface:
// udegree=3, vdegree=3, nu=5, nv=6;
real[] uknot={0,0,0,0,0.5,1,1,1,1};
real[] vknot={0,0,0,0,0.4,0.6,1,1,1,1};

triple[][] P={{
  (-31.2061,12.001,6.45082),
  (-31.3952,14.7353,6.53707),
  (-31.5909,21.277,6.70051),
  (-31.4284,25.4933,6.76745),
  (-31.5413,30.3485,6.68777),
  (-31.4896,32.2839,6.58385),
  },{
  (-28.279,12.001,7.89625),
  (-28.4187,14.7353,8.00954),
  (-28.5633,21.277,8.22422),
  (-28.4433,25.4933,8.31214),
  (-28.5266,30.3485,8.20749),
  (-28.4885,32.2839,8.07099),
  },{
  (-20,12.001,10.0379),
  (-20,14.7353,10.2001),
  (-20,21.277,10.5076),
  (-20,25.4933,10.6335),
  (-20,30.3485,10.4836),
  (-20,32.2839,10.2881),
  },{
  (-11.721,12.001,7.84024),
  (-11.5813,14.7353,7.95269),
  (-11.4367,21.277,8.16575),
  (-11.5567,25.4933,8.25302),
  (-11.4734,30.3485,8.14915),
  (-11.5115,32.2839,8.01367),
  },{
  (-8.79391,12.001,6.39481),
  (-8.60483,14.7353,6.48022),
  (-8.40905,21.277,6.64204),
  (-8.57158,25.4933,6.70832),
  (-8.45874,30.3485,6.62943),
  (-8.51041,32.2839,6.52653)
  }};

draw(P,uknot,vknot,new pen[] {red,green,blue,magenta});

// Rational Bezier patch:
// udegree=3, vdegree=3, nu=4, nv=4;
real[] uknot={0,0,0,0,1,1,1,1};
real[] vknot={0,0,0,0,1,1,1,1};
triple[][] P=scale3(20)*octant1.P;

// Optional weights:
real[][] weights=array(P.length,array(P[0].length,1.0));
weights[1][2]=0.5;

draw(P,uknot,vknot,weights,blue);
Figure 0015
Figure 0015: Pythagoras.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,150);
import geometry;

real a=3;
real b=4;
real c=hypot(a,b);

pair z1=(0,b);
pair z2=(a,0);
pair z3=(a+b,0);
perpendicular(z1,NE,z1--z2,blue);
perpendicular(z3,NW,blue);
draw(square((0,0),z3));
draw(square(z1,z2));

real d=0.3;
pair v=unit(z2-z1);
draw(baseline("$a$"),-d*I--z2-d*I,red,Bars,Arrows,PenMargins);
draw(baseline("$b$"),z2-d*I--z3-d*I,red,Arrows,Bars,PenMargins);
draw("$c$",z3+z2*I-d*v--z2-d*v,red,Arrows,PenMargins);
draw("$a$",z3+d--z3+z2*I+d,red,Arrows,Bars,PenMargins);
draw("$b$",z3+z2*I+d--z3+z3*I+d,red,Arrows,Bars,PenMargins);
Figure 0016
Figure 0016: PythagoreanTree.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(250);

real a=3;
real b=4;
real c=hypot(a,b);

transform ta=shift(c,c)*rotate(-aCos(a/c))*scale(a/c)*shift(-c);
transform tb=shift(0,c)*rotate(aCos(b/c))*scale(b/c);

picture Pythagorean(int n) {
  picture pic;
  fill(pic,scale(c)*unitsquare,1/(n+1)*green+n/(n+1)*brown);
  if(n == 0) return pic;
  picture branch=Pythagorean(--n);
  add(pic,ta*branch);
  add(pic,tb*branch);
  return pic;
}

add(Pythagorean(12));
Figure 0017
Figure 0017: RiemannSurface.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import palette;
       
size(200,300,keepAspect=false);
//settings.nothin=true;
       
currentprojection=orthographic(10,10,30);
currentlight=(10,10,5);
triple f(pair t) {return (exp(t.x)*cos(t.y),exp(t.x)*sin(t.y),t.y);}
       
surface s=surface(f,(-4,-2pi),(0,4pi),8,16,Spline);
s.colors(palette(s.map(zpart),Rainbow()));
draw(s);
Figure 0018
Figure 0018: RiemannSurfaceRoot.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
// Riemann surface of z^{1/n}
import graph3;
import palette;
 
int n=3;

size(200,300,keepAspect=false);
//settings.nothin=true; 
 
currentprojection=orthographic(10,10,30);
currentlight=(10,10,5);
triple f(pair t) {return (t.x*cos(t.y),t.x*sin(t.y),t.x^(1/n)*sin(t.y/n));}
 
surface s=surface(f,(0,0),(1,2pi*n),8,16,Spline);
s.colors(palette(s.map(zpart),Rainbow()));

draw(s,meshpen=black);
Figure 0019
Figure 0019: Sierpinski.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(10cm);

// Draw Sierpinski triangle with top vertex A, side s, and depth q.
void Sierpinski(pair A, real s, int q, bool top=true)
{
  pair B=A-(1,sqrt(2))*s/2;
  pair C=B+s;
  if(top) draw(A--B--C--cycle);
  draw((A+B)/2--(B+C)/2--(A+C)/2--cycle);
  if(q > 0) {
    Sierpinski(A,s/2,q-1,false);
    Sierpinski((A+B)/2,s/2,q-1,false);
    Sierpinski((A+C)/2,s/2,q-1,false);
  }
}

Sierpinski((0,1),1,5);
Figure 0020
Figure 0020: advection.asy
(Compiled with Asymptote version 1.87svn-r4643) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,22cm);

texpreamble("
\usepackage{bm}
\def\v{\bm}
\def\grad{\v\nabla}
\def\cross{{\v\times}}
\def\curl{\grad\cross}
\def\del{\nabla}
");

defaultpen(fontsize(10pt));

real margin=1.5mm;

object IC=draw("initial condition $\v U_0$",box,(0,1),
               margin,black,FillDraw(palegray));
object Adv0=draw("Lagrangian state $\v U(t)$",ellipse,(1,1),
                 margin,red,FillDraw(palered));
object Adv=draw("Lagrangian prediction $\v U(t+\tau)$",ellipse,(1,0),
                margin,red,FillDraw(palered));
object AdvD=draw("diffused parcels",ellipse,(1.8,1),
                 margin,red,FillDraw(palered));
object Ur=draw("rearranged $\v \widetilde U$",box,(0,0),
               margin,orange+gray,FillDraw(paleyellow));
object Ui=draw("interpolated $\v \widetilde U$",box,(1,-1),
               margin,blue,FillDraw(paleblue));
object Crank=draw("${\cal L}^{-1}(-\tau){\cal L}(\tau)\v \widetilde U$",
                  box,(0.5,-1),margin,blue,FillDraw(paleblue));
object CrankR=draw("${\cal L}^{-1}(-\tau){\cal L}(\tau)\v \widetilde U$",
                   box,(0,-1),margin,orange+gray,FillDraw(paleyellow));
object Urout=draw(minipage("\center{Lagrangian rearranged solution~$\v U_R$}",
                           100pt),box,(0,-2),margin,orange+gray,
                  FillDraw(paleyellow));
object Diff=draw("$\v D\del^2 \v \widetilde U$",box,(0.75,-1.5),
                 margin,blue,FillDraw(paleblue));
object UIout=draw(minipage("\center{semi-Lagrangian solution~$\v U_I$}",80pt),
                  box,(0.5,-2),margin,FillDraw(palered+paleyellow));
object psi=draw("$\psi=\del^{-2}\omega$",box,(1.6,-1),
                margin,darkgreen,FillDraw(palegreen));
object vel=draw("$\v v=\v{\hat z} \cross\grad\psi$",box,(1.6,-0.5),
                margin,darkgreen,FillDraw(palegreen));

add(new void(frame f, transform t) {
    pair padv=0.5*(point(Adv0,S,t)+point(Adv,N,t));
    picture pic;
    draw(pic,"initialize",point(IC,E,t)--point(Adv0,W,t),RightSide,Arrow,
         PenMargin);
    draw(pic,minipage("\flushright{advect: Runge-Kutta}",80pt),
         point(Adv0,S,t)--point(Adv,N,t),RightSide,red,Arrow,PenMargin);
    draw(pic,Label("Lagrange $\rightarrow$ Euler",0.45),
         point(Adv,W,t)--point(Ur,E,t),5LeftSide,orange+gray,
         Arrow,PenMargin);
    draw(pic,"Lagrange $\rightarrow$ Euler",point(Adv,S,t)--point(Ui,N,t),
         RightSide,blue,Arrow,PenMargin);
    draw(pic,point(Adv,E,t)--(point(AdvD,S,t).x,point(Adv,E,t).y),red,
         Arrow(Relative(0.7)),PenMargin);
    draw(pic,minipage("\flushleft{diffuse: multigrid Crank--Nicholson}",80pt),
         point(Ui,W,t)--point(Crank,E,t),5N,blue,MidArrow,PenMargin);
    draw(pic,minipage("\flushleft{diffuse: multigrid Crank--Nicholson}",80pt),
         point(Ur,S,t)--point(CrankR,N,t),LeftSide,orange+gray,Arrow,PenMargin);
    draw(pic,"output",point(CrankR,S,t)--point(Urout,N,t),RightSide,
         orange+gray,Arrow,PenMargin);
    draw(pic,point(Ui,S,t)--point(Diff,N,t),blue,MidArrow,PenMargin);
    draw(pic,point(Crank,S,t)--point(Diff,N,t),blue,MidArrow,PenMargin);
    label(pic,"subtract",point(Diff,N,t),12N,blue);
    draw(pic,Label("Euler $\rightarrow$ Lagrange",0.5),
         point(Diff,E,t)--(point(AdvD,S,t).x,point(Diff,E,t).y)--
         (point(AdvD,S,t).x,point(Adv,E,t).y),RightSide,blue,
         Arrow(position=1.5),PenMargin);
    dot(pic,(point(AdvD,S,t).x,point(Adv,E,t).y),red);
    draw(pic,(point(AdvD,S,t).x,point(Adv,E,t).y)--point(AdvD,S,t),red,Arrow,
         PenMargin);
    draw(pic,"output",point(Crank,S,t)--point(UIout,N,t),RightSide,brown,Arrow,
         PenMargin);
    draw(pic,Label("$t+\tau\rightarrow t$",0.45),
         point(AdvD,W,t)--point(Adv0,E,t),2.5LeftSide,red,Arrow,PenMargin);
    draw(pic,point(psi,N,t)--point(vel,S,t),darkgreen,Arrow,PenMargin);
    draw(pic,Label("self-advection",4.5),point(vel,N,t)--
         arc((point(vel,N,t).x,point(Adv,E,t).y),5,270,90)--
         (point(vel,N,t).x,padv.y)--
         padv,LeftSide,darkgreen,Arrow,PenMargin);
    draw(pic,Label("multigrid",0.5,S),point(Ui,E,t)--point(psi,W,t),darkgreen,
         Arrow,PenMargin);

    add(f,pic.fit());
  });
Figure 0021
Figure 0021: alignbox.asy
(Compiled with Asymptote version 1.87svn-r4643) 
/* This code comes from The Official Asymptote Gallery */
    
real margin=1.5mm;

object left=align(object("$x^2$",ellipse,margin),W);
add(left);
object right=align(object("$\sin x$",ellipse,margin),4E);
add(right);
currentpicture.add(new void(frame f, transform t) {
    draw(f,point(left,NE,t)--point(right,W,t));
  });
Figure 0022
Figure 0022: alignedaxis.asy
(Compiled with Asymptote version 1.87svn-r4643) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

real Freq=60.0;
real margin=5mm;

pair exp(pair x) {
  return exp(x.x)*(cos(x.y)+I*sin(x.y));
}

real Merr(real x, real w) {
  real tau=x/(2*Freq);
  return 20*log(abs((tau*w+tau/(exp(I*2*pi*Freq*tau)-1))*(I*2*pi*Freq)));
}

real Aerr(real x, real w) {
  real tau=x/(2*Freq);
  return degrees((tau*w+tau/(exp(I*2*pi*Freq*tau)-1))*(I*2*pi*Freq));
}

picture pic1;
scale(pic1,Log,Linear);
real Merr1(real x){return Merr(x,1);}
draw(pic1,graph(pic1,Merr1,1e-4,1),black+1.2);

ylimits(pic1,-60,20);
yaxis(pic1,"magnitude (dB)",LeftRight,RightTicks(new
                                                 real[] {-60,-40,-20,0,20}));
xaxis(pic1,"$f/f_\mathrm{Ny}$",BottomTop,LeftTicks(N=5));
yequals(pic1,0,Dotted);
yequals(pic1,-20,Dotted);
yequals(pic1,-40,Dotted);
xequals(pic1,1e-3,Dotted);
xequals(pic1,1e-2,Dotted);
xequals(pic1,1e-1,Dotted);

size(pic1,100,100,point(pic1,SW),point(pic1,NE));

label(pic1,"$\theta=1$",point(pic1,N),2N);

frame f1=pic1.fit();
add(f1);

picture pic1p;
scale(pic1p,Log,Linear);
real Aerr1(real x){return Aerr(x,1);}
draw(pic1p,graph(pic1p,Aerr1,1e-4,1),black+1.2);

ylimits(pic1p,-5,95);
yaxis(pic1p,"phase (deg)",LeftRight,RightTicks(new real[] {0,45,90}));
xaxis(pic1p,"$f/f_\mathrm{Ny}$",BottomTop,LeftTicks(N=5));
yequals(pic1p,0,Dotted);
yequals(pic1p,45,Dotted);
yequals(pic1p,90,Dotted);
xequals(pic1p,1e-3,Dotted);
xequals(pic1p,1e-2,Dotted);
xequals(pic1p,1e-1,Dotted);

size(pic1p,100,100,point(pic1p,SW),point(pic1p,NE));

frame f1p=pic1p.fit();
f1p=shift(0,min(f1).y-max(f1p).y-margin)*f1p;
add(f1p);

picture pic2;
scale(pic2,Log,Linear);
real Merr2(real x){return Merr(x,0.75);}
draw(pic2,graph(pic2,Merr2,1e-4,1),black+1.2);

ylimits(pic2,-60,20);
yaxis(pic2,"magnitude (dB)",LeftRight,RightTicks(new
                                                 real[] {-60,-40,-20,0,20}));
xaxis(pic2,"$f/f_\mathrm{Ny}$",BottomTop,LeftTicks(N=5));
yequals(pic2,0,Dotted);
yequals(pic2,-20,Dotted);
yequals(pic2,-40,Dotted);
xequals(pic2,1e-3,Dotted);
xequals(pic2,1e-2,Dotted);
xequals(pic2,1e-1,Dotted);

size(pic2,100,100,point(pic2,SW),point(pic2,NE));

label(pic2,"$\theta=0.75$",point(pic2,N),2N);

frame f2=pic2.fit();
f2=shift(max(f1).x-min(f2).x+margin)*f2;
add(f2);

picture pic2p;
scale(pic2p,Log,Linear);
real Aerr2(real x){return Aerr(x,0.75);}
draw(pic2p,graph(pic2p,Aerr2,1e-4,1),black+1.2);

ylimits(pic2p,-5,95);
yaxis(pic2p,"phase (deg)",LeftRight,RightTicks(new real[] {0,45.1,90}));
xaxis(pic2p,"$f/f_\mathrm{Ny}$",BottomTop,LeftTicks(N=5));
yequals(pic2p,0,Dotted);
yequals(pic2p,45,Dotted);
yequals(pic2p,90,Dotted);
xequals(pic2p,1e-3,Dotted);
xequals(pic2p,1e-2,Dotted);
xequals(pic2p,1e-1,Dotted);

size(pic2p,100,100,point(pic2p,SW),point(pic2p,NE));

frame f2p=pic2p.fit();
f2p=shift(max(f1p).x-min(f2p).x+margin,min(f2).y-max(f2p).y-margin)*f2p;
add(f2p);
Figure 0023
Figure 0023: arrows3.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

size(15cm);

currentprojection=perspective(24,14,13);
currentlight=light(gray(0.5),specularfactor=3,viewport=false,
                   (0.5,-0.5,-0.25),(0.5,0.5,0.25),(0.5,0.5,1),(-0.5,-0.5,-1));

defaultpen(0.75mm);

path3 g=arc(O,1,90,-60,90,60);
transform3 t=shift(invert(3S,O));

draw(g,blue,Arrows3(TeXHead3),currentlight);
draw(scale3(3)*g,green,ArcArrows3(HookHead3),currentlight);
draw(scale3(6)*g,red,Arrows3(DefaultHead3),currentlight);

draw(t*g,blue,Arrows3(TeXHead2),currentlight);
draw(t*scale3(3)*g,green,ArcArrows3(HookHead2,NoFill),currentlight);
draw(t*scale3(6)*g,red,Arrows3(DefaultHead2(normal=Z)),currentlight);
Figure 0024
Figure 0024: axis3.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size(0,200);
size3(200,IgnoreAspect);

currentprojection=perspective(5,2,2);

scale(Linear,Linear,Log);

xaxis3("$x$",0,1,red,OutTicks(2,2));
yaxis3("$y$",0,1,red,OutTicks(2,2));
zaxis3("$z$",1,30,red,OutTicks(beginlabel=false));
Figure 0025
Figure 0025: basealign.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import fontsize;
import three;
currentprojection=orthographic(Z);

defaultpen(fontsize(100pt));

dot(O);

label("acg",O,align=N,basealign);
label("ace",O,align=N,red);
label("acg",O,align=S,basealign);
label("ace",O,align=S,red);
label("acg",O,align=E,basealign);
label("ace",O,align=E,red);
label("acg",O,align=W,basealign);
label("ace",O,align=W,red);

picture pic;
dot(pic,(labelmargin(),0,0),blue);
dot(pic,(-labelmargin(),0,0),blue);
dot(pic,(0,labelmargin(),0),blue);
dot(pic,(0,-labelmargin(),0),blue);
add(pic,O);

dot((0,0));

label("acg",(0,0),align=N,basealign);
label("ace",(0,0),align=N,red);
label("acg",(0,0),align=S,basealign);
label("ace",(0,0),align=S,red);
label("acg",(0,0),align=E,basealign);
label("ace",(0,0),align=E,red);
label("acg",(0,0),align=W,basealign);
label("ace",(0,0),align=W,red);

picture pic;
dot(pic,(labelmargin(),0),blue);
dot(pic,(-labelmargin(),0),blue);
dot(pic,(0,labelmargin()),blue);
dot(pic,(0,-labelmargin()),blue);
add(pic,(0,0));
Figure 0026
Figure 0026: bezier2.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import beziercurve;

pair midpoint(pair a, pair b) {return interp(a,b,0.5);}

pair m0=midpoint(z0,c0);
pair m1=midpoint(c0,c1);
pair m2=midpoint(c1,z1);

draw(m0--m1--m2,dashed);
dot("$m_0$",m0,NW,red);
dot("$m_1$",m1,N,red);
dot("$m_2$",m2,red);

pair m3=midpoint(m0,m1);
pair m4=midpoint(m1,m2);
pair m5=midpoint(m3,m4);

draw(m3--m4,dashed);
dot("$m_3$",m3,NW,red);
dot("$m_4$",m4,NE,red);
dot("$m_5$",m5,N,red);
Figure 0027
Figure 0027: beziercurve.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(400);
pair z0=(0,0);
pair c0=(1,1);
pair c1=(2,1);
pair z1=(3,0);
draw(z0..controls c0 and c1 .. z1,blue);

draw(z0--c0--c1--z1,dashed);
dot("$z_0$",z0,W,red);
dot("$c_0$",c0,NW,red);
dot("$c_1$",c1,NE,red);
dot("$z_1$",z1,red);
Figure 0028
Figure 0028: binarytreetest.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import binarytree;

picture pic,pic2;

binarytree bt=binarytree(1,2,4,nil,5,nil,nil,0,nil,nil,3,6,nil,nil,7);
draw(pic,bt);

binarytree st=searchtree(10,5,2,1,3,4,7,6,8,9,15,13,12,11,14,17,16,18,19);
draw(pic2,st,blue);

add(pic.fit(),(0,0),10N);
add(pic2.fit(),(0,0),10S);
Figure 0029
Figure 0029: brokenaxis.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(200,150,IgnoreAspect);

// Break the x axis at 3; restart at 8:
real a=3, b=8;

// Break the y axis at 100; restart at 1000:
real c=100, d=1000;

scale(Broken(a,b),BrokenLog(c,d));

real[] x={1,2,4,6,10};
real[] y=x^4;

draw(graph(x,y),red,MarkFill[0]);

xaxis("$x$",BottomTop,LeftTicks(Break(a,b)));
yaxis("$y$",LeftRight,RightTicks(Break(c,d)));

label(rotate(90)*Break,(a,point(S).y));
label(rotate(90)*Break,(a,point(N).y));
label(Break,(point(W).x,ScaleY(c)));
label(Break,(point(E).x,ScaleY(c)));
Figure 0030
Figure 0030: buildcycle.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);

real w=1.35;

path[] p;
for(int k=0; k < 2; ++k) {
  int i=2+2*k;
  int ii=i^2;
  p[k]=(w/ii,1){1,-ii}::(w/i,1/i)::(w,1/ii){ii,-1};
}

path q0=(0,0)--(w,0.5);
path q1=(0,0)--(w,1.5);
draw(q0); draw(p[0]); draw(q1); draw(p[1]);
path s=buildcycle(q0,p[0],q1,p[1]);
fill(s,mediumgrey);

label("$P$",intersectionpoint(p[0],q0),N);
label("$Q$",intersectionpoint(p[0],q1),E);
label("$R$",intersectionpoint(p[1],q1),W);
label("$S$",intersectionpoint(p[1],q0),S);
label("$f > 0$",0.5*(min(s)+max(s)),UnFill);
Figure 0031
Figure 0031: cardioid.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(0,100);

real f(real t) {return 1+cos(t);}

path g=polargraph(f,0,2pi,operator ..)--cycle;
filldraw(g,pink);

xaxis("$x$",above=true);
yaxis("$y$",above=true);

dot("$(a,0)$",(1,0),N);
dot("$(2a,0)$",(2,0),N+E);
Figure 0032
Figure 0032: centroidfg.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(0,150);

int a=-1, b=1;

real f(real x) {return x^3-x+2;}
real g(real x) {return x^2;}

draw(graph(f,a,b,operator ..),red);
draw(graph(g,a,b,operator ..),blue);
 
xaxis(); 

int n=5;

real width=(b-a)/(real) n;
for(int i=0; i <= n; ++i) {
  real x=a+width*i;
  draw((x,g(x))--(x,f(x)));
}
 
labelx("$a$",a);
labelx("$b$",b);
draw((a,0)--(a,g(a)),dotted);
draw((b,0)--(b,g(b)),dotted);

real m=a+0.73*(b-a);
arrow("$f(x)$",(m,f(m)),N,red);
arrow("$g(x)$",(m,g(m)),E,0.8cm,blue);

int j=2;
real xi=b-j*width;
real xp=xi+width;
real xm=0.5*(xi+xp);
pair dot=(xm,0.5*(f(xm)+g(xm)));
dot(dot,darkgreen+4.0);
arrow("$\left(x,\frac{f(x)+g(x)}{2}\right)$",dot,NE,2cm,darkgreen);
Figure 0033
Figure 0033: cheese.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import palette;
import contour3;
size(400);

real f(real x, real y, real z) {
  return cos(x)*sin(y)+cos(y)*sin(z)+cos(z)*sin(x);
}

surface sf=surface(contour3(f,(-2pi,-2pi,-2pi),(2pi,2pi,2pi),12));
sf.colors(palette(sf.map(abs),Gradient(red,yellow)));
draw(sf,nolight);
Figure 0034
Figure 0034: circles.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(6cm,0);
import math;

currentpen=magenta;

real r1=1;
real r2=sqrt(7);
real r3=4;
pair O=0;

path c1=circle(O,r1);
draw(c1,green);
draw(circle(O,r2),green);
draw(circle(O,r3),green);

real x=-0.6;
real y=-0.8;
real yD=0.3;
pair A=(sqrt(r1^2-y^2),y);
pair B=(-sqrt(r2^2-y^2),y);
pair C=(x,sqrt(r3^2-x^2));

pair d=A+r2*dir(B--C);
pair D=intersectionpoint(c1,A--d);

draw(A--B--C--cycle);
draw(interp(A,D,-0.5)--interp(A,D,1.5),blue);

dot("$O$",O,S,red);
dot("$A$",A,dir(C--A,B--A),red);
dot("$B$",B,dir(C--B,A--B),red);
dot("$C$",C,dir(A--C,B--C),red);
dot("$D$",D,red);
Figure 0035
Figure 0035: coag.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,200);
import graph;

pair z0=(0,0);
pair m0=(0,1);
pair tg=(1.5,0);
pair mt=m0+tg;
pair tf=(3,0);

draw(m0--mt{dir(-70)}..{dir(0)}2tg+m0/4);
xtick("$T_g$",tg,N);
label("$M(t)$",mt,2NE);
labely("$M_0$",m0);

xaxis(Label("$t$",align=2S),Arrow);
yaxis(Arrow);
Figure 0036
Figure 0036: colons.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
draw((0,0){up}::(100,25){right}::(200,0){down});
Figure 0037
Figure 0037: colorplanes.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(6cm,0);
import bsp;

real u=2.5;
real v=1;

currentprojection=oblique;

path3 y=plane((2u,0,0),(0,2v,0),(-u,-v,0));
path3 l=rotate(90,Z)*rotate(90,Y)*y;
path3 g=rotate(90,X)*rotate(90,Y)*y;

face[] faces;
pen[] p={red,green,blue,black};
int[] edges={0,0,0,2};
gouraudshade(faces.push(y),project(y),p,edges);
gouraudshade(faces.push(l),project(l),p,edges);
gouraudshade(faces.push(g),project(g),new pen[]{cyan,magenta,yellow,black},
             edges);

add(faces);
Figure 0038
Figure 0038: colors.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
int i=0;
int j=0;

bool components=false;

pen p;

void col(bool fill=false ... string[] s) {
  for(int n=0; n < s.length; ++n) {
    j -= 10;
    string s=s[n];
    eval("p="+s+";",true);
    if(components) {
      real[] a=colors(p);
      for(int i=0; i < a.length; ++i)
        s += " "+(string) a[i];
    }
    if(fill) label(s,(i+10,j),E,p,Fill(gray));
    else label(s,(i+10,j),E,p);
    fill(box((i,j-5),(i+10,j+5)),p);
  }
}

col("palered");
col("lightred");
col("mediumred");
col("red");
col("heavyred");
col("brown");
col("darkbrown");
j -= 10;

col("palegreen");
col("lightgreen");
col("mediumgreen");
col("green");
col("heavygreen");
col("deepgreen");
col("darkgreen");
j -= 10;

col("paleblue");
col("lightblue");
col("mediumblue");
col("blue");
col("heavyblue");
col("deepblue");
col("darkblue");
j -= 10;

i += 150;
j=0;

col("palecyan");
col("lightcyan");
col("mediumcyan");
col("cyan");
col("heavycyan");
col("deepcyan");
col("darkcyan");
j -= 10;

col("pink");
col("lightmagenta");
col("mediummagenta");
col("magenta");
col("heavymagenta");
col("deepmagenta");
col("darkmagenta");
j -= 10;

col("paleyellow");
col("lightyellow");
col("mediumyellow");
col("yellow");
col("lightolive");
col("olive");
col("darkolive");
j -= 10;

col("palegray");
col("lightgray");
col("mediumgray");
col("gray");
col("heavygray");
col("deepgray");
col("darkgray");
j -= 10;

i += 150;
j=0;

col("black");
col("white",fill=true);
j -= 10;

col("orange");
col("fuchsia");
j -= 10;
col("chartreuse");
col("springgreen");
j -= 10;
col("purple");
col("royalblue");
j -= 10;

col("Cyan");
col("Magenta");
col("Yellow");
col("Black");

j -= 10;

col("cmyk(red)");
col("cmyk(blue)");
col("cmyk(green)");
Figure 0039
Figure 0039: condor.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
// Peter Luschny's Condor function
// http://www.luschny.de/math/asy/ElCondorYElGamma.html

import palette;
import graph3;

size(300,300,IgnoreAspect);
currentprojection=orthographic(0,-1,0,center=true);
currentlight=White;
real K=7;

triple condor(pair t)
{
  real y=t.y;
  real x=t.x*y;
  real e=gamma(y+1);
  real ymx=y-x;
  real ypx=y+x;
  real a=gamma((ymx+1)/2);
  real b=gamma((ymx+2)/2);
  real c=gamma((ypx+1)/2);
  real d=gamma((ypx+2)/2);
  real A=cos(pi*ymx);
  real B=cos(pi*ypx);
  return (x,y,log(e)+log(a)*((A-1)/2)+log(b)*((-A-1)/2)+log(c)*((B-1)/2)+
          log(d)*((-B-1)/2));
}

surface s=surface(condor,(-1,0),(1,K),16,Spline);
s.colors(palette(s.map(zpart),Rainbow()));

draw(s);
Figure 0040
Figure 0040: cones.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import solids;

size(200);
currentprojection=orthographic(5,4,2);

revolution upcone=cone(-Z,1,1);
revolution downcone=cone(Z,1,-1);
draw(surface(upcone),green);
draw(surface(downcone),green);
draw(upcone,5,blue,longitudinalpen=nullpen);
draw(downcone,5,blue,longitudinalpen=nullpen);

revolution cone=shift(2Y-2X)*cone(1,1);

draw(surface(cone),green);
draw(cone,5,blue);
Figure 0041
Figure 0041: conicurv.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
// Original name : conicurv.mp 
// Author : L. Nobre G.
// Translators : J. Pienaar (2004) and John Bowman (2005)

import three;
texpreamble("\usepackage{bm}");

size(300,0);

currentprojection=perspective(10,-5,5.44); 

real theta=30, width=3, shortradius=2, bord=2, refsize=1, vecsize=2;
real height=0.3, anglar=1.75, totup=3;
real longradius=shortradius+width*Cos(theta), updiff=width*Sin(theta);

triple iplow=(0,shortradius,0), iphig=(0,longradius,updiff);
triple oplow=(-shortradius,0,0), ophig=(-longradius,0,updiff);
triple aplow=-iplow, aphig=(0,-longradius,updiff);
triple eplow=-oplow, ephig=(longradius,0,updiff);
triple anglebase=(0,longradius,0), centre=interp(iplow,iphig,0.5)+(0,0,height);
triple central=(0,0,centre.z), refo=(0,0.5*centre.y,centre.z);
triple refx=refsize*(0,Cos(theta),Sin(theta));
triple refy=refsize*(0,-Sin(theta),Cos(theta));

draw("$\theta$",arc(iplow,iplow+0.58*(iphig-iplow),anglebase),E);

draw(central,linewidth(2bp));
draw(iplow--iphig);
draw(oplow--ophig);
draw(aplow--aphig);
draw(eplow--ephig);
draw(iphig--anglebase--aplow,dashed);
draw(oplow--eplow,dashed);
draw(central--centre,dashed);

draw((0,0,-bord)--(0,longradius+bord,-bord)--(0,longradius+bord,totup)
     --(0,0,totup)--cycle);
draw(Label("$y$",1),refo--refo+refy,SW,Arrow3);
draw(Label("$x$",1),refo--refo+refx,SE,Arrow3);

draw(Label("$\vec{R}_N$",1),centre--centre+vecsize*refy,E,Arrow3);
draw(Label("$\vec{F}_a$",1),centre--centre+vecsize*refx,N,Arrow3);
draw(Label("$\vec{F}_c$",1),centre--centre+vecsize*Y,NE,Arrow3);
draw(Label("$\vec{P}$",1),centre--centre-vecsize*Z,E,Arrow3);
draw(Label("$\vec{v}$",1),centre--centre+vecsize*X,E,Arrow3);
draw(centre,10pt+blue);

draw(circle((0,0,updiff),longradius),linewidth(2bp));
draw(circle(O,shortradius),linewidth(2bp));
Figure 0042
Figure 0042: controlsystem.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,4cm);
import flowchart;

block delay=roundrectangle("$e^{-sT_t}$",(0.33,0));
block system=roundrectangle("$\frac{s+3}{s^2+0.3s+1}$",(0.6,0));
block controller=roundrectangle("$0.06\left( 1 + \frac{1}{s}\right)$",
                                (0.45,-0.25));
block sum1=circle("",(0.15,0),mindiameter=0.3cm);
block junction1=circle("",(0.75,0),fillpen=currentpen);

draw(delay);
draw(system);
draw(controller);
draw(sum1);
draw(junction1);

add(new void(picture pic, transform t) {
    draw(pic,Label("$u$",0.5,N),path(new pair[]{t*(0,0),sum1.left(t)},
                                     Horizontal),Arrow,PenMargin);

    draw(pic,path(new pair[]{sum1.right(t),delay.left(t)},Horizontal),Arrow,
         PenMargin);
    label(pic,"-",sum1.bottom(t),ESE);

    draw(pic,path(new pair[]{delay.right(t),system.left(t)},Horizontal),Arrow,
         PenMargin);

    draw(pic,path(new pair[]{system.right(t),junction1.left(t)},Horizontal),
         PenMargin);

    draw(pic,Label("$y$",0.5,N),path(new pair[]{junction1.right(t),t*(0.9,0)},
                                   Horizontal),Arrow,PenMargin);

    draw(pic,path(new pair[]{junction1.bottom(t),controller.right(t)},Vertical),
         Arrow,PenMargin);

    draw(pic,path(new pair[]{controller.left(t),sum1.bottom(t)},Horizontal),
         Arrow,PenMargin);
  });
Figure 0043
Figure 0043: cos2theta.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(0,100);

real f(real t) {return cos(2*t);}

path g=polargraph(f,0,2pi,operator ..)--cycle;
fill(g,green+white);
xaxis("$x$",above=true);
yaxis("$y$",above=true);
draw(g);

dot(Label,(1,0),NE);
dot(Label,(0,1),NE);
Figure 0044
Figure 0044: cosaddition.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,200);
import geometry;

real A=130;
real B=40;

pair O=(0,0); 
pair R=(1,0);
pair P=dir(A);
pair Q=dir(B);

draw(circle(O,1.0));
draw(Q--O--P);
draw(P--Q,red);
draw(O--Q--R--cycle);

draw("$A$",arc(R,O,P,0.3),blue,Arrow,PenMargin);
draw("$B$",arc(R,O,Q,0.6),blue,Arrow,PenMargin);
pair S=(Cos(B),0);
draw(Q--S,blue);
perpendicular(S,NE,blue);

dot(O);
dot("$R=(1,0)$",R);
dot("$P=(\cos A,\sin A)$",P,dir(O--P)+W);
dot("$Q=(\cos B,\sin B)$",Q,dir(O--Q));
Figure 0045
Figure 0045: cube.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;
dotgranularity=0; // Render dots as spheres.

currentprojection=orthographic(5,4,2,center=true);

size(5cm);
size3(3cm,5cm,8cm);

draw(unitbox);

dot(unitbox,red);

label("$O$",(0,0,0),NW);
label("(1,0,0)",(1,0,0),S);
label("(0,1,0)",(0,1,0),E);
label("(0,0,1)",(0,0,1),Z);
Figure 0046
Figure 0046: curvedlabel.asy
(Compiled with Asymptote version 1.87svn-r4643) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);
import labelpath;
labelpath("This is a test of curved labels in Asymptote (implemented with the {\tt PSTricks pstextpath} macro).",reverse(rotate(-90)*unitcircle));
Figure 0047
Figure 0047: curvedlabel3.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);
import labelpath3;

path3 g=(1,0,0)..(0,1,1)..(-1,0,0)..(0,-1,1)..cycle;
path3 g2=shift(-Z)*reverse(unitcircle3);

string txt1="\hbox{This is a test of \emph{curved} 3D labels in
\textbf{Asymptote} (implemented with {\tt texpath}).}";

string txt2="This is a test of curved labels in Asymptote\\(implemented
without the {\tt PSTricks pstextpath} macro)."; 

draw(surface(g),paleblue+opacity(0.5));
draw(labelpath(txt1,subpath(g,0,reltime(g,0.95)),angle=-90),orange);

draw(g2,1bp+red);
draw(labelpath(txt2,subpath(g2,0,3.9),angle=180,optional=rotate(-70,X)*Z));
Figure 0048
Figure 0048: cyclohexane.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

currentprojection = perspective(300,-650,500);

surface carbon = scale3(70)*unitsphere; // 70 pm
surface hydrogen = scale3(25)*unitsphere; // 25 pm

real alpha = 90+aSin(1/3);

real CCbond = 156; // 156 pm
real CHbond = 110; // 110 pm

triple c1 = (0,0,0);
triple h1 = c1+CHbond*Z;
triple c2 = rotate(alpha,c1,c1+Y)*(CCbond*Z);
triple h2 = rotate(120,c1,c2)*h1;
triple h3 = c2-CHbond*Z;
triple h4 = rotate(120,c2,c1)*h3;

triple c3 = rotate(120,c2,h3)*c1;
triple h5 = c3+CHbond*Z;
triple h6 = rotate(-120,c3,c2)*h5;

triple c4 = rotate(-120,c3,h5)*c2;
triple h7 = c4-CHbond*Z;
triple h8 = rotate(120,c4,c3)*h7;

triple c5 = rotate(120,c4,h7)*c3;
triple h9 = c5+CHbond*Z;
triple h10 = rotate(-120,c5,c4)*h9;

triple c6 = rotate(-120,c5,h9)*c4;
triple h11 = c6-CHbond*Z;
triple h12 = rotate(120,c6,c5)*h11;

draw(shift(c1)*carbon,black);
draw(shift(c2)*carbon,black);
draw(shift(c3)*carbon,black);
draw(shift(c4)*carbon,black);
draw(shift(c5)*carbon,black);
draw(shift(c6)*carbon,black);


draw(shift(h1)*hydrogen,lightgray);
draw(shift(h2)*hydrogen,lightgray);
draw(shift(h3)*hydrogen,lightgray);
draw(shift(h4)*hydrogen,lightgray);
draw(shift(h5)*hydrogen,lightgray);
draw(shift(h6)*hydrogen,lightgray);
draw(shift(h7)*hydrogen,lightgray);
draw(shift(h8)*hydrogen,lightgray);
draw(shift(h9)*hydrogen,lightgray);
draw(shift(h10)*hydrogen,lightgray);
draw(shift(h11)*hydrogen,lightgray);
draw(shift(h12)*hydrogen,lightgray);


pen thick = linewidth(10);

draw(c1--c2--c3--c4--c5--c6--cycle,thick);

draw(c1--h1,thick);
draw(c1--h2,thick);
draw(c2--h3,thick);
draw(c2--h4,thick);
draw(c3--h5,thick);
draw(c3--h6,thick);
draw(c4--h7,thick);
draw(c4--h8,thick);
draw(c5--h9,thick);
draw(c5--h10,thick);
draw(c6--h11,thick);
draw(c6--h12,thick);
Figure 0049
Figure 0049: cylinder.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import solids;

size(0,100);

revolution r=cylinder(O,1,1.5,Y+Z);
draw(surface(r),green);
draw(r,blue);
Figure 0050
Figure 0050: cylinderskeleton.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import solids;

size(0,100);

revolution r=cylinder(O,1,1.5,Y+Z);
draw(r,heavygreen);
Figure 0051
Figure 0051: datagraph.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(200,150,IgnoreAspect);

real[] x={0,1,2,3};
real[] y=x^2;

draw(graph(x,y),red);

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,
      RightTicks(Label(fontsize(8pt)),new real[]{0,4,9}));
Figure 0052
Figure 0052: delu.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(7cm,0);

pair z1=(1,-0.25);
pair v1=dir(45);
pair z2=-z1;
pair v2=0.75*dir(260);
pair z3=(z1.x,-3);

// A centered random number
real crand() {return unitrand()-0.5;}

guide g;
pair lastz;
for(int i=0; i < 60; ++i) {
  pair z=0.75*lastz+(crand(),crand());
  g=g..2.5*z;
  lastz=z;
}
g=shift(0,-.5)*g..cycle;

draw(g,gray(0.7));

draw("$r$",z1--z2,RightSide,red,Arrows,DotMargins);
draw(z1--z1+v1,Arrow);
draw(z2--z2+v2,Arrow);
draw(z3--z3+v1-v2,green,Arrow);

dot("1",z1,S,blue);
dot("2",z2,NW,blue);
Figure 0053
Figure 0053: diatom.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(15cm,12cm,IgnoreAspect);

real minpercent=20;
real ignorebelow=0;
string data="diatom.csv";
string[] group;
int[] begin,end;

defaultpen(fontsize(8pt)+overwrite(MoveQuiet));

file in=line(csv(input(data)));

string depthlabel=in;
string yearlabel=in;
string[] taxa=in;
group=in;
begin=in;
real[] depth;
int[] year;
real[][] percentage;

while(true) {
  real d=in;
  if(eof(in)) break;
  depth.push(d);
  year.push(in);
  percentage.push(in);
}

percentage=transpose(percentage);
real depthmin=-min(depth);
real depthmax=-max(depth);

int n=percentage.length;

int final;
for(int taxon=0; taxon < n; ++taxon) {
  real[] P=percentage[taxon];
  if(max(P) < ignorebelow) continue;
  final=taxon;
}  

real angle=45;
real L=3cm;
pair Ldir=L*dir(angle);
real ymax=-infinity;
real margin=labelmargin();

real location=0;

for(int i=0; i < begin.length-1; ++i) end[i]=begin[i+1]-1;
end[begin.length-1]=n-1;

typedef void drawfcn(frame f);
drawfcn[] draw=new drawfcn[begin.length];

pair z0;

for(int taxon=0; taxon < n; ++taxon) {
  real[] P=percentage[taxon];
  real maxP=max(P);
  if(maxP < ignorebelow) continue;
  picture pic;
  real x=1;
  if(maxP < minpercent) x=minpercent/maxP;
  if(maxP > 100) x=50/maxP;
  scale(pic,Linear(true,x),Linear(-1));
  filldraw(pic,(0,depthmin)--graph(pic,P,depth)--(0,depthmax)--cycle,
           gray(0.9));
  xaxis(pic,Bottom,LeftTicks("$%.3g$",beginlabel=false,0,2),above=true);
  xaxis(pic,Top,above=true);

  frame label;
  label(label,rotate(angle)*TeXify(taxa[taxon]),(0,0),N);

  pair z=point(pic,N);
  pair v=max(label);
  int taxon=taxon;
  pic.add(new void(frame f, transform t) {
      pair z1=t*z+v;
      ymax=max(ymax,z1.y+margin);
    });

  for(int i=0; i < begin.length; ++i) {
    pair z=point(pic,N);
    pair v=max(label);
    if(taxon == begin[i]) {
      pic.add(new void(frame f, transform t) {
          pair Z=t*z+v;
          z0=Z;
          pair w0=Z+Ldir;
        });
    } else if(taxon == end[i]) {
      int i=i;
      pair align=2N;
      pic.add(new void(frame, transform t) {
          pair z0=z0;
          pair z1=t*z+v;
          pair w1=z1+Ldir;
          draw[i]=new void(frame f) {
            path g=z0--(z0.x+(ymax-z0.y)/Tan(angle),ymax)--
            (z1.x+(ymax-z1.y)/Tan(angle),ymax)--z1;
            draw(f,g);
            label(f,group[i],point(g,1.5),align);
          };
        });
    }
  }

  add(pic,label,point(pic,N));

  if(taxon == 0) yaxis(pic,depthlabel,Left,RightTicks(0,10),above=true);
  if(taxon == final) yaxis(pic,Right,LeftTicks("%",0,10),above=true);
 
  add(shift(location,0)*pic);
  location += pic.userMax.x;
}

add(new void(frame f, transform) {
    for(int i=0; i < draw.length; ++i)
      draw[i](f);
  });

for(int i=0; i < year.length; ++i)
  if(year[i] != 0) label((string) year[i],(location,-depth[i]),E);

label("\%",(0.5*location,point(S).y),5*S);
Figure 0054
Figure 0054: dimension.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(12cm,0); 
 
void distance(picture pic=currentpicture, pair A, pair B, Label L="", real n=0,
              pen p=currentpen) 
{
  real d=3mm;
  path g=A--B;
  transform T=shift(-n*d*unit(B-A)*I);
  pic.add(new void(frame f, transform t) {
      picture opic;
      path G=T*t*g;
      draw(opic,Label(L,Center,UnFill(1)),G,p,Arrows(NoFill),Bars,PenMargins); 
      add(f,opic.fit());
    });
  pic.addBox(min(g),max(g),T*min(p),T*max(p));
} 
 
pair A=(0,0), B=(3,3); 
 
dot(A); 
dot(B); 
 
distance(A,B,"$\ell$",1);
Figure 0055
Figure 0055: dots.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
draw((0,0){up}..(100,25){right}..(200,0){down});
Figure 0056
Figure 0056: dragon.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
pair crease(pair z1, pair z2, bool left)
{
  pair dz = z2 - z1;

  if (left)
    return z1 + dz * (0.5, 0.5);
  else
    return z1 + dz * (0.5, -0.5);
}

pair[] fold(pair[] oldz)
{
  int n = oldz.length;
  pair[] newz = new pair[2n-1];

  for (int i = 0; i < n-1; ++i)
    {
      newz[2i] = oldz[i];
      newz[2i+1] = crease(oldz[i], oldz[i+1], i%2==0);
    }

  newz[2(n-1)] = oldz[n-1];

  return newz;
}

pair[] dragon(int n, pair[] base={})
{
  if (base.length == 0)
    if (n%2 == 0)
      base = new pair[] {(0,0), (1,1) };
    else
      base = new pair[] {(0,0), (1,0) };

  pair[] z = base;

  for (int i = 1; i < n; ++i)
    z = fold(z);

  return z;
}

void drawtris(pair[] z, pen p = currentpen)
{
  int n = z.length;

  for (int i = 0; i < n-2; i+=2)
    fill(z[i]--z[i+1]--z[i+2]--cycle, p);
}

void drawtris(pair[] z, pen p1, pen p2)
{
  int n = z.length;

  for (int i = 0; i < n-2; i+=2)
    fill(z[i]--z[i+1]--z[i+2]--cycle, 2i < n-1 ? p1 : p2);
}

size(500,0);

int n = 10;

drawtris(dragon(n, new pair[] {(0,0), (1,0)}), black);
drawtris(dragon(n, new pair[] {(0,0), (0,-1)}), blue);
drawtris(dragon(n, new pair[] {(0,0), (-1,0)}), red);
drawtris(dragon(n, new pair[] {(0,0), (0,1)}),  green);
Figure 0057
Figure 0057: eetomumu.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import feynman;


// set default line width to 0.8bp
currentpen = linewidth(0.8);

// scale all other defaults of the feynman module appropriately
fmdefaults();

// define vertex and external points

real L = 50;

pair zl = (-0.75*L,0);
pair zr = (+0.75*L,0);

pair xu = zl + L*dir(+120);
pair xl = zl + L*dir(-120);

pair yu = zr + L*dir(+60);
pair yl = zr + L*dir(-60);


// draw propagators and vertices

drawFermion(xu--zl);
drawFermion(zl--xl);

drawPhoton(zl--zr);

drawFermion(yu--zr);
drawFermion(zr--yl);

drawVertex(zl);
drawVertex(zr);


// draw momentum arrows and momentum labels

drawMomArrow(xl--zl, Relative(left));
label(Label("$k'$",2RightSide), xl--zl);

label(Label("$k$",2LeftSide), xu--zl);

drawMomArrow(zl--zr, Relative(left));
label(Label("$q$",2RightSide), zl--zr);

drawMomArrow(zr--yu, Relative(right));
label(Label("$p'$",2LeftSide), zr--yu);

label(Label("$p$",2RightSide), zr--yl);


// draw particle labels

label("$e^-$", xu, left);
label("$e^+$", xl, left);

label("$\mu^+$", yu, right);
label("$\mu^-$", yl, right);
Figure 0058
Figure 0058: electromagnetic.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph; 
import palette;
texpreamble("\usepackage[amssymb,thinqspace,thinspace]{SIunits}"); 
 
size(800,200); 
 
real c=3e8;
real nm=1e-9;
real freq(real lambda) {return c/(lambda*nm);} 
real lambda(real f) {return c/(f*nm);} 
 
real fmin=10; 
real fmax=1e23; 
 
scale(Log(true),Linear(true)); 
xlimits(fmin,fmax); 
ylimits(0,1); 
 
real uv=freq(400);
real ir=freq(700);
 
bounds visible=bounds(Scale(uv).x,Scale(ir).x);
palette(visible,uv,ir+(0,2),Bottom,Rainbow(),invisible);

xaxis(Label("\hertz",1),Bottom,RightTicks,above=true); 
 
real log10Left(real x) {return -log10(x);}
real pow10Left(real x) {return pow10(-x);}

scaleT LogLeft=scaleT(log10Left,pow10Left,logarithmic=true);

picture q=secondaryX(new void(picture p) { 
    scale(p,LogLeft,Linear); 
    xlimits(p,lambda(fmax),lambda(fmin));
    ylimits(p,0,1); 
    xaxis(p,Label("\nano\metre",1),Top,LeftTicks(DefaultLogFormat,n=10)); 
  }); 
 
add(q,above=true); 

margin margin=PenMargin(0,0);
draw("radio",Scale((10,1))--Scale((5e12,1)),N,Arrow); 
draw("infrared",Scale((1e12,1.5))--Scale(shift(0,1.5)*ir),Arrows,margin);
draw("UV",Scale(shift(0,1.5)*uv)--Scale((1e17,1.5)),Arrows,margin);
draw("x-rays",Scale((1e16,1))--Scale((1e21,1)),N,Arrows); 
draw("$\gamma$-rays",Scale((fmax,1.5))--Scale((2e18,1.5)),Arrow);
Figure 0059
Figure 0059: elevation.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import grid3;
import palette;

currentprojection=orthographic(0.8,1,1);

size(400,300,IgnoreAspect);

real f(pair z) {return cos(2*pi*z.x)*sin(2*pi*z.y);}

surface s=surface(f,(-1/2,-1/2),(1/2,1/2),50,Spline);

draw(s,mean(palette(s.map(zpart),Rainbow())),black);

grid3(XYZgrid);
Figure 0060
Figure 0060: elliptic.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
struct curve {
  real a=0;
  real b=8;

  real y2(real x) {
    return x^3+a*x+b;
  }

  real disc() {
    return -16*(4*a*a*a+27*b*b);
  }

  real lowx () {
    return sqrt(-a/3);
  }

  int comps() {
    if (a < 0) {
      real x=sqrt(-a/3);
      return y2(x) < 0 ? 2 : 1;
    }
    return 1;
  }

  void locus(picture pic=currentpicture, real m, real M, int n=100,
             pen p=currentpen) {
    path flip(path p, bool close) {
      path pp=reverse(yscale(-1)*p)..p;
      return close ? pp..cycle : pp;
    }
    path section(real m, real M, int n) {
      guide g;
      real width=(M-m)/n;
      for(int i=0; i <= n; ++i) {
        real x=m+width*i;
        real yy=y2(x);
        if (yy > 0)
          g=g..(x,sqrt(yy));
      }
      return g;
    }

    if (comps() == 1) {
      draw(pic,flip(section(m,M,n),false),p);
    }
    else {
      real x=lowx(); // The minimum on x^3+ax+b
      if (m < x)
        draw(pic,flip(section(m,min(x,M),n),true),p);
      if (x < M)
        draw(pic,flip(section(max(x,m),M,n),false),p);
    }
  }

  pair neg(pair P) {
    return finite(P.y) ? yscale(-1)*P : P;
  }

  pair add(pair P, pair Q) {
    if (P.x == Q.x && P.x != Q.x)
      return (0,infinity);
    else {
      real lambda=P == Q ? (3*P.x^2+a)/(2*P.y) : (Q.y-P.y)/(Q.x-P.x);
      real Rx=lambda^2-P.x-Q.x;
      return (Rx,(P.x-Rx)*lambda-P.y);
    }
  }
}

import graph;
import math;

size(0,200);

curve c; c.a=-1; c.b=4;

pair oncurve(real x) 
{
  return (x,sqrt(c.y2(x)));
}

picture output;

axes();
c.locus(-4,3,.3red+.7blue);

pair P=oncurve(-1),Q=oncurve(1.2);
pair PP=c.add(P,P),sum=c.add(P,Q);

save();

drawline(P,Q,dashed);
drawline(c.neg(sum),sum,dashed);
dot("$P$", P, NW);
dot("$Q$", Q, SSE);
dot(c.neg(sum));
dot("$P+Q$", sum, 2SW);

add(output,currentpicture.fit(),(-0.5cm,0),W);

restore();

save();

drawline(P,c.neg(PP),dashed);
drawline(c.neg(PP),PP,dashed);
dot("$P$", P, NW);
dot(c.neg(PP));
dot("$2P$", PP, SW);

add(output,currentpicture.fit(),(0.5cm,0),E);

shipout(output);
    
restore();
Figure 0061
Figure 0061: epix.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size(200,200,IgnoreAspect);

currentprojection=perspective(4,2,3);

real f(pair z) {return z.y^3/2-3z.x^2*z.y;}

draw(surface(f,(-1,-1),(1,1),nx=10,Spline),green);
draw(Label("$y$",1),(0,0,0)--(0,2,0),red,Arrow3);

draw(Label("$x$",1),(0,0,0)--(2,0,0),red,Arrow3);
draw(Label("$z$",1),(0,0,0)--(0,0,2.5),red,Arrow3);
label("$z=\frac{1}{2}y^3-3x^2y$",(1,1,1),NE);
Figure 0062
Figure 0062: equilateral.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(10cm,0);
import math;

pair b=(0,0), c=(1,0);
pair a=extension(b,b+dir(60),c,c+dir(120));
pair d=extension(b,b+dir(30),a,a+dir(270));

draw(a--b--c--a--d--b^^d--c);
label("$A$",a,N);
label("$B$",b,W);
label("$C$",c,E);
label("$D$",d,S);
Figure 0063
Figure 0063: equilchord.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size(0,150);
currentprojection=perspective(5,-4,6);
currentlight=(-1,-1,2);
real t=0.5;

real F(pair z) {
  return (z.x^2+z.y^2 <= 1) ? sqrt(3)*(sqrt(1-z.x^2)-abs(z.y)) : 0; 
}

real a=1.5;
draw((-a,-a,0)--(-a,a,0)--(a,a,0)--(a,-a,0)--cycle,lightgray);

xaxis3(Label("$x$",1),red,Arrow3);
yaxis3(Label("$y$",1),red,Arrow3);
draw(circle((0,0,0),1),dashed);
draw(surface(F,(-1,-1),(t,1),20,monotonic),green,black);
real y=sqrt(1-t^2);
draw((t,y,0)--(t,-y,0)--(t,0,sqrt(3)*y)--cycle,blue);
label("$1$",(1,0,0),-Y+X);
Figure 0064
Figure 0064: errorbars.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

picture pic;
real xsize=200, ysize=140;
size(pic,xsize,ysize,IgnoreAspect);

pair[] f={(5,5),(50,20),(90,90)};
pair[] df={(0,0),(5,7),(0,5)};

errorbars(pic,f,df,red);
draw(pic,graph(pic,f),"legend",
     marker(scale(0.8mm)*unitcircle,red,FillDraw(blue),above=false));

scale(pic,true);

xaxis(pic,"$x$",BottomTop,LeftTicks);
yaxis(pic,"$y$",LeftRight,RightTicks);
add(pic,legend(pic),point(pic,NW),20SE,UnFill);

picture pic2;
size(pic2,xsize,ysize,IgnoreAspect);

frame mark;
filldraw(mark,scale(0.8mm)*polygon(6),green,green);
draw(mark,scale(0.8mm)*cross(6),blue);

draw(pic2,graph(pic2,f),marker(mark,markuniform(5)));

scale(pic2,true);

xaxis(pic2,"$x$",BottomTop,LeftTicks);
yaxis(pic2,"$y$",LeftRight,RightTicks);

yequals(pic2,55.0,red+Dotted);
xequals(pic2,70.0,red+Dotted);

// Fit pic to W of origin:
add(pic.fit(),(0,0),W);

// Fit pic2 to E of (5mm,0):
add(pic2.fit(),(5mm,0),E);
Figure 0065
Figure 0065: exp.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(150,0);

real f(real x) {return exp(x);}
pair F(real x) {return (x,f(x));}

xaxis("$x$");
yaxis("$y$",0);

draw(graph(f,-4,2,operator ..),red);

labely(1,E);
label("$e^x$",F(1),SE);
Figure 0066
Figure 0066: extrudedcontour.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import contour;
import palette;
import graph3;
currentprojection=orthographic(25,10,10);
size(0,12cm);
real a=3;
real b=4;
real f(pair z) {return (z.x+z.y)/(2+cos(z.x)*sin(z.y));}
guide[][] g=contour(f,(-10,-10),(10,10),new real[]{8},150);

for(guide p:g[0]){
  draw(extrude(p,8Z),palered);
  draw(path3(p),red+2pt);
}

draw(lift(f,g),red+2pt);

surface s=surface(f,(0,0),(10,10),20,Spline);
s.colors(palette(s.map(zpart),Rainbow()+opacity(0.5)));
draw(s);
axes3("$x$","$y$","$z$",Arrow3);
Figure 0067
Figure 0067: fano.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import math;

size(100,0);

pair z4=(0,0);
pair z7=(2,0);
pair z1=point(rotate(60)*(z4--z7),1);

pair z5=interp(z4,z7,0.5);
pair z3=interp(z7,z1,0.5);
pair z2=interp(z1,z4,0.5);
pair z6=extension(z4,z3,z7,z2);

draw(z4--z7--z1--cycle);
draw(z4--z3);
draw(z7--z2);
draw(z1--z5);
draw(circle(z6,abs(z3-z6)));

label("1",z1,dir(z5--z1));
label("2",z2,dir(z7--z2));
label("3",z3,dir(z4--z3));
label("4",z4,dir(z3--z4));
label("5",z5,dir(z1--z5));
label("6",z6,2.5E+0.1*N);
label("7",z7,dir(z2--z7));
Figure 0068
Figure 0068: fermi.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import feynman;

// set default line width to 0.8bp
currentpen = linewidth(0.8);

// scale all other defaults of the feynman module appropriately
fmdefaults();

// disable middle arrows
currentarrow = None;

// define vertex and external points

pair xu = (-40,+45);
pair xl = (-40,-45);
pair yu = (+40,+45);
pair yl = (+40,-45);

pair zu = (  0,+ 5);
pair zl = (  0,- 5);

// define mid points

pair mxu = (xu+zu)/2;
pair mxl = (xl+zl)/2;
pair myu = (yu+zu)/2;
pair myl = (yl+zl)/2;

// draw fermion lines
drawFermion(xu--zu--yu);
drawFermion(xl--zl--yl);

// draw vertices
drawVertexOX(zu);
drawVertexOX(zl);

// draw gluon. Note that the underlying fermion line is blotted out.
drawGluon(arc((0,0),mxu,myl,CW));

// shipout
Figure 0069
Figure 0069: filegraph.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(200,150,IgnoreAspect);

file in=line(input("filegraph.dat"));
real[][] a=dimension(in,0,0);
a=transpose(a);

real[] x=a[0];
real[] y=a[1];

draw(graph(x,y),red);

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
Figure 0070
Figure 0070: filesurface.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import palette;

size3(200,IgnoreAspect);

file in=line(input("filesurface.dat"));
real[] x=in;
real[] y=in;

real[][] f=dimension(in,0,0);

triple f(pair t) {
  int i=round(t.x);
  int j=round(t.y);
  return (x[i],y[j],f[i][j]);
}

surface s=surface(f,(0,0),(x.length-1,y.length-1),x.length-1,y.length-1);
real[] level=uniform(min(f)*(1-sqrtEpsilon),max(f)*(1+sqrtEpsilon),4);

s.colors(palette(s.map(new real(triple v) {return find(level >= v.z);}),
                 Rainbow())); 

draw(s,meshpen=thick());

triple m=currentpicture.userMin;
triple M=currentpicture.userMax;
triple target=0.5*(m+M);
currentprojection=perspective(camera=target+realmult(dir(68,225),M-m),
                              target=target);

xaxis3("$x$",Bounds,InTicks);
yaxis3("$y$",Bounds,InTicks(Step=1,step=0.1));
zaxis3("$z$",Bounds,InTicks);
Figure 0071
Figure 0071: fillcontour.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
import palette;
import contour;

size(12cm,IgnoreAspect);

pair a=(pi/2,0);
pair b=(1.5*pi+epsilon,2pi);

real f(real x, real y) {return cos(x)*sin(y);}

int N=100;
int Divs=10;

defaultpen(1bp);

bounds range=bounds(-1,1);
    
real[] Cvals=uniform(range.min,range.max,Divs);
guide[][] g=contour(f,a,b,Cvals,N,operator --);

pen[] Palette=quantize(Rainbow(),Divs);

pen[][] interior=interior(g,extend(Palette,grey,black));
fill(g,interior);
draw(g);

palette("$f(x,y)$",range,point(SE)+(0.5,0),point(NE)+(1,0),Right,Palette,
        PaletteTicks("$%+#0.1f$",N=Divs));
Figure 0072
Figure 0072: fin.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;
import palette;

int N = 26;
real[] C = array(N,0); 
real[][] A = new real[N][N];
for(int i = 0; i < N; ++i)
  for(int j = 0; j < N; ++j)
    A[i][j] = 0;

real Tb = 100; // deg C
real h = 240; // 240 W/m^2 K
real k = 240; // W/m K
real Tinf = 20; // deg C
real L = 12; // cm
real t = 2; // cm

real delta = 0.01; // 1 cm = 0.01 m

// (1,2)-(2,2)-(3,2)-...-(13,2)
//   |     |     |          |
// (1,1)-(2,1)-(3,1)-...-(13,1)
//
//        |
//       \ /
//        V
//
// 13-14-15-...-24-25
//  |  |  | ...  |  |
//  0- 1- 2-...-11-12

// but, note zero-based array indexing, so counting starts at 0
int indexof(int m, int n)
{
  return 13(n-1)+m-1;
}

int i = 0;

// fixed temperature bottom left
A[i][indexof(1,1)] = 1; C[i] = Tb;
++i;
// fixed temperature middle left
A[i][indexof(1,2)] = 1; C[i] = Tb;
++i;

// interior nodes
for(int m = 2; m<13; ++m)
{
  A[i][indexof(m,2)] = -4;
  A[i][indexof(m-1,2)] = A[i][indexof(m+1,2)] = 1;
  A[i][indexof(m,1)] = 2;
  C[i] = 0;
  ++i;
}

// convective bottom side nodes
for(int m = 2; m<13; ++m)
{
  A[i][indexof(m,1)] = -(2+h*delta/k);
  A[i][indexof(m-1,1)] = A[i][indexof(m+1,1)] = 0.5;
  A[i][indexof(m,2)] = 1;
  C[i] = -h*delta*Tinf/k;
  ++i;
}

// convective bottom right corner node
A[i][indexof(13,2)] = A[i][indexof(12,1)] = 0.5;
A[i][indexof(13,1)] = -(1+h*delta/k);
C[i] = -h*delta*Tinf/k;
++i;

// convective middle right side node
A[i][indexof(13,2)] = -(2+h*delta/k);
A[i][indexof(13,1)] = 1;
A[i][indexof(12,2)] = 1;
C[i] = -h*delta*Tinf/k;
++i;

real[] T = solve(A,C);

pen[] Palette = Gradient(256,blue,cyan,yellow,orange,red);

real[][] T = {T[0:13],T[13:26],T[0:13]};
T = transpose(T);

size3(15cm);
real w = 10;
real h = 5;
currentprojection = orthographic(2*(L,h,w),Y);
draw((L,t,0)--(L,0,0)--(L,0,w)--(0,0,w)--(0,-h,w));
draw((0,t,w)--(0,t+h,w)--(0,t+h,0)--(0,t,0));
draw((L,0,w)--(L,t,w)--(0,t,w)--(0,t,0)--(L,t,0)--(L,t,w));

real wo2 = 0.5*w;
draw((0,0,wo2)--(0,t,wo2)--(L,t,wo2)--(L,0,wo2)--cycle);

// centre points
surface square = surface(shift(-0.5,-0.5,wo2)*unitsquare3);
surface bottomsquare = surface(shift(-0.5,-0.5,wo2)*scale(1,0.5,1)*unitsquare3);
surface topsquare = surface(shift(-0.5,0,wo2)*scale(1,0.5,1)*unitsquare3);
surface leftsquare = surface(shift(-0.5,-0.5,wo2)*scale(0.5,1,1)*unitsquare3);
surface rightsquare = surface(shift(0,-0.5,wo2)*scale(0.5,1,1)*unitsquare3);
surface NEcorner = surface(shift(0,0,wo2)*scale(0.5,0.5,1)*unitsquare3);
surface SEcorner = surface(shift(0,-0.5,wo2)*scale(0.5,0.5,1)*unitsquare3);
surface SWcorner = surface(shift(-0.5,-0.5,wo2)*scale(0.5,0.5,1)*unitsquare3);
surface NWcorner = surface(shift(-0.5,0,wo2)*scale(0.5,0.5,1)*unitsquare3);

material lookupColour(int m,int n)
{
  int index = round(Palette.length*(T[m-1][n-1]-60)/(100-60));
  if(index >= Palette.length) index = Palette.length-1;
  return emissive(Palette[index]);
}

draw(shift(0,1,0)*rightsquare,lookupColour(1,2));
for(int i = 2; i < 13; ++i)
{
  draw(shift(i-1,1,0)*square,lookupColour(i,2));
}
draw(shift(12,1,0)*leftsquare,lookupColour(13,2));

draw(shift(0,2,0)*SEcorner,lookupColour(1,3));
draw(shift(0,0,0)*NEcorner,lookupColour(1,1));
for(int i = 2; i < 13; ++i)
{
  draw(shift(i-1,0,0)*topsquare,lookupColour(i,1));
  draw(shift(i-1,2,0)*bottomsquare,lookupColour(i,3));
}
draw(shift(12,2,0)*SWcorner,lookupColour(13,3));
draw(shift(12,0,0)*NWcorner,lookupColour(13,1));

// annotations
draw("$x$",(0,-h/2,w)--(L/4,-h/2,w),Y,Arrow3(HookHead2(normal=Z)),BeginBar3(Y));
draw("$y$",(0,0,1.05*w)--(0,2t,1.05*w),Z,Arrow3(HookHead2(normal=X)),
     BeginBar3(Z));
draw("$z$",(L,-h/2,0)--(L,-h/2,w/4),Y,Arrow3(HookHead2(normal=X)),BeginBar3(Y));

draw("$L$",(0,-h/4,w)--(L,-h/4,w),-Y,Arrows3(HookHead2(normal=Z)),
     Bars3(Y),PenMargins2);
draw("$w$",(L,-h/4,0)--(L,-h/4,w),-Y,Arrows3(HookHead2(normal=X)),
     Bars3(Y),PenMargins2);
draw("$t$",(1.05*L,0,0)--(1.05*L,t,0),-2Z,Arrows3(HookHead2(normal=Z)),
     Bars3(X),PenMargins2);

label(ZY()*"$T_b$",(0,t+h/2,wo2));

label("$h$,$T_\infty$",(L/2,t+h/2,0),Y);
path3 air = (L/2,t+h/3,w/3.5)--(1.5*L/2,t+2*h/3,w/8);
draw(air,EndArrow3(TeXHead2));
draw(shift(0.5,0,0)*air,EndArrow3(TeXHead2));
draw(shift(1.0,0,0)*air,EndArrow3(TeXHead2));
Figure 0073
Figure 0073: fjortoft.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(15cm,0);

pair d=(1.5,1);
real s=d.x+1;

picture box(string s) {
  picture pic;
  draw(pic,box(0,d));
  label(pic,s,d/2);
  return pic;
}

add(box("$k_1$"));
add(shift(s)*box("$k_2$"));
add(shift(s)^2*box("$k_3$"));

path g=(d.x,d.y/2)--(s,d.y/2);
path G=(d.x/2,-(s-d.x))--(d.x/2,0);

draw(Label(baseline("$\ldots$")),shift(-s)*g,BeginArrow,BeginPenMargin);
draw(Label("$Z_1$"),g,BeginArrow,BeginPenMargin);
draw(Label("$E_1$",LeftSide),g,Blank);
draw(Label("$Z_3$"),shift(s)*g,Arrow,PenMargin);
draw(Label("$E_3$",LeftSide),shift(s)*g,Blank);
draw(Label("$Z_2$"),shift(s)*G,Arrow,PenMargin);
draw(Label("$E_2$",LeftSide),shift(s)*G,Blank);
draw(Label(baseline("$\ldots$")),shift(s)^2*g,Arrow,PenMargin);
Figure 0074
Figure 0074: floatingdisk.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import trembling; 
settings.outformat="pdf"; 
size(6cm,0); 
 
real R=1/5; 
real h=0.5; 
real d=1/12; 
real l=.7; 
 
pair pA=(-l,0); 
pair pB=(l,0); 
 
path waterline=tremble(addnodes(pA..pB,1),angle=10,frequency=0.1,random=50); 
path disk=shift(0,-d)*(scale(R)*unitcircle); 
path water=waterline--(l,-h)--(-l,-h)--(-l,0)--cycle; 
path container=(l,1/7)--(l,-h)--(-l,-h)--(-l,1/7); 
 
filldraw(disk,red,linewidth(.3)); 
fill(water,mediumgrey+opacity(0.5)); 
draw(waterline); 
 
draw(container,linewidth(1.5)); 
 
shipout(bbox(2mm,Fill(white)));
Figure 0075
Figure 0075: floor.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
unitsize(1cm);

real Floor(real x) {return floor(x);}

pair[] Close;
pair[] Open;

bool3 branch(real x) {
  static real lasty;
  static bool first=true;
  real y=floor(x);
  bool samebranch=first || lasty == y; 
  first=false;
  if(samebranch) lasty=x;
  else {
    Close.push((x,lasty));
    Open.push((x,y));
  }
  lasty=y;
  return samebranch ? true : default;
};

draw(graph(Floor,-5.5,5.5,500,branch)); 
axes("$x$",rotate(0)*"$\lfloor x\rfloor$",red);

dot(Close);
dot(Open,UnFill);
Figure 0076
Figure 0076: flow.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
defaultpen(1.0);

size(0,150,IgnoreAspect);

real arrowsize=4mm;
real arrowlength=2arrowsize;

typedef path vector(real);

// Return a vector interpolated linearly between a and b.
vector vector(pair a, pair b) {
  return new path(real x) {
    return (0,0)--arrowlength*interp(a,b,x);
  };
}

real f(real x) {return 1/x;}

real epsilon=0.5;
path g=graph(f,epsilon,1/epsilon);

int n=3;
draw(g);
xaxis("$x$");
yaxis("$y$");

add(vectorfield(vector(W,W),g,n,true));
add(vectorfield(vector(NE,NW),(0,0)--(point(E).x,0),n,true));
add(vectorfield(vector(NE,NE),(0,0)--(0,point(N).y),n,true));
Figure 0077
Figure 0077: flowchartdemo.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,300);

import flowchart;

block block1=rectangle(Label("Example",magenta),
                       pack(Label("Start:",heavygreen),"",Label("$A:=0$",blue),
                            "$B:=1$"),(-0.5,3),palegreen,paleblue,red);
block block2=diamond(Label("Choice?",blue),(0,2),palegreen,red);
block block3=roundrectangle("Do something",(-1,1));
block block4=bevel("Don't do something",(1,1));
block block5=circle("End",(0,0));

draw(block1);
draw(block2);
draw(block3);
draw(block4);
draw(block5);

add(new void(picture pic, transform t) {
    draw(pic,path(new pair[]{block1.right(t),block2.top(t)},Horizontal),
         Arrow,PenMargin);
    draw(pic,Label("Yes",0.5,NW),path(new pair[]{block2.left(t),block3.top(t)},
                                   Horizontal),Arrow,PenMargin);
    draw(pic,Label("No",0.5,NE),path(new pair[]{block2.right(t),block4.top(t)},
                                    Horizontal),Arrow,PenMargin);
    draw(pic,path(new pair[]{block3.bottom(t),block5.left(t)},Vertical),
         Arrow,PenMargin);
    draw(pic,path(new pair[]{block4.bottom(t),block5.right(t)},Vertical),
         Arrow,PenMargin);
  });
Figure 0078
Figure 0078: fractaltree.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);

path ltrans(path p,int d)
{
  path a=rotate(65)*scale(0.4)*p;
  return shift(point(p,(1/d)*length(p))-point(a,0))*a;
}
path rtrans(path p, int d)
{
  path a=reflect(point(p,0),point(p,length(p)))*rotate(65)*scale(0.35)*p;
  return shift(point(p,(1/d)*length(p))-point(a,0))*a;
}

void drawtree(int depth, path branch)
{
  if(depth == 0) return;
  real breakp=(1/depth)*length(branch);
  draw(subpath(branch,0,breakp),deepgreen);
  drawtree(depth-1,subpath(branch,breakp,length(branch)));
  drawtree(depth-1,ltrans(branch,depth));
  drawtree(depth-1,rtrans(branch,depth));
  return;
}

path start=(0,0)..controls (-1/10,1/3) and (-1/20,2/3)..(1/20,1);
drawtree(6,start);
Figure 0079
Figure 0079: functionshading.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);

settings.tex="pdflatex";

// PostScript Calculator routine to convert from [0,1]x[0,1] to RG:
string redgreen="0";

// PostScript Calculator routine to convert from [0,1]x[0,1] to HS to RGB:
// (http://www.texample.net/tikz/examples/hsv-shading):
string hsv="0.5 sub exch 0.5 sub exch
2 copy 2 copy 0 eq exch 0 eq and { pop pop 0.0 } {atan 360.0 div}
ifelse dup 360 eq { pop 0.0 }{} ifelse 3 1 roll dup mul exch dup mul add
sqrt 2.5 mul 0.25 sub 1 1 index 1.0
eq { 3 1 roll pop pop dup dup } { 3 -1 roll 6.0 mul dup 4 1 roll floor dup
5 1 roll 3 index sub neg 1.0 3 index sub 2 index mul 6 1 roll dup 3 index
mul neg 1.0 add 2 index mul 7 1 roll neg 1.0 add 2 index mul neg 1.0 add 1
index mul 7 2 roll pop pop dup 0 eq { pop exch pop } { dup 1 eq { pop exch
4 1 roll exch pop } { dup 2 eq { pop 4 1 roll pop } { dup 3 eq { pop exch 4
2 roll pop } { dup 4 eq { pop exch pop 3 -1 roll } { pop 3 1 roll exch pop
} ifelse } ifelse } ifelse } ifelse } ifelse } ifelse cvr 3 1 roll cvr 3 1
roll cvr 3 1 roll";

path p=unitcircle;
functionshade(p,rgb(zerowinding),redgreen);
layer();
draw(p);

path g=shift(2*dir(-45))*p;
functionshade(g,rgb(zerowinding),hsv);
layer();
draw(g);
Figure 0080
Figure 0080: galleon.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import obj;

size(15cm);
currentprojection=orthographic(0,2,5,up=Y);

// A compressed version of the required data file may be obtained from:
// http://www.cs.technion.ac.il/~irit/data/Viewpoint/galleon.obj.gz

pen[] surfacepen={darkred,brown,darkred+orange,heavyred,heavyred,darkred+orange,
                  palegreen+blue+lightgrey,darkred,darkred,yellow,darkred,white,
                  white,white,white,white,white};
surfacepen.cyclic=true;

draw(obj("galleon.obj",verbose=false,surfacepen));
Figure 0081
Figure 0081: gamma.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(300,IgnoreAspect);

bool3 branch(real x)
{
  static int lastsign=0;
  if(x <= 0 && x == floor(x)) return false;
  int sign=sgn(gamma(x));
  bool b=lastsign == 0 || sign == lastsign;
  lastsign=sign;
  return b ? true : default;
}

draw(graph(gamma,-4,4,n=2000,branch),red);
 
scale(false);
xlimits(-4,4);
ylimits(-6,6);
crop();

xaxis("$x$",RightTicks(NoZero));
yaxis(LeftTicks(NoZero));

label("$\Gamma(x)$",(1,2),red);
Figure 0082
Figure 0082: gamma3.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import palette;

size(12cm,IgnoreAspect);
currentprojection=orthographic(1,-2,1);

real X=4.5;
real M=abs(gamma((X,0)));

pair Gamma(pair z) 
{
  return (z.x > 0 || z != floor(z.x)) ? gamma(z) : M;
}

real f(pair z) {return min(abs(Gamma(z)),M);}

surface s=surface(f,(-2.1,-2),(X,2),70,Spline);

real Arg(triple v)
{
  return degrees(Gamma((v.x,v.y)),warn=false);
}

s.colors(palette(s.map(Arg),Wheel()));
draw(s);

xaxis3("$\mathop{\rm Re} z$",Bounds,InTicks);
yaxis3("$\mathop{\rm Im} z$",Bounds,InTicks(beginlabel=false));
zaxis3("$|\Gamma(z)|$",Bounds,InTicks);
Figure 0083
Figure 0083: generalaxis.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(0,100);

path g=ellipse((0,0),1,2);

scale(true);

axis(Label("C",align=10W),g,LeftTicks(endlabel=false,8,end=false),
     ticklocate(0,360,new real(real v) {
         path h=(0,0)--max(abs(max(g)),abs(min(g)))*dir(v);
         return intersect(g,h)[0];}));
Figure 0084
Figure 0084: generalaxis3.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size(0,100);

path3 g=yscale3(2)*unitcircle3;
currentprojection=perspective(10,10,10);

axis(Label("C",position=0,align=15X),g,InTicks(endlabel=false,8,end=false),
     ticklocate(0,360,new real(real v) {
         path3 h=O--max(abs(max(g)),abs(min(g)))*dir(90,v);
         return intersect(g,h)[0];},
       new triple(real t) {return cross(dir(g,t),Z);}));
Figure 0085
Figure 0085: graphmarkers.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(200,100,IgnoreAspect);

markroutine marks() {
  return new void(picture pic=currentpicture, frame f, path g) {
    path p=scale(1mm)*unitcircle;
    for(int i=0; i <= length(g); ++i) {
      pair z=point(g,i);
      frame f;
      if(i % 4 == 0) {
        fill(f,p);
        add(pic,f,z);
      } else {
        if(z.y > 50) {
          pic.add(new void(frame F, transform t) {
              path q=shift(t*z)*p;
              unfill(F,q);
              draw(F,q);
            });
        } else {
          draw(f,p);
          add(pic,f,z);
        }
      }
    }
  };
}

pair[] f={(5,5),(40,20),(55,51),(90,30)};

draw(graph(f),marker(marks()));

scale(true);

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
Figure 0086
Figure 0086: grid.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import math;
size(100,0);

add(shift(-5,-5)*grid(10,10));

dot((0,0),red);
Figure 0087
Figure 0087: grid3xyz.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import grid3;

size(8cm,0,IgnoreAspect);
currentprojection=orthographic(0.5,1,0.5);

scale(Linear, Linear, Log);

limits((-2,-2,1),(0,2,100));

grid3(XYZgrid);

xaxis3(Label("$x$",position=EndPoint,align=S),Bounds(Min,Min),
       OutTicks());
yaxis3(Label("$y$",position=EndPoint,align=S),Bounds(Min,Min),OutTicks());
zaxis3(Label("$z$",position=EndPoint,align=(-1,0.5)),Bounds(Min,Min),
       OutTicks(beginlabel=false));
Figure 0088
Figure 0088: hatch.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,100);
import patterns;

add("hatch",hatch());
add("hatchback",hatch(NW));
add("crosshatch",crosshatch(3mm));

real s=1.25;
filldraw(unitsquare,pattern("hatch"));
filldraw(shift(s,0)*unitsquare,pattern("hatchback"));
filldraw(shift(2s,0)*unitsquare,pattern("crosshatch"));
Figure 0089
Figure 0089: helix.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size(0,200);
size3(200,IgnoreAspect);

currentprojection=orthographic(4,6,3);

real x(real t) {return cos(2pi*t);}
real y(real t) {return sin(2pi*t);}
real z(real t) {return t;}

path3 p=graph(x,y,z,0,2.7,operator ..);

draw(p,Arrow3);

scale(true);

xaxis3(XZ()*"$x$",Bounds,red,InTicks(Label,2,2));
yaxis3(YZ()*"$y$",Bounds,red,InTicks(beginlabel=false,Label,2,2));
zaxis3(XZ()*"$z$",Bounds,red,InTicks);
Figure 0090
Figure 0090: hierarchy.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
texpreamble("\def\Ham{\mathop {\rm Ham}\nolimits}");
pair align=2N;
frame f;
ellipse(f,Label("$\Ham(r,2)$",(0,0)),lightblue,Fill,above=false);
ellipse(f,Label("BCH Codes",point(f,N),align),green,Fill,above=false);
ellipse(f,Label("Cyclic Codes",point(f,N),align),lightmagenta,Fill,above=false);
ellipse(f,Label("Linear Codes",point(f,N),align),-4mm,orange,Fill,above=false);
box(f,Label("General Codes",point(f,N),align),2mm,yellow,Fill,above=false);
add(f);
Figure 0091
Figure 0091: histogram.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
import stats;

size(400,200,IgnoreAspect);

int n=10000;
real[] a=new real[n];
for(int i=0; i < n; ++i) a[i]=Gaussrand();

draw(graph(Gaussian,min(a),max(a)),blue);

// Optionally calculate "optimal" number of bins a la Shimazaki and Shinomoto.
int N=bins(a);

histogram(a,min(a),max(a),N,normalize=true,low=0,lightred,black,bars=false);

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$dP/dx$",LeftRight,RightTicks(trailingzero));
Figure 0092
Figure 0092: hyperboloid.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);
import solids;

currentprojection=perspective(4,4,3);
revolution hyperboloid=revolution(new real(real x) {return sqrt(1+x*x);},
                                  -2,2,20,operator..,X);
draw(surface(hyperboloid),green);
draw(hyperboloid,6,blue,longitudinalpen=nullpen);
Figure 0093
Figure 0093: hyperboloidsilhouette.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);
import solids;
settings.render=0;
settings.prc=false;

currentprojection=perspective(4,4,3);
revolution hyperboloid=revolution(new real(real x) {return sqrt(1+x*x);},
                                  -2,2,20,operator..,X);
draw(hyperboloid.silhouette(64),blue);
Figure 0094
Figure 0094: icon.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(30,30,IgnoreAspect);

real f(real t) {return t < 0 ? -1/t : -0.5/t;}

picture logo(pair s=0, pen q) 
{
  picture pic;
  pen p=linewidth(3)+q;
  real a=-0.5;
  real b=1;
  real eps=0.1;
  draw(pic,shift((eps,-f(a)))*graph(f,a,-eps),p);
  real c=0.5*a;
  pair z=(0,f(c)-f(a));
  draw(pic,z+c+eps--z,p);
  yaxis(pic,p);
  return shift(s)*pic;
} 

add(logo(red));
Figure 0095
Figure 0095: image.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(12cm,12cm);

import graph;
import palette;

int n=256;
real ninv=2pi/n;
real[][] v=new real[n][n];

for(int i=0; i < n; ++i)
  for(int j=0; j < n; ++j)
    v[i][j]=sin(i*ninv)*cos(j*ninv);

pen[] Palette=BWRainbow();

picture bar;

bounds range=image(v,(0,0),(1,1),Palette);
palette(bar,"$A$",range,(0,0),(0.5cm,8cm),Right,Palette,
        PaletteTicks("$%+#.1f$"));
add(bar.fit(),point(E),30E);
Figure 0096
Figure 0096: imagecontour.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
import palette;
import contour;

size(10cm,10cm,IgnoreAspect);

pair a=(0,0);
pair b=(2pi,2pi);

real f(real x, real y) {return cos(x)*sin(y);}

int N=200;
int Divs=10;
int divs=2;

defaultpen(1bp);
pen Tickpen=black;
pen tickpen=gray+0.5*linewidth(currentpen);
pen[] Palette=BWRainbow();

scale(false);

bounds range=image(f,Automatic,a,b,N,Palette);
    
// Major contours

real[] Cvals=uniform(range.min,range.max,Divs);
draw(contour(f,a,b,Cvals,N,operator --),Tickpen);

// Minor contours
real[] cvals;
for(int i=0; i < Cvals.length-1; ++i)
  cvals.append(uniform(Cvals[i],Cvals[i+1],divs)[1:divs]);
draw(contour(f,a,b,cvals,N,operator --),tickpen);

xaxis("$x$",BottomTop,LeftTicks,above=true);
yaxis("$y$",LeftRight,RightTicks,above=true);

palette("$f(x,y)$",range,point(NW)+(0,0.5),point(NE)+(0,1),Top,Palette,
        PaletteTicks(N=Divs,n=divs,Tickpen,tickpen));
Figure 0097
Figure 0097: imagehistogram.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import stats;
import graph; 
import palette; 
import contour; 
 
size(20cm);

scale(false);

pair[] data=new pair[50000];
for(int i=0; i < data.length; ++i)
  data[i]=Gaussrandpair(); 
 
// Histogram limits and number of bins 
pair datamin=(-0.15,-0.15); 
pair datamax=(0.15,0.15); 
int Nx=30; 
int Ny=30; 

int[][] bins=frequency(data,datamin,datamax,Nx,Ny);
 
real[] values=new real[Nx*Ny]; 
pair[] points=new pair[Nx*Ny];
int k=0; 
real dx=(datamax.x-datamin.x)/Nx;
real dy=(datamax.y-datamin.y)/Ny;
for(int i=0; i < Nx; ++i) {
  for(int j=0; j < Ny; ++j) {
    values[k]=bins[i][j]; 
    points[k]=(datamin.x+(i+0.5)*dx,datamin.y+(j+0.5)*dy); 
    ++k; 
  }
} 
 
// Create a color palette 
pen[] InvGrayscale(int NColors=256) {
  real ninv=1.0/(NColors-1.0); 
  return sequence(new pen(int i) {return gray(1-17*i*ninv);},NColors); 
} 
 
// Draw the histogram, with axes 
bounds range=image(points,values,Range(0,40),InvGrayscale()); 
draw(contour(points,values,new real[] {1,2,3,4,8,12,16,20,24,28,32,36,40},
             operator--),blue); 
xaxis("$x$",BottomTop,LeftTicks,above=true); 
yaxis("$y$",LeftRight,RightTicks,above=true);
Figure 0098
Figure 0098: impact.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
// Contributed by Philippe Ivaldi.

import graph3 ;
import contour;
size (6cm,0);
currentprojection=orthographic(1,1,1) ;

real rc=1, hc=2, c=rc/hc;
draw(shift(hc*Z)*scale(rc,rc,-hc)*unitcone,blue);

triple Os=(0.5,0.5,1);
real r=0.5;
draw(shift(Os)*scale3(r)*unitsphere,red);

real a=1+1/c^2;
real b=abs(Os)^2-r^2;

real f(pair z)
{
  real x=z.x, y=z.y;
  return a*x^2-2*Os.x*x+a*y^2-2*Os.y*y-2*Os.z*sqrt(x^2+y^2)/c+b;
}

real g(pair z){return (sqrt(z.x^2+z.y^2))/c;}

draw(lift(g,contour(f,(-rc,-rc),(rc,rc),new real[]{0})),linewidth(2bp)+yellow);

axes3("$x$","$y$","$z$",Arrow3);
Figure 0099
Figure 0099: integraltest.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(300,150,IgnoreAspect);

real f(real x) {return 1/x^(1.1);}
pair F(real x) {return (x,f(x));}

dotfactor=7;

void subinterval(real a, real b)
{
  path g=box((a,0),(b,f(b)));
  filldraw(g,lightgray); 
  draw(box((a,f(a)),(b,0)));
}

int a=1, b=9;
  
xaxis("$x$",0,b); 
yaxis("$y$",0); 
 
draw(graph(f,a,b,operator ..),red);
 
int n=2;

for(int i=a; i <= b; ++i) {
  if(i < b) subinterval(i,i+1);
  if(i <= n) labelx(i);
  dot(F(i));
}

int i=n;
labelx("$\ldots$",++i);
labelx("$k$",++i);
labelx("$k+1$",++i);
labelx("$\ldots$",++i);

arrow("$f(x)$",F(i-1.5),NE,1.5cm,red,Margin(0,0.5));
Figure 0100
Figure 0100: irregularcontour.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import contour;

size(200);

int n=100;

pair[] points=new pair[n];
real[] values=new real[n];

real f(real a, real b) {return a^2+b^2;}

real r() {return 1.1*(rand()/randMax*2-1);}

for(int i=0; i < n; ++i) {
  points[i]=(r(),r());
  values[i]=f(points[i].x,points[i].y);
}

draw(contour(points,values,new real[]{0.25,0.5,1},operator ..),blue);
Figure 0101
Figure 0101: join.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(300,0);
pair[] z=new pair[10];

z[0]=(0,100); z[1]=(50,0); z[2]=(180,0);

for(int n=3; n <= 9; ++n)
  z[n]=z[n-3]+(200,0);

path p=z[0]..z[1]---z[2]::{up}z[3]
&z[3]..z[4]--z[5]::{up}z[6]
&z[6]::z[7]---z[8]..{up}z[9];

draw(p,grey+linewidth(4mm));

dot(z);
Figure 0102
Figure 0102: join3.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size(200);

currentprojection=orthographic(500,-500,500);

triple[] z=new triple[10];

z[0]=(0,100,0); z[1]=(50,0,0); z[2]=(180,0,0);

for(int n=3; n <= 9; ++n)
  z[n]=z[n-3]+(200,0,0);

path3 p=z[0]..z[1]---z[2]::{Y}z[3]
&z[3]..z[4]--z[5]::{Y}z[6]
&z[6]::z[7]---z[8]..{Y}z[9];

draw(p,grey+linewidth(4mm)+opacity(0.5));

xaxis3(Label(XY()*"$x$",align=-3Y),red,above=true);
yaxis3(Label(XY()*"$y$",align=-3X),red,above=true);

dot(z);
Figure 0103
Figure 0103: jump.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(4inches,0);

real f1(real x) {return (1+x^2);} 
real f2(real x) {return (4-x);}

xaxis("$x$",LeftTicks,Arrow);
yaxis("$y$",RightTicks,Arrow);

draw("$y=1+x^2$",graph(f1,-2,1)); 
dot((1,f1(1)),UnFill);

draw("$y=4-x$",graph(f2,1,5),LeftSide,red,Arrow);
dot((1,f2(1)),red);
Figure 0104
Figure 0104: knots.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import syzygy;

Braid initial;
initial.n = 4;
initial.add(bp,1);
initial.add(bp,0);
initial.add(bp,2);
initial.add(bp,1);
initial.add(phi,2);
initial.add(phi,0);

Syzygy pp;
pp.lsym="\Phi\Phi"; pp.codename="PhiAroundPhi";

pp.number=true;
pp.initial=initial;
pp.apply(r4b,2,1);
pp.apply(r4b,0,0);
pp.apply(r4a,1,0);
pp.swap(0,1);
pp.apply(-r4b,1,0);
pp.apply(-r4a,0,1);
pp.apply(-r4a,2,0);
pp.swap(4,5);

pp.draw();
Figure 0105
Figure 0105: label3.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

currentprojection=perspective(1,1,1,up=Y);
currentlight=Headlamp;

label(scale(4)*"$\displaystyle\int_{-\infty}^{+\infty} e^{-\alpha x^2}\,dx=
\sqrt{\frac{\pi}{\alpha}}$",O,blue);
Figure 0106
Figure 0106: label3solid.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

currentprojection=perspective(100,100,200,up=Y);
currentlight=Headlamp;

draw(scale3(4)*extrude("$\displaystyle\int_{-\infty}^{+\infty}
e^{-\alpha x^2}\,dx=\sqrt{\frac{\pi}{\alpha}}$",2Z),blue);
Figure 0107
Figure 0107: labelbox.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,100);
real margin=2mm;
pair z1=(0,1);
pair z0=(0,0);

object label1=draw("small box",box,z1,margin);
object label0=draw("LARGE ELLIPSE",ellipse,z0,margin);

add(new void(frame f, transform t) {
    draw(f,point(label1,SW,t){SW}..{SW}point(label0,NNE,t));
  });
Figure 0108
Figure 0108: labelsquare.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,3cm);
draw(unitsquare);
label("$A$",(0,0),SW);
label("$B$",(1,0),SE);
label("$C$",(1,1),NE);
label("$D$",(0,1),NW);
Figure 0109
Figure 0109: laserlattice.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
import palette;

int n=256;
pen[] Palette=BWRainbow();

real w(real w0, real z0, real z) {return w0*sqrt(1+(z/z0)^2);}

real pot(real lambda, real w0, real r, real z)
{
  real z0=pi*w0^2/lambda, kappa=2pi/lambda;
  return exp(-2*(r/w(w0,z0,z))^2)*cos(kappa*z)^2;
}

picture make_field(real lambda, real w0)
{
  real[][] v=new real[n][n];
  for(int i=0; i < n; ++i)
    for(int j=0; j < n; ++j)
      v[i][j]=pot(lambda,w0,i-n/2,abs(j-n/2));

  picture p=new picture;
  size(p,250,250,IgnoreAspect);
  real xm=-n/lambda, ym=-n/(2*w0), xx=n/lambda, yx=n/(2*w0);
  image(p,v,(xm,ym),(xx,yx),Palette);
  xlimits(p,xm,xx);
  ylimits(p,ym,yx);
  xaxis(p,"{\Large $z/\frac{\lambda}{2}$}",BottomTop,LeftTicks);
  yaxis(p,"{\Large $r/w_0$}",LeftRight,RightTicks);
  label(p,format("{\LARGE $w_0/\lambda=%.2f$}",w0/lambda),point(p,NW),5N);

  return p;
}

picture p=make_field(160,80);
picture q=make_field(80,80);
picture r=make_field(16,80);
picture s=make_field(2,80);

real margin=1cm;
add(p.fit(),(0,0),margin*NW);
add(q.fit(),(0,0),margin*NE);
add(r.fit(),(0,0),margin*SW);
add(s.fit(),(0,0),margin*SE);
Figure 0110
Figure 0110: latticeshading.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);

pen[][] p={{white,grey,black},
           {red,green,blue},
           {cyan,magenta,yellow}};

latticeshade(unitsquare,p);
Figure 0111
Figure 0111: layers.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
usepackage("ocg");
settings.tex="pdflatex";

size(0,150);

pen colour1=red;
pen colour2=green;

pair z0=(0,0);
pair z1=(-1,0);
pair z2=(1,0);
real r=1.5;
path c1=circle(z1,r);
path c2=circle(z2,r);

begin("A");
fill(c1,colour1);
end();

fill(c2,colour2);

picture intersection;
fill(intersection,c1,colour1+colour2);
clip(intersection,c2);

add(intersection);

draw(c1);
draw(c2);

label("$A$",z1);

begin("B");
label("$B$",z2);
end();

pair z=(0,-2);
real m=3;
margin BigMargin=Margin(0,m*dot(unit(z1-z),unit(z0-z)));

draw(Label("$A\cap B$",0),conj(z)--z0,Arrow,BigMargin);
draw(Label("$A\cup B$",0),z--z0,Arrow,BigMargin);
draw(z--z1,Arrow,Margin(0,m));
draw(z--z2,Arrow,Margin(0,m));
Figure 0112
Figure 0112: leastsquares.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(400,200,IgnoreAspect);

import graph;
import stats;

file fin=line(input("leastsquares.dat"));

real[][] a=dimension(fin,0,0);
a=transpose(a);

real[] t=a[0], rho=a[1];

// Read in parameters from the keyboard:
//real first=getreal("first");
//real step=getreal("step");
//real last=getreal("last");

real first=100;
real step=50;
real last=700;

// Remove negative or zero values of rho:
t=rho > 0 ? t : null;
rho=rho > 0 ? rho : null;
    
scale(Log(true),Linear(true));

int n=step > 0 ? ceil((last-first)/step) : 0;

real[] T,xi,dxi;

for(int i=0; i <= n; ++i) {
  real first=first+i*step;
  real[] logrho=(t >= first & t <= last) ? log(rho) : null;
  real[] logt=(t >= first & t <= last) ? -log(t) : null;
  
  if(logt.length < 2) break;
  
  // Fit to the line logt=L.m*logrho+L.b:
  linefit L=leastsquares(logt,logrho);
    
  T.push(first);
  xi.push(L.m);
  dxi.push(L.dm);
} 
    
draw(graph(T,xi),blue);
errorbars(T,xi,dxi,red);

crop();

ylimits(0);

xaxis("$T$",BottomTop,LeftTicks);
yaxis("$\xi$",LeftRight,RightTicks);
Figure 0113
Figure 0113: legend.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph; 
size(8cm,6cm,IgnoreAspect); 
 
typedef real realfcn(real); 
realfcn F(real p) { 
  return new real(real x) {return sin(p*x);}; 
}; 
 
for(int i=1; i < 5; ++i)
  draw(graph(F(i*pi),0,1),Pen(i),
       "$\sin("+(i == 1 ? "" : (string) i)+"\pi x)$"); 
xaxis("$x$",BottomTop,LeftTicks); 
yaxis("$y$",LeftRight,RightTicks(trailingzero)); 
 
attach(legend(2),(point(S).x,truepoint(S).y),10S,UnFill);
Figure 0114
Figure 0114: lever.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200,0);

pair z0=(0,0);
pair z1=(2,0);
pair z2=(5,0);
pair zf=z1+0.75*(z2-z1);

draw(z1--z2);
dot(z1,red+0.15cm);
dot(z2,darkgreen+0.3cm);
label("$m$",z1,1.2N,red);
label("$M$",z2,1.5N,darkgreen);
label("$\hat{\ }$",zf,0.2*S,fontsize(24pt)+blue);

pair s=-0.2*I;
draw("$x$",z0+s--z1+s,N,red,Arrows,Bars,PenMargins);

s=-0.5*I;
draw("$\bar{x}$",z0+s--zf+s,blue,Arrows,Bars,PenMargins);

s=-0.95*I;
draw("$X$",z0+s--z2+s,darkgreen,Arrows,Bars,PenMargins);
Figure 0115
Figure 0115: limit.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200,200,IgnoreAspect);
import graph;

real L=1;
real epsilon=0.25;

real a(int n) {return L+1/n;}

for(int i=1; i < 20; ++i)
  dot((i,a(i)));

real N=1/epsilon;

xaxis(Label("$n$",align=2S));
yaxis(Label("$a_n$",0.85));

xtick("$2$",2);
ytick("$\frac{3}{2}$",3/2);
ytick("$2$",2);

yequals(Label("$L$",0,up),L,extend=true,blue);
yequals(Label("$L+\epsilon$",1,NW),L+epsilon,extend=true,red+dashed);
yequals(Label("$L-\epsilon$",1,SW),L-epsilon,extend=true,red+dashed);

xequals(N,extend=true,darkgreen+dashed);
labelx(shift(0,-10)*"$N=\frac{1}{\epsilon}$",N,E,darkgreen);

label("$a_n=1+\frac{1}{n},\quad \epsilon=\frac{1}{4}$",point((0,1)),10S+E);
Figure 0116
Figure 0116: lineargraph.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(250,200,IgnoreAspect);

real Sin(real t) {return sin(2pi*t);}
real Cos(real t) {return cos(2pi*t);}

draw(graph(Sin,0,1),red,"$\sin(2\pi x)$");
draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$");

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks(trailingzero));

label("LABEL",point(0),UnFill(1mm));

attach(legend(),truepoint(E),20E,UnFill);
Figure 0117
Figure 0117: lineargraph0.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(400,200,IgnoreAspect);

real Sin(real t) {return sin(2pi*t);}
real Cos(real t) {return cos(2pi*t);}

draw(graph(Sin,0,1),red,"$\sin(2\pi x)$");
draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$");

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks(trailingzero));

label("LABEL",point(0),UnFill(1mm));

add(legend(),point(E),20E,UnFill);
Figure 0118
Figure 0118: lines.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import math;

int n=7;

size(200,0);

draw(unitcircle,red);
for (int i=0; i < n-1; ++i)
  for (int j=i+1; j < n; ++j)
    drawline(unityroot(n,i),unityroot(n,j),blue);
Figure 0119
Figure 0119: linetype.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
void testline(real y) {
  draw((0,y)--(100,y),currentpen+solid);
  draw((0,y-10)--(100,y-10),currentpen+dotted);
  draw((0,y-20)--(100,y-20),currentpen+dashed);
  draw((0,y-30)--(100,y-30),currentpen+longdashed);
  draw((0,y-40)--(100,y-40),currentpen+dashdotted);
  draw((0,y-50)--(100,y-50),currentpen+longdashdotted);
  draw((0,y-60)--(100,y-60),currentpen+Dotted);
} 

currentpen=linewidth(0.5);
testline(100);
Figure 0120
Figure 0120: lmfit1.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import lmfit;
import graph;

size(10cm, 7cm, IgnoreAspect);

real[] date = { 1790, 1800, 1810, 1820, 1830, 1840, 1850, 1860, 1870, 1880,
1890, 1900, 1910, 1920, 1930, 1940, 1950, 1960, 1970, 1980, 1990 };
real[] population = { 3.929, 5.308, 7.240, 9.638, 12.866, 17.069, 23.192, 31.443,
38.558, 50.156, 62.948, 75.996, 91.972, 105.711, 122.775, 131.669, 150.697,
179.323, 203.185, 226.546, 248.710 };

real t0 = 1776;

real P(real[] params, real t) {
  real P0 = params[0];
  real K = params[1];
  real r = params[2];
  return (K * P0) / (P0 + (K - P0) * exp(-r * (t - t0)));
}

real[] params = { 10, 500, 0.1 };

real res = lmfit.fit(date, population, P, params).norm;

write("P_0 = ", params[0]);
write("K = ", params[1]);
write("r = ", params[2]);
write("error = ", res);

real P(real t) {
  return P(params, t);
}

draw(graph(date, population), blue);
draw(graph(P, t0, 2000), red);
xaxis("Year", BottomTop, LeftTicks);
yaxis("Population in millions", LeftRight, RightTicks);
Figure 0121
Figure 0121: log.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(150,0);

real f(real x) {return log(x);}
pair F(real x) {return (x,f(x));}

xaxis("$x$",0);
yaxis("$y$");

draw(graph(f,0.01,10,operator ..));

labelx(1,SSE);
label("$\log x$",F(7),SE);
Figure 0122
Figure 0122: log2graph.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(200,IgnoreAspect);

// Base-2 logarithmic scale on y-axis:

real log2(real x) {static real log2=log(2); return log(x)/log2;}
real pow2(real x) {return 2^x;}

scaleT yscale=scaleT(log2,pow2,logarithmic=true);
scale(Linear,yscale);

real f(real x) {return 1+x^2;}

draw(graph(f,-4,4));

yaxis("$y$",ymin=1,ymax=f(5),RightTicks(Label(Fill(white))),EndArrow);
xaxis("$x$",xmin=-5,xmax=5,LeftTicks,EndArrow);
Figure 0123
Figure 0123: logdown.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(200,IgnoreAspect);

real log10Down(real x) {return -log10(x);}
real pow10Down(real x) {return pow10(-x);}

scaleT LogDown=scaleT(log10Down,pow10Down,logarithmic=true);
scale(Linear,LogDown);

draw(graph(exp,-5,5));

yaxis("$y$",RightTicks(Label(Fill(white)),DefaultLogFormat),BeginArrow);
xaxis("$x$",LeftTicks(NoZero),EndArrow);
Figure 0124
Figure 0124: loggraph.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(200,200,IgnoreAspect);

real f(real t) {return 1/t;}

scale(Log,Log);

draw(graph(f,0.1,10));

//xlimits(1,10,Crop);
//ylimits(0.1,1,Crop);

dot(Label("(3,5)",align=S),Scale((3,5)));

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
Figure 0125
Figure 0125: loggrid.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(200,200,IgnoreAspect);

real f(real t) {return 1/t;}

scale(Log,Log);
draw(graph(f,0.1,10),red);
pen thin=linewidth(0.5*linewidth());
xaxis("$x$",BottomTop,LeftTicks(begin=false,end=false,extend=true,
                                ptick=thin));
yaxis("$y$",LeftRight,RightTicks(begin=false,end=false,extend=true,
                                 ptick=thin));
Figure 0126
Figure 0126: logimage.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
import palette;

size(10cm,10cm,IgnoreAspect);

real f(real x, real y) {
  return 0.9*pow10(2*sin(x/5+2*y^0.25)) + 0.1*(1+cos(10*log(y)));
}

scale(Linear,Log,Log);

pen[] Palette=BWRainbow();

bounds range=image(f,Automatic,(0,1),(100,100),nx=200,Palette);

xaxis("$x$",BottomTop,LeftTicks,above=true);
yaxis("$y$",LeftRight,RightTicks,above=true);

palette("$f(x,y)$",range,(0,200),(100,250),Top,Palette,
        PaletteTicks(ptick=linewidth(0.5*linewidth())));
Figure 0127
Figure 0127: logo.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(140,80,IgnoreAspect);

picture logo(pair s=0, pen q) 
{
  picture pic;
  pen p=linewidth(2)+fontsize(24pt)+q;
  real a=-0.4;
  real b=0.95;
  real y1=-5;
  real y2=-3y1/2;
  path A=(a,0){dir(10)}::{dir(89.5)}(0,y2);
  draw(pic,A,p);
  draw(pic,(0,y1){dir(88.3)}::{dir(20)}(b,0),p);
  real c=0.5*a;
  pair z=(0,2.5);
  label(pic,"{\it symptote}",z,0.25*E+0.169S,p);
  pair w=(0,1.7);
  draw(pic,intersectionpoint(A,w-1--w)--w,p);
  draw(pic,(0,y1)--(0,y2),p);
  draw(pic,(a,0)--(b,0),p);
  return shift(s)*pic;
} 

pair z=(-0.015,0.08);
for(int x=0; x < 10; ++x)
  add(logo(0.1*x*z,gray(0.04*x)));

add(logo(red));
Figure 0128
Figure 0128: logo3.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

size(560,320,IgnoreAspect);
size3(140,80,15);
currentprojection=perspective(-3,20,10,up=Y);
currentlight=White;

path[] outline;

real a=-0.4;
real b=0.95;
real y1=-5;
real y2=-3y1/2;
path A=(a,0){dir(10)}::{dir(89.5)}(0,y2);
outline.push(A);
outline.push((0,y1){dir(88.3)}::{dir(20)}(b,0));
real c=0.5*a;
pair z=(0,2.5);
path[] text = shift(0,2)*scale(0.01,0.15)*
  texpath(Label("{\it symptote}",z,0.25*E+0.169S,fontsize(24pt)));
outline.append(text);
pair w=(0,1.7);
outline.push(intersectionpoint(A,w-1--w)--w);
outline.push((0,y1)--(0,y2));
outline.push((a,0)--(b,0));

for(path p : outline)
  draw(extrude(p,-0.1Z),material(lightgray,shininess=1.0));

draw(path3(outline),red+linewidth(0));

draw(surface(text),red,nolight);
Figure 0129
Figure 0129: logticks.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(300,175,IgnoreAspect);
scale(Log,Log);
draw(graph(identity,5,20));
xlimits(5,20);
ylimits(1,100);
xaxis("$M/M_\odot$",BottomTop,LeftTicks(DefaultFormat,
                                        new real[] {6,10,12,14,16,18}));
yaxis("$\nu_{\rm upp}$ [Hz]",LeftRight,RightTicks(DefaultFormat));
Figure 0130
Figure 0130: lowint.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(100,0);
import graph;
import lowupint;

real a=-0.8, b=1.2;
real c=1.0/sqrt(3.0);

partition(a,b,c,min);

arrow("$f(x)$",F(0.5*(a+b)),NNE,red);
label("$\cal{L}$",(0.5*(a+b),f(0.5*(a+b))/2));
Figure 0131
Figure 0131: magnetic.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import contour3;

size(200,0);
currentprojection=orthographic((6,8,2),up=Y);

real a(real z) {return (z < 6) ? 1 : exp((abs(z)-6)/4);}
real b(real z) {return 1/a(z);}
real B(real z) {return 1-0.5cos(pi*z/10);}

real f(real x, real y, real z) {return 0.5B(z)*(a(z)*x^2+b(z)*y^2)-1;}

draw(surface(contour3(f,(-2,-2,-10),(2,2,10),10)),blue+opacity(0.75));

xaxis3(Label("$x$",1),red);
yaxis3(Label("$y$",1),red);
zaxis3(Label("$z$",1),red);
Figure 0132
Figure 0132: makepen.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);
pen convex=makepen(scale(10)*polygon(8))+grey;
draw((1,0.4),convex);
draw((0,0)---(1,1)..(2,0)--cycle,convex);

pen nonconvex=scale(10)*
  makepen((0,0)--(0.25,-1)--(0.5,0.25)--(1,0)--(0.5,1.25)--cycle)+red;
draw((0.5,-1.5),nonconvex);
draw((0,-1.5)..(1,-0.5)..(2,-1.5),nonconvex);
Figure 0133
Figure 0133: markers1.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(12cm,0);
import markers;

pair A=(0,0), B=(1,0), C=(2,0), D=(3,0);
path p=A--B--C--D;
transform T=shift(-4,-1);
transform t=shift(4,0);

//line 1 **********
draw(p,marker(markinterval(3,dotframe,true)));
label("$1$",point(p,0),3W);

//line 2 **********
p=t*p;
draw(p,marker(stickframe,markuniform(4)));
label("$2$",point(p,0),3W);

//line 3 **********
p=T*p;
draw(p,marker(stickframe(red),markinterval(3,dotframe(blue),true)));
label("$3$",point(p,0),3W);

//line 4 **********
p=t*p;
draw(p,StickIntervalMarker(3,2,blue,dotframe(red)));
label("$4$",point(p,0),3W);

//line 5 **********
p=T*p;
pen pn=linewidth(4bp);
draw(p,pn,StickIntervalMarker(3,3,angle=25,pn,dotframe(red+pn)));
label("$5$",point(p,0),3W);

//line 6 **********
p=t*p;
draw(p,StickIntervalMarker(3,5,angle=25,size=4mm,space=2mm,offset=I*2mm,
                           scale(2)*dotframe(red)));
label("$6$",point(p,0),3W);

//line 7 **********
p=T*p;
draw(p,StickIntervalMarker(n=3,angle=45,size=10mm,space=3mm,dotframe));
label("$7$",point(p,0),3W);

//line 8 **********
p=t*p;
draw(p,CircleBarIntervalMarker(n=2,dotframe));
label("$8$",point(p,0),3W);

//line 9 **********
p=T*p;
draw(p,CircleBarIntervalMarker(n=3,angle=30,barsize=8mm,radius=2mm,
                               FillDraw(.8red),
                               dotframe));
label("$9$",point(p,0),3W);

//line 10 **********
p=t*p;
draw(p,CircleBarIntervalMarker(n=3,angle=30,barsize=8mm,radius=2mm,
                               FillDraw(.8red),circleabove=true,dotframe));
label("$10$",point(p,0),3W);

//line 11 **********
p=T*p;
draw(p,CircleBarIntervalMarker(n=3,angle=30,barsize=8mm,radius=2mm,
                               FillDraw(.8red),circleabove=true,dotframe,
                               above=false));
label("$11$",point(p,0),3W);

//line 12 **********
p=t*p;
draw(p,TildeIntervalMarker(i=3,dotframe));
label("$12$",point(p,0),3W);

//line 13 **********
p=T*p;
draw(p,TildeIntervalMarker(i=3,n=2,angle=-20,dotframe));
label("$13$",point(p,0),3W);

//line 14 **********
p=t*p;
draw(p,CrossIntervalMarker(3,3,dotframe));
label("$14$",point(p,0),3W);

//line 15 **********
p=shift(.25S)*T*p;
path cle=shift(relpoint(p,.5))*scale(abs(A-D)/4)*unitcircle;
draw(cle,StickIntervalMarker(5,3,dotframe(6bp+red)));
label("$15$",point(p,0),3W);

//line 16 **********
cle=t*cle;
p=t*p;
frame a;
label(a,"$a$",(0,-2labelmargin()));
draw(cle,marker(dotframe(6bp+red),markinterval(5,a,true)));
label("$16$",point(p,0),3W);

// line 17 **********
p=T*shift(relpoint(p,.5)+.65S)*scale(.5)*shift(-relpoint(p,.5))*rotate(45,relpoint(p,.5))*p;
draw(p,TildeIntervalMarker(size=5mm,rotated=false,dotframe));
label("$17$",point(p,0),3W);
Figure 0134
Figure 0134: markers2.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(10cm,0);
import markers;
import geometry;
import math;

pair A=0, B=(1,0), C=(0.7,1), D=(-0.5,0), F=rotate(-90)*(C-B)/2+B;

draw(A--B);
draw(A--C);
pen p=linewidth(1mm);
draw(B--C,p);
draw(A--D);
draw(B--F,p);
label("$A$",A,SW);
label("$B$",B,S);
label("$C$",C,N);
dot(Label("$D$",D,S));
dot(Label("$F$",F,N+NW));

markangle(A,C,B);

markangle(scale(1.5)*"$\theta$",radius=40,C,B,A,ArcArrow(2mm),1mm+red);
markangle(scale(1.5)*"$-\theta$",radius=-70,A,B,C,ArcArrow,green);

markangle(Label("$\gamma$",Relative(0.25)),n=2,radius=-30,A,C,B,p=0.7blue+2);

markangle(n=3,B,A,C,marker(markinterval(stickframe(n=2),true)));

pen RedPen=0.7red+1bp;
markangle(C,A,D,RedPen,marker(markinterval(2,stickframe(3,4mm,RedPen),true)));
drawline(A,A+dir(A--D,A--C),dotted);

perpendicular(B,NE,F-B,size=10mm,1mm+red,
              TrueMargin(linewidth(p)/2,linewidth(p)/2),Fill(yellow));
Figure 0135
Figure 0135: markregular.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(10cm,0);

real xmin=-4,xmax=4;
real ymin=-2,ymax=10;

real f(real x) {return x^2;}

marker cross=marker(scale(4)*rotate(45)*cross(4),
                    markuniform(new pair(real t) {return Scale((t,f(t)));},
                                xmin,xmax,round(2*(xmax-xmin))),1bp+red);

draw(graph(f,xmin,xmax,n=400),linewidth(1bp),cross);

ylimits(-2.5,10,Crop);

xaxis(Label("$x$",position=EndPoint, align=NE),xmin=xmin,xmax=xmax,
      Ticks(scale(.7)*Label(align=E),NoZero,begin=false,beginlabel=false,
            end=false,endlabel=false,Step=1,step=.25,
            Size=1mm, size=.5mm,pTick=black,ptick=gray),Arrow);

yaxis(Label("$y$",position=EndPoint, align=NE),ymin=ymin,ymax=ymax,
      Ticks(scale(.7)*Label(),NoZero,begin=false,beginlabel=false,
            end=false,endlabel=false,Step=1,step=.25,Size=1mm,size=.5mm,
            pTick=black,ptick=gray),Arrow);
Figure 0136
Figure 0136: mexicanhat.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);

real mexican(real x) {return (1-8x^2)*exp(-(4x^2));}

int n=30;
real a=1.5;
real width=2a/n;

guide hat;
path solved;

for(int i=0; i < n; ++i) {
  real t=-a+i*width;
  pair z=(t,mexican(t));
  hat=hat..z;
  solved=solved..z;
}

draw(hat);
dot(hat,red);
draw(solved,dashed);
Figure 0137
Figure 0137: monthaxis.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(400,150,IgnoreAspect);

real[] x=sequence(12);
real[] y=sin(2pi*x/12);

scale(false);

string[] month={"Jan","Feb","Mar","Apr","May","Jun",
                "Jul","Aug","Sep","Oct","Nov","Dec"};

draw(graph(x,y),red,MarkFill[0]);

xaxis(BottomTop,LeftTicks(new string(real x) {
      return month[round(x % 12)];}));
yaxis("$y$",LeftRight,RightTicks(4));
Figure 0138
Figure 0138: mosaic.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
// Calendar example contributed by Jens Schwaiger

// transformations
path similarpath(pair a, pair b, path p) {
  // transform p into a path starting at a and ending at b
  pair first;
  pair last;
  path p_;
  first=point(p,0);
  last=point(p,length(p));
  p_=shift(-first)*p;
  p_=rotate(degrees(b-a))*p_;
  p_=scale(abs(b-a)/abs(last-first))*p_;
  p_=shift(a)*p_;
  return p_;
}

path c_line(path p) {
  // returns the path obtained by adding to p a copy rotated
  // around the endpoint of p by 180 degrees
  // works only if the initial point and the endpoint of p are different
  // a c_line is symetric with respect to the center of 
  // the straight line between its endpoints
  //
  return p..rotate(180,point(p,length(p)))*reverse(p);
}

path tounitcircle(path p, int n=300) {
  // the transformation pair x --> x/sqrt(1+abs(x)^2)
  // is a bijection from the plane to the open unitdisk
  real l=arclength(p);
  path ghlp;
  for(int i=0; i <= n; ++i) {
    real at=arctime(p,l/n*i);
    pair phlp=point(p,at);
    real trhlp=1/(1+abs(phlp)^2)^(1/2);
    ghlp=ghlp--trhlp*phlp;
  }
  if(cyclic(p)) {ghlp=ghlp--cycle;}
  return ghlp;
}

void centershade(picture pic=currentpicture, path p, pen in, pen out,
                 pen drawpen=currentpen) { 
  pair center=0.5(max(p)+min(p));
  real radius=0.5abs(max(p)-min(p));
  radialshade(pic,p,in,center,0,out,center,radius);
  draw(pic,p,drawpen);
}

pair zentrum(path p) {return 0.5(min(p)+max(p));}

//%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

real scalefactor=19/13; // For output: height=scalefactor*width
real outputwidth=13cm;
picture kalender;// at first we produce a calendar for february 2006
texpreamble("\usepackage[latin1]{inputenc}");
size(outputwidth,0);
real yc=0.5;
pair diff=(-3.5,5*yc);
pen farbe(int j) {
  pen hlp=0.8white;
  if(j % 7 == 6) {hlp=red+white;}
  return hlp;}

// farbe=German word for color
path kasten=yscale(yc)*unitsquare;
// Kasten is a German word meaning something like box
path Gkasten=shift((0,2*yc)+diff)*xscale(7)*yscale(2)*kasten;
path tage[]= new path[7]; // Tag=day
string wochentag[]={"MO","DI","MI","DO","FR","SA","SO"};
path[][] bx= new path[6][7];
string[][] entry= new string[6][7];
bool[][] holiday=new bool[6][7];

// Now the necessary information for February 2006
int start=2;
int days=28;
for(int i=0; i < entry.length; ++i) {
  for(int j=0; j < entry[0].length; ++j) {
    int day=i*7+j-start+1;
    entry[i][j]=(day > 0 && day <= days ? (string) day : "");
    holiday[i][j]=false;
  }
}

for(int j=0; j < 7; ++j) {
  tage[j]=shift((j,yc)+diff)*kasten; 
  filldraw(tage[j],farbe(j),black+2bp);
  label(wochentag[j],zentrum(tage[j]),Palatino());
  for(int i=0; i < 6; ++i) {bx[i][j]=shift((j,-yc*i)+diff)*kasten;
    filldraw(bx[i][j],farbe(j),black+2bp);
    if(holiday[i][j]) {filldraw(bx[i][j],farbe(6),black+2bp);};
  };
};
filldraw(Gkasten,0.3white,black+2bp); 
for(int j=0; j < 7; ++j)
  for(int i=0; i < 6 ; ++i) {label(entry[i][j],zentrum(bx[i][j]),Palatino());}
label("\Huge Februar 2006",zentrum(Gkasten),Palatino()+white); 
// Zentrum=center; Februar=february
add(kalender,currentpicture);
erase();

// Now the mosaic is constructed
pair a[]=new pair[4];
path p[]=new path[4];
path q[]=new path[4];
path kontur[]=new path[5];
picture temppic;

a[1]=(0,0);
a[2]=(1,0);
a[3]=(0,1); // a triangle with abs(a[2]-a[1])=abs(a[3]-a[1]
            // and a right angle at a[1];
q[1]=(0,0){dir(-20)}::{dir(20)}(0.2,0){dir(-140)}..{dir(0)}(0.3,-0.2){dir(0)}..
{dir(140)}(0.4,0){dir(20)}..{dir(-20)}(1,0);
q[2]=(0,0){dir(20)}..{dir(-20)}(0.8,0){dir(-140)}..{dir(0)}(0.9,-0.3){dir(0)}..
{dir(140)}(1,0);
q[2]=c_line(q[2]);
p[1]=similarpath(a[1],a[2],q[1]);// arbitrary path from a[1] to a[2]
p[2]=similarpath(a[2],a[3],q[2]);// arbitrary c_line from a[2] to a[3]
p[3]=rotate(90,a[1])*reverse(p[1]);//
kontur[1]=p[1]..p[2]..p[3]..cycle;// first tile
kontur[2]=rotate(90,a[1])*kontur[1];// second
kontur[3]=rotate(180,a[1])*kontur[1];// third
kontur[4]=rotate(270,a[1])*kontur[1];// fourth
pair tri=2*(interp(a[2],a[3],0.5)-a[1]);
pair trii=rotate(90)*tri;
// translations of kontur[i], i=1,2,3,4, with respect to
// j*tri+k*trii
// fill the plane

for(int j=-4; j < 4; ++j)
  for(int k=-4; k < 4; ++k) {
    transform tr=shift(j*tri+k*trii);
    for(int i=1; i < 5; ++i) {
      centershade(temppic,tr*kontur[i],(1-i/10)*white,
                  (1-i/10)*chartreuse,black+2bp);
    }
  }
  
// Now we produce the bijective images inside 
// a suitably scaled unitcircle            
for(int k=-1; k < 2; ++k)
  for(int l=-1; l < 2; ++l) {
    transform tr=shift(k*tri+l*trii);
    for(int i=1; i < 5; ++i) {
      centershade(temppic,scale(2.5)*tounitcircle(tr*kontur[i],380),
                  (1-i/10)*white,(1-i/10)*orange,black+2bp);
    }
  }         
          
add(temppic); 

// We clip the picture to a suitable box 
pair piccenter=0.5*(temppic.min()+temppic.max());
pair picbox=temppic.max()-temppic.min();
real picwidth=picbox.x;
transform trialtrans=shift(0,-1.5)*shift(piccenter)*yscale(scalefactor)*
  scale(0.25picwidth)*shift((-0.5,-0.5))*identity();
clip(trialtrans*unitsquare);

// add the calendar at a suitable position
add(kalender.fit(0.75*outputwidth),interp(point(S),point(N),1/13));
Figure 0139
Figure 0139: mosquito.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(9cm,10cm,IgnoreAspect);

pair d=(1,0.25);
real s=1.6d.x;
real y=0.6;
defaultpen(fontsize(8pt));

picture box(string s, pair z=(0,0)) {
  picture pic;
  draw(pic,box(-d/2,d/2));
  label(pic,s,(0,0));
  return shift(z)*pic;
}

label("Birds",(0,y));
picture removed=box("Removed ($R_B$)");
picture infectious=box("Infectious ($I_B$)",(0,-1.5));
picture susceptible=box("Susceptible ($S_B$)",(0,-3));

add(removed);
add(infectious);
add(susceptible);

label("Mosquitoes",(s,y));
picture larval=box("Larval ($L_M$)",(s,0));
picture susceptibleM=box("Susceptible ($S_M$)",(s,-1));
picture exposed=box("Exposed ($E_M$)",(s,-2));
picture infectiousM=box("Infectious ($I_M$)",(s,-3));

add(larval);
add(susceptibleM);
add(exposed);
add(infectiousM);

path ls=point(larval,S)--point(susceptibleM,N);
path se=point(susceptibleM,S)--point(exposed,N);
path ei=point(exposed,S)--point(infectiousM,N);
path si=point(susceptible,N)--point(infectious,S);

draw(minipage("\flushright{recovery rate ($g$) \& death rate from virus
($\mu_V$)}",40pt),point(infectious,N)--point(removed,S),LeftSide,Arrow,
     PenMargin);

draw(si,LeftSide,Arrow,PenMargin);

draw(minipage("\flushright{maturation rate ($m$)}",50pt),ls,RightSide,
     Arrow,PenMargin);
draw(minipage("\flushright{viral incubation rate ($k$)}",40pt),ei,
     RightSide,Arrow,PenMargin);

path ise=point(infectious,E)--point(se,0.5);
  
draw("$(ac)$",ise,LeftSide,dashed,Arrow,PenMargin);
label(minipage("\flushleft{biting rate $\times$ transmission
probability}",50pt),point(infectious,SE),dir(-60)+S);

path isi=point(infectiousM,W)--point(si,2.0/3);

draw("$(ab)$",isi,LeftSide,dashed,Arrow,PenMargin);
draw(se,LeftSide,Arrow,PenMargin);
      
real t=2.0;
draw("$\beta_M$",
     point(susceptibleM,E){right}..tension t..{left}point(larval,E),
     2*(S+SE),red,Arrow(Fill,0.5));
draw(minipage("\flushleft{birth rate ($\beta_M$)}",20pt),
     point(exposed,E){right}..tension t..{left}point(larval,E),2SW,red,
     Arrow(Fill,0.5));
draw("$\beta_M$",
     point(infectiousM,E){right}..tension t..{left}point(larval,E),2SW,
     red,Arrow(Fill,0.5));

path arrow=(0,0)--0.75cm*dir(35);
draw(point(larval,NNE),
     Label(minipage("\flushleft{larval death rate ($\mu_L$)}",45pt),1),
     arrow,blue,Arrow);
draw(point(susceptibleM,NNE),
     Label(minipage("\flushleft{adult death rate ($\mu_A$)}",20pt),1),
     arrow,N,blue,Arrow);
draw(point(exposed,NNE),Label("$\mu_A$",1),arrow,blue,Arrow);
draw(point(infectiousM,NNE),Label("$\mu_A$",1),arrow,blue,Arrow);
Figure 0140
Figure 0140: multicontour.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import contour;

size(200);

real f(real x, real y) {return x^2-y^2;}
int n=10;
real[] c=new real[n];
for(int i=0; i < n; ++i) c[i]=(i-n/2)/n;

pen[] p=sequence(new pen(int i) {
    return (c[i] >= 0 ? solid : dashed)+fontsize(6pt);
  },c.length);

Label[] Labels=sequence(new Label(int i) {
    return Label(c[i] != 0 ? (string) c[i] : "",Relative(unitrand()),(0,0),
                 UnFill(1bp));
  },c.length);

draw(Labels,contour(f,(-1,-1),(1,1),c),p);
Figure 0141
Figure 0141: near_earth.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;
import math;
texpreamble("\usepackage{bm}");

size(300,0);

pen thickp=linewidth(0.5mm);
real radius=0.8, lambda=37, aux=60;

currentprojection=perspective(4,1,2); 

// Planes
pen bg=gray(0.9)+opacity(0.5);
draw(surface((1.2,0,0)--(1.2,0,1.2)--(0,0,1.2)--(0,0,0)--cycle),bg);
draw(surface((0,1.2,0)--(0,1.2,1.2)--(0,0,1.2)--(0,0,0)--cycle),bg);
draw(surface((1.2,0,0)--(1.2,1.2,0)--(0,1.2,0)--(0,0,0)--cycle),bg);

real r=1.5;
pen p=rgb(0,0.7,0);
draw(Label("$x$",1),O--r*X,p,Arrow3);
draw(Label("$y$",1),O--r*Y,p,Arrow3);
draw(Label("$z$",1),O--r*Z,p,Arrow3);
label("$\rm O$",(0,0,0),W);
  
// Point Q
triple pQ=radius*dir(lambda,aux);
draw(O--radius*dir(90,aux),dashed);
label("$\rm Q$",pQ,N+3*W);
draw("$\lambda$",arc(O,0.15pQ,0.15*Z),N+0.3E);

// Particle
triple m=pQ-(0.26,-0.4,0.28);
real width=5;
dot("$m$",m,SE,linewidth(width));
draw("$\bm{\rho}$",(0,0,0)--m,Arrow3,PenMargin3(0,width));
draw("$\bm{r}$",pQ--m,Arrow3,PenMargin3(0,width));

// Spherical octant
real r=sqrt(pQ.x^2+pQ.y^2);
draw(arc((0,0,pQ.z),(r,0,pQ.z),(0,r,pQ.z)),dashed);
draw(arc(O,radius*Z,radius*dir(90,aux)),dashed);
draw(arc(O,radius*Z,radius*X),thickp);
draw(arc(O,radius*Z,radius*Y),thickp);
draw(arc(O,radius*X,radius*Y),thickp);

// Moving axes
triple i=dir(90+lambda,aux);
triple k=unit(pQ);
triple j=cross(k,i);

draw(Label("$x$",1),pQ--pQ+0.2*i,2W,red,Arrow3);
draw(Label("$y$",1),pQ--pQ+0.32*j,red,Arrow3);
draw(Label("$z$",1),pQ--pQ+0.26*k,red,Arrow3);

draw("$\bm{R}$",O--pQ,Arrow3,PenMargin3);
draw("$\omega\bm{K}$",arc(0.9Z,0.2,90,-120,90,160,CW),1.2N,Arrow3);
Figure 0142
Figure 0142: odetest.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import ode;

write("integration test");
real f(real t, real x) {return cos(x);}
write(integrate(1,f,0,10,0.1,dynamic=true,0.0002,0.0004,RK3BS,verbose=true));
write();

write("system integration test");
real[] f(real t, real[] x) {return new real[] {x[1],1.5*x[0]^2};}
write(integrate(new real[] {4,-8},f,0,1,n=100,dynamic=true,tolmin=0.0002,
                tolmax=0.0004,RK3BS,verbose=true));
write();

write("simultaneous newton test");
real[] function(real[] x) {
  return new real[] {x[0]^2+x[1]^2-25,(x[0]-6)^2+x[1]^2-25};
}
real[][] fJac(real[] x) {
  return new real[][] {{2*x[0],2*x[1]},{2*(x[0]-6),2*x[1]}};
}
write(newton(function,fJac,new real[] {0,-1}));
write();


write("BVP solver test");
write("Finding initial conditions that solve w''(t)=1.5*w(t), w(0)=4, w(1)=1");
real[] initial(real[] x) {
  return new real[] {4,x[0]};
}

real[] discrepancy(real[] x) {
  write("Error: ",x[0]-1);
  return new real[] {x[0]-1};
}

write(solveBVP(f,0,1,n=10,initial,discrepancy,guess=new real[] {-30},RK4,
               iterations=10));
write();
write(solveBVP(f,0,1,n=100,initial,discrepancy,guess=new real[] {-30},RK4,
               iterations=10));
write();
write(solveBVP(f,0,1,n=10000,initial,discrepancy,guess=new real[] {-30},RK4,
               iterations=10));
write();
Figure 0143
Figure 0143: onecontour.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import contour;
size(75);

real f(real a, real b) {return a^2+b^2;}
draw(contour(f,(-1,-1),(1,1),new real[] {1}));
Figure 0144
Figure 0144: oneoverx.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(200,IgnoreAspect);

real f(real x) {return 1/x;};

bool3 branch(real x)
{
  static int lastsign=0;
  if(x == 0) return false;
  int sign=sgn(x);
  bool b=lastsign == 0 || sign == lastsign; 
  lastsign=sign;
  return b ? true : default;
}

draw(graph(f,-1,1,branch));
axes("$x$","$y$",red);
Figure 0145
Figure 0145: orthocenter.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import geometry;
import math;

size(7cm,0);

real theta=degrees(asin(0.5/sqrt(7)));

pair B=(0,sqrt(7));
pair A=B+2sqrt(3)*dir(270-theta);
pair C=A+sqrt(21);
pair O=0;

pair Ap=extension(A,O,B,C);
pair Bp=extension(B,O,C,A);
pair Cp=extension(C,O,A,B);

perpendicular(Ap,NE,Ap--O,blue);
perpendicular(Bp,NE,Bp--C,blue);
perpendicular(Cp,NE,Cp--O,blue);

draw(A--B--C--cycle);

currentpen=black;

draw("1",A--O,-0.25*I*dir(A--O));
draw(O--Ap);
draw("$\sqrt{7}$",B--O,LeftSide);
draw(O--Bp);
draw("4",C--O);
draw(O--Cp);

dot("$O$",O,1.5*dir(B--Bp,Cp--C),red);
dot("$A$",A,1.5*dir(C--A,B--A),red);
dot("$B$",B,NW,red);
dot("$C$",C,dir(A--C,B--C),red);
dot("$A'$",Ap,dir(A--Ap),red);
dot("$B'$",Bp,dir(B--Bp),red);
dot("$C'$",Cp,dir(C--Cp),red);

label(graphic("piicon.eps","width=2.5cm"),Ap,5ENE,red);
Figure 0146
Figure 0146: p-orbital.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3; 
import palette; 
size(200); 
currentprojection=orthographic(6,8,2); 
 
real c0=0.1; 

real f(real r) {return r*(1-r/6)*exp(-r/3);}

triple f(pair t) {
  real r=t.x;
  real phi=t.y;
  real f=f(r);
  real s=max(min(c0/f,1),-1);
  real R=r*sqrt(1-s^2);
  return (R*cos(phi),R*sin(phi),r*s);
}

bool cond(pair t) {return f(t.x) != 0;}

real R=abs((20,20,20));
surface s=surface(f,(0,0),(R,2pi),100,8,Spline,cond);

s.colors(palette(s.map(abs),Gradient(palegreen,heavyblue))); 
draw(s); 
draw(zscale3(-1)*s); 
 
axes3("$x$","$y$","$z$",Arrow3);
Figure 0147
Figure 0147: parametricelevation.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import palette;
size(200);

currentprojection=orthographic(4,2,4);

triple f(pair z) {return expi(z.x,z.y);}

surface s=surface(f,(0,0),(pi,2pi),10,Spline);
draw(s,mean(palette(s.map(zpart),BWRainbow())),black,nolight);
Figure 0148
Figure 0148: parametricgraph.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(0,200);

real x(real t) {return cos(2pi*t);}
real y(real t) {return sin(2pi*t);}

draw(graph(x,y,0,1));

//xlimits(0,1,Crop);
//ylimits(-1,0,Crop);

xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks(trailingzero));
Figure 0149
Figure 0149: parametricsurface.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size(200,0);
currentprojection=orthographic(4,0,2);

real R=2;
real a=1.9;

triple f(pair t) {
  return ((R+a*cos(t.y))*cos(t.x),(R+a*cos(t.y))*sin(t.x),a*sin(t.y));
}

pen p=rgb(0.2,0.5,0.7);

// surface only
draw(surface(f,(0,0),(2pi,2pi),8,8,Spline),lightgray);

// mesh only
//draw(surface(f,(0,0),(2pi,2pi),8,8,Spline),nullpen,meshpen=p);

// surface & mesh
//draw(surface(f,(0,0),(2pi,2pi),8,8,Spline),lightgray,meshpen=p);
Figure 0150
Figure 0150: partialsurface.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import palette;

size(0,300);
currentprojection=perspective(3,-2,2);

real V(real r) {return r^4-r^2;}
real V(pair pos) {return V(abs(pos));}

real R=1/sqrt(2);
real z=-0.2;

bool active(pair pos) {return abs(pos) < R;}
bool above(pair pos) {return V(pos) >= z;}

pair a=(-1.5,-1);
pair b=(0.5,1);
real f=1.2;

draw(plane(f*(b.x-a.x,0,z),(0,f*(b.y-a.y),z),(a.x,a.y,z)),
     lightgrey+opacity(0.5));

surface s=surface(V,a,b,40,Spline,active);
draw(s,mean(palette(s.map(new real(triple v) {
          return above((v.x,v.y)) ? 1 : 0;}),
      new pen[] {lightblue,lightgreen})),black);

xaxis3(Label("$\phi^\dagger\phi$",1),red,Arrow3);
zaxis3(Label("$V(\phi^\dagger\phi)$",1),0,0.3,red,Arrow3);
Figure 0151
Figure 0151: pathintersectsurface.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(500);
import graph3;

path3 g=randompath3(10);

draw(g,red+thin());

triple[][] P={
  {(0,0,0),(1,0,0),(1,0,0),(2,0,0)},
  {(0,4/3,0),(2/3,4/3,2),(4/3,4/3,2),(2,4/3,0)},
  {(0,2/3,0),(2/3,2/3,0),(4/3,2/3,0),(2,2/3,0)},
  {(0,2,0),(2/3,2,0),(4/3,2,0),(2,2,0)}};

surface s=surface(patch(P));
s.append(unitplane);

draw(s,lightgray+opacity(0.9));
dot(intersectionpoints(g,s),blue);
Figure 0152
Figure 0152: pdb.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;
import cpkcolors;

// A sample Protein Data Bank file for this example is available from
// http://ndbserver.rutgers.edu/ftp/NDB/coordinates/na-biol/100d.pdb1

bool getviews=true;

currentlight=White;
//currentlight=nolight;

size(200);
currentprojection=perspective(30,30,15);

// Uncomment this line for more accurate (but slower) PDF rendering
//dotgranularity=0;

pen chainpen=green;
pen hetpen=purple;

string filename="100d.pdb1";
//string filename=getstring("filename");

string prefix=stripextension(filename);
file data=input(filename);

pen color(string e) 
{
  e=replace(e," ","");
  int n=length(e);
  if(n < 1) return currentpen;
  if(n > 1) e=substr(e,0,1)+downcase(substr(e,1,n-1));
  int index=find(Element == e);
  if(index < 0) return currentpen;
  return rgb(Hexcolor[index]);
}       

// ATOM
string[] name,altLoc,resName,chainID,iCode,element,charge;
int[] serial,resSeq;
real[][] occupancy,tempFactor;

bool newchain=true;

struct bond 
{
  int i,j;
  void operator init(int i, int j) {
    this.i=i;
    this.j=j;
  }
}

bond[] bonds;

struct atom 
{
  string name;
  triple v;
  void operator init(string name, triple v) {
    this.name=name;
    this.v=v;
  }
}

struct chain
{
  int[] serial;
  atom[] a;
}

int[] serials;
chain[] chains;
atom[] atoms;

while(true) {
  string line=data;
  if(eof(data)) break;
  string record=replace(substr(line,0,6)," ","");
  if(record == "TER") {newchain=true; continue;}
  bool ATOM=record == "ATOM";
  bool HETATOM=record == "HETATM";
  int serial;

  atom a;
  if(ATOM || HETATOM) {
    serial=(int) substr(line,6,5);
    a.name=substr(line,76,2);
    a.v=((real) substr(line,30,8),
         (real) substr(line,38,8),
         (real) substr(line,46,8));
  }
  if(ATOM) {
    if(newchain) {
      chains.push(new chain);
      newchain=false;
    }
    chain c=chains[chains.length-1];
    c.serial.push(serial);
    c.a.push(a);
    continue;
  }
  if(HETATOM) {
    serials.push(serial);
    atoms.push(a);
  }
  if(record == "CONECT") {
    int k=0;
    int i=(int) substr(line,6,5);
    while(true) {
      string s=replace(substr(line,11+k,5)," ","");
     if(s == "") break;
      k += 5;
      int j=(int) s;
      if(j <= i) continue;
      bonds.push(bond(i,j));
     }
  }
}

write("Number of atomic chains: ",chains.length);

int natoms;
for(chain c : chains) {
  for(int i=0; i < c.a.length-1; ++i)
    draw(c.a[i].v--c.a[i+1].v,chainpen,currentlight);
  for(atom a : c.a)
    dot(a.v,color(a.name),currentlight);
  natoms += c.a.length;
}

write("Number of chained atoms: ",natoms);
write("Number of hetero atoms: ",atoms.length);

for(atom h : atoms)
  dot(h.v,color(h.name),currentlight);

write("Number of hetero bonds: ",bonds.length);

for(bond b : bonds) {
  triple v(int i) {return atoms[find(serials == i)].v;}
  draw(v(b.i)--v(b.j),hetpen,currentlight);
}

string options;
string viewfilename=prefix+".views";

if(!error(input(viewfilename,check=false)))
  options="3Dviews="+viewfilename;

if(getviews) {
  picture pic;
  add(pic,embed("label",currentpicture,options=options),(0,0),N);
  label(pic,cameralink("label"),(0,0),S,fontsize(12pt));
  shipout(prefix,pic,options=options);
} else
  shipout(prefix,options=options);
Figure 0153
Figure 0153: penimage.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);

import palette;

int n=256;
real ninv=2pi/n;
pen[][] v=new pen[n][n];

for(int i=0; i < n; ++i)
  for(int j=0; j < n; ++j)
    v[i][j]=rgb(0.5*(1+sin(i*ninv)),0.5*(1+cos(j*ninv)),0);

image(v,(0,0),(1,1));
Figure 0154
Figure 0154: phase.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(8cm,6cm,IgnoreAspect);

pair S0=(4,0.2);
pair S1=(2,3);
pair S8=(0.5,0);

xaxis("$S$");
yaxis(Label("$I$",0.5));

draw(S0{curl 0}..tension 1.5..S1{W}..tension 1.5..{curl 0}S8,Arrow(Fill,0.4));
draw((S1.x,0)..S1,dashed);
draw((0,S1.y)..S1,dotted);

labelx("$\frac{\gamma}{\beta}$",S1.x);
labelx("$S_\infty$",S8.x);
labely("$I_{\max}$",S1.y);
Figure 0155
Figure 0155: pipeintersection.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

currentprojection=orthographic(5,4,2);
currentlight=Headlamp;

size(12cm,0);

real f(pair z) {return min(sqrt(1-z.x^2),sqrt(1-z.y^2));}

surface s=surface(f,(0,0),(1,1),40,Spline);

transform3 t=rotate(90,O,Z), t2=t*t, t3=t2*t, i=xscale3(-1)*zscale3(-1);
draw(surface(s,t*s,t2*s,t3*s,i*s,i*t*s,i*t2*s,i*t3*s),blue);
Figure 0156
Figure 0156: planeproject.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size3(200,IgnoreAspect);

currentprojection=orthographic(4,6,3);

real x(real t) {return 1+cos(2pi*t);}
real y(real t) {return 1+sin(2pi*t);}
real z(real t) {return t;}

path3 p=graph(x,y,z,0,1,operator ..);

draw(p,Arrow3);
draw(planeproject(XY*unitsquare3)*p,red,Arrow3);
draw(planeproject(YZ*unitsquare3)*p,green,Arrow3);
draw(planeproject(ZX*unitsquare3)*p,blue,Arrow3);

axes3("$x$","$y$","$z$");
Figure 0157
Figure 0157: planes.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(6cm,0);
import bsp;

real u=2.5;
real v=1;

currentprojection=oblique;

path3 y=plane((2u,0,0),(0,2v,0),(-u,-v,0));
path3 l=rotate(90,Z)*rotate(90,Y)*y;
path3 g=rotate(90,X)*rotate(90,Y)*y;

face[] faces;
filldraw(faces.push(y),project(y),yellow);
filldraw(faces.push(l),project(l),lightgrey);
filldraw(faces.push(g),project(g),green);

add(faces);
Figure 0158
Figure 0158: polararea.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import math;
import graph;

size(0,150);

real f(real t) {return 5+cos(10*t);}

xaxis("$x$");
yaxis("$y$");

real theta1=pi/8;
real theta2=pi/3;
path k=graph(f,theta1,theta2,operator ..);
real rmin=min(k).y;
real rmax=max(k).y;
draw((0,0)--rmax*expi(theta1),dotted);
draw((0,0)--rmax*expi(theta2),dotted);

path g=polargraph(f,theta1,theta2,operator ..);
path h=(0,0)--g--cycle;
fill(h,lightgray);
draw(h);

real thetamin=3*pi/10;
real thetamax=2*pi/10;
pair zmin=polar(f(thetamin),thetamin);
pair zmax=polar(f(thetamax),thetamax);
draw((0,0)--zmin,dotted+red);
draw((0,0)--zmax,dotted+blue);

draw("$\theta_*$",arc((0,0),0.5*rmin,0,degrees(thetamin)),red+fontsize(10pt),
     PenMargins);
draw("$\theta^*$",arc((0,0),0.5*rmax,0,degrees(thetamax)),blue+fontsize(10pt),
     PenMargins);

draw(arc((0,0),rmin,degrees(theta1),degrees(theta2)),red,PenMargins);
draw(arc((0,0),rmax,degrees(theta1),degrees(theta2)),blue,PenMargins);
Figure 0159
Figure 0159: polarcircle.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import math;
import graph;
size(0,100);

real f(real t) {return 2*cos(t);}
pair F(real x) {return (x,f(x));}

draw(polargraph(f,0,pi,operator ..));

defaultpen(fontsize(10pt));

xaxis("$x$");
yaxis("$y$");

real theta=radians(50);
real r=f(theta);
draw("$\theta$",arc((0,0),0.5,0,degrees(theta)),red,Arrow,PenMargins);

pair z=polar(r,theta);
draw(z--(z.x,0),dotted+red);
draw((0,0)--(z.x,0),dotted+red);
label("$r\cos\theta$",(0.5*z.x,0),0.5*S,red);
label("$r\sin\theta$",(z.x,0.5*z.y),0.5*E,red);
dot("$(x,y)$",z,N);
draw("r",(0,0)--z,0.5*unit(z)*I,blue,Arrow,DotMargin);

dot("$(a,0)$",(1,0),NE);
dot("$(2a,0)$",(2,0),NE);
Figure 0160
Figure 0160: poster.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
orientation=Landscape;
import slide;
import graph;

defaultpen(deepblue);

real f(real x) {return (x != 0) ? x*sin(1/x) : 0;}
pair F(real x) {return (x,f(x));}

xaxis(background,grey);
yaxis(background,-0.25,0.25,grey);
real a=1.2/pi;
draw(background,graph(background,f,-a,a,10000),grey);
label(background,"$x\sin\frac{1}{x}$",F(0.92/pi),3SE,grey+fontsize(14pt));
frame f=background.fit();
box(f,RadialShade(yellow,0.6*yellow+red),above=false);
background.erase();
add(background,f);  

title("Young Researchers' Conference",align=3S,fontsize(48pt));
center("University of Alberta, Edmonton, April 1--2, 2006");

skip(4);

center("A general conference for\\
the mathematical and statistical sciences\\
for graduate students, by graduate students.",fontsize(32pt));

label("Registration and abstract submission online.",(0,-0.5));

label("\tt http://www.pims.math.ca/science/2006/06yrc/",point(SW),NE,
      black+fontsize(18pt));
Figure 0161
Figure 0161: projectelevation.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import grid3;
import palette;

currentprojection=orthographic(0.8,1,2);

size(400,300,IgnoreAspect);

real f(pair z) {return cos(2*pi*z.x)*sin(2*pi*z.y);}

surface s=surface(f,(-1/2,-1/2),(1/2,1/2),50,Spline);

surface S=planeproject(unitsquare3)*s;
S.colors(palette(s.map(zpart),Rainbow()));
draw(S,nolight);
draw(s,lightgray+opacity(0.7));

grid3(XYZgrid);
Figure 0162
Figure 0162: projectrevolution.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import solids; 
import palette; 
 
currentprojection=orthographic(20,0,3); 
 
size(400,300,IgnoreAspect); 
 
revolution r=revolution(new real(real x) {return sin(x)*exp(-x/2);},
                          0,2pi,operator ..,Z); 
surface s=surface(r); 
 
surface S=planeproject(shift(-Z)*unitsquare3)*s;
S.colors(palette(s.map(zpart),Rainbow()));
draw(S);
draw(s,lightgray);
Figure 0163
Figure 0163: quartercircle.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(100,0);
draw((1,0){up}..{left}(0,1));
Figure 0164
Figure 0164: rainbow.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);

pen indigo=rgb(102/255,0,238/255);

void rainbow(path g) {
  draw(new path[] {scale(1.3)*g,scale(1.2)*g,scale(1.1)*g,g,
        scale(0.9)*g,scale(0.8)*g,scale(0.7)*g},
    new pen[] {red,orange,yellow,green,blue,indigo,purple});
}

rainbow((1,0){N}..(0,1){W}..{S}(-1,0));
rainbow(scale(4)*shift(-0.5,-0.5)*unitsquare);
Figure 0165
Figure 0165: randompath3.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;
size(300);
draw(randompath3(100),red,currentlight);
Figure 0166
Figure 0166: ring.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,100);
path unitcircle=E..N..W..S..cycle;
path g=scale(2)*unitcircle;
radialshade(unitcircle^^g,yellow+evenodd,(0,0),1.0,yellow+brown,(0,0),2);
Figure 0167
Figure 0167: roll.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size(200,0);

triple f(pair t) {
return(t.x+t.y/4+sin(t.y),cos(t.y),sin(t.y));
}

surface s=surface(f,(0,0),(2pi,2pi),7,20,Spline);
draw(s,olive);
Figure 0168
Figure 0168: roundpath.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
// example file for 'roundedpath.asy'
// written by stefan knorr

// import needed packages
import roundedpath;

// define open and closed path
path A = (0,0)--(10,10)--(30,10)--(20,0)--(30,-10)--(10,-10);
path B = A--cycle;

draw(shift(-60,0)*A, green);
draw(shift(-30,0)*roundedpath(A,1), red);

// draw open path and some modifications
for (int i = 1; i < 20; ++i)
  draw(roundedpath(A,i/4), rgb(1 - i*0.049, 0, i*0.049) + linewidth(0.5));

draw(shift(-60,-30)*B, green);
draw(shift(-30,-30)*roundedpath(B,1), red);

//draw closed path and some modifications
for (int i = 1; i < 20; ++i)                          // only round edges
  draw(shift(0,-30)*roundedpath(B,i/4), rgb(0.5, i*0.049,0) + linewidth(0.5));

for (int i = 1; i < 20; ++i)                          // round edged and scale 
  draw(shift(0,-60)*roundedpath(B,i/4,1-i/50), rgb(1, 1 - i*0.049,i*0.049) + linewidth(0.5));

for (int i = 1; i < 50; ++i)                          // shift (round edged und scaled shifted version)
  draw(shift(-30,-60)*shift(10,0)*roundedpath(shift(-10,0)*B,i/10,1-i/80), rgb( i*0.024, 1 - i*0.024,0) + linewidth(0.5));

for (int i = 1; i < 20; ++i)                          // shift (round edged und scaled shifted version)
  draw(shift(-60,-60)*shift(10,0)*roundedpath(shift(-10,0)*B,i/4,1-i/50), gray(i/40));
Figure 0169
Figure 0169: sacone.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,150);

pair z0=(0,0);
real r=1;
real h=1;
real l=sqrt(r^2+h^2);
real a=(1-r/l)*360;
real a1=a/2;
real a2=360-a/2;
path g=arc(z0,r,a1,a2);
fill((0,0)--g--cycle,lightgreen);
draw(g);
pair z1=point(g,0);
pair z2=point(g,length(g));

real r2=1.1*r;
path c=arc(0,r2,a1,a2);
draw("$2\pi r$",c,red,Arrows,Bars,PenMargins);
pen edge=blue+0.5mm;
draw("$\ell$",z0--z1,0.5*SE,edge);
draw(z0--z2,edge);
draw(arc(z0,r,a2-360,a1),grey+dashed);
dot(0);
Figure 0170
Figure 0170: sacone3D.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import solids;

size(0,75);
real r=1;
real h=1;

revolution R=cone(r,h);
draw(surface(R),lightgreen+opacity(0.5));
pen edge=blue+0.25mm;
draw("$\ell$",(0,r,0)--(0,0,h),W,edge);
draw("$r$",(0,0,0)--(r,0,0),red+dashed);
draw((0,0,0)--(0,0,h),red+dashed);
dot(h*Z);
Figure 0171
Figure 0171: sacylinder.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(0,100);

real r=1;
real h=3;

yaxis(dashed);

real m=0.475*h;

draw((r,0)--(r,h));
label("$L$",(r,0.5*h),E);

real s=4;

pair z1=(s,0);
pair z2=z1+(2*pi*r,h);
filldraw(box(z1,z2),lightgreen);
pair zm=0.5*(z1+z2);
label("$L$",(z1.x,zm.y),W);
label("$2\pi r$",(zm.x,z2.y),N);
draw("$r$",(0,m)--(r,m),N,red,Arrows);

draw((0,1.015h),yscale(0.5)*arc(0,0.25cm,-250,70),red,ArcArrow);
Figure 0172
Figure 0172: sacylinder3D.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import solids;
size(0,100);

real r=1;
real h=3;

revolution R=cylinder(-h/2*Z,r,h);
draw(surface(R),lightgreen+opacity(0.5));
draw((0,0,-h/2)--(0,0,h/2),dashed);
dot((0,0,-h/2));
dot((0,0,h/2));
draw("$L$",(0,r,-h/2)--(0,r,h/2),W,black);
draw("$r$",(0,0,-h/2)--(0,r,-h/2),red);
draw(arc(O,1,90,90,90,0),red,Arrow3);
Figure 0173
Figure 0173: saddle.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

size(100,0);
path3 g=(1,0,0)..(0,1,1)..(-1,0,0)..(0,-1,1)..cycle;
draw(g);
draw(((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle));
dot(g,red);
Figure 0174
Figure 0174: scaledgraph.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

axiscoverage=0.9;
size(200,IgnoreAspect);

real[] x={-1e-11,1e-11};
real[] y={0,1e6};

real xscale=round(log10(max(x)));
real yscale=round(log10(max(y)))-1;

draw(graph(x*10^(-xscale),y*10^(-yscale)),red);

xaxis("$x/10^{"+(string) xscale+"}$",BottomTop,LeftTicks);
yaxis("$y/10^{"+(string) yscale+"}$",LeftRight,RightTicks(trailingzero));
Figure 0175
Figure 0175: secondaryaxis.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(9cm,6cm,IgnoreAspect);
string data="secondaryaxis.csv";

file in=line(csv(input(data)));

string[] titlelabel=in;
string[] columnlabel=in;

real[][] a=dimension(in,0,0);
a=transpose(a);
real[] t=a[0], susceptible=a[1], infectious=a[2], dead=a[3], larvae=a[4];
real[] susceptibleM=a[5], exposed=a[6],infectiousM=a[7];

scale(true);

draw(graph(t,susceptible,t >= 10 & t <= 15));
draw(graph(t,dead,t >= 10 & t <= 15),dashed);

xaxis("Time ($\tau$)",BottomTop,LeftTicks);
yaxis(Left,RightTicks);

picture secondary=secondaryY(new void(picture pic) {
    scale(pic,Linear(true),Log(true));
    draw(pic,graph(pic,t,infectious,t >= 10 & t <= 15),red);
    yaxis(pic,Right,red,LeftTicks(begin=false,end=false));
  });
                             
add(secondary);
label(shift(5mm*N)*"Proportion of crows",point(NW),E);
Figure 0176
Figure 0176: shade.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    

size(100,0);
radialshade(unitsquare,yellow,(0,0),0,red,(0,0),1);
Figure 0177
Figure 0177: shadedtiling.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,100);
import patterns;

real d=4mm;
picture tiling;
path square=scale(d)*unitsquare;
axialshade(tiling,square,white,(0,0),black,(d,d));
fill(tiling,shift(d,d)*square,blue);
add("shadedtiling",tiling);

filldraw(unitcircle,pattern("shadedtiling"));
Figure 0178
Figure 0178: shadestroke.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(100);

radialshade(W..N..E--(0,0),stroke=true,
            red+linewidth(30),(0,0),0.25,yellow,(0,0),1);
Figure 0179
Figure 0179: shellmethod.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import solids;

size(400);
currentprojection=perspective(0,-1,30,up=Y);
currentlight=light(gray(0.75),(0.25,-0.25,1),(0,1,0));

pen color=green;
real alpha=240;

real f(real x) {return 2x^2-x^3;}
pair F(real x) {return (x,f(x));}
triple F3(real x) {return (x,f(x),0);}

int n=10;
path3[] blocks=new path3[n];
for(int i=1; i <= n; ++i) {
  real height=f((i-0.5)*2/n);
  real left=(i-1)*2/n;
  real right=i*2/n;
  blocks[i-1]=
    (left,0,0)--(left,height,0)--(right,height,0)--(right,0,0)--cycle;
}

path p=graph(F,0,2,n,operator ..)--cycle;
surface s=surface(p);
path3 p3=path3(p);

revolution a=revolution(p3,Y,0,alpha);
draw(surface(a),color);
draw(rotate(alpha,Y)*s,color);
for(int i=0; i < n; ++i)
  draw(surface(blocks[i]),color+opacity(0.5),black);
draw(p3);

xaxis3(Label("$x$",1,align=2X),Arrow3);
yaxis3(Label("$y$",1,align=2Y),ymax=1.4,dashed,Arrow3);
arrow("$y=2x^2-x^3$",XYplane(F(1.8)),X+Z,1.5cm,red,Arrow3(DefaultHead2));
draw(arc(1.17Y,0.3,90,0,7.5,180),ArcArrow3);
Figure 0180
Figure 0180: shellsqrtx01.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import solids;
size(0,150);
currentprojection=orthographic(1,0,10,up=Y);
pen color=green;
real alpha=-240;

real f(real x) {return sqrt(x);}
pair F(real x) {return (x,f(x));}
triple F3(real x) {return (x,f(x),0);}

path p=graph(F,0,1,n=30,operator ..)--(1,0)--cycle;
path3 p3=path3(p);

revolution a=revolution(p3,X,alpha,0);
draw(surface(a),color);
draw(p3,blue);

surface s=surface(p);
draw(s,color);
draw(rotate(alpha,X)*s,color);

xaxis3(Label("$x$",1),xmax=1.25,dashed,Arrow3);
yaxis3(Label("$y$",1),Arrow3);

dot("$(1,1)$",(1,1,0));
arrow("$y=\sqrt{x}$",F3(0.8),Y,0.75cm,red);

real r=0.4;
draw(F3(r)--(1,f(r),0),red);
real x=(1+r)/2;

draw("$r$",(x,0,0)--(x,f(r),0),X+0.2Z,red,Arrow3,PenMargin3);
draw(arc(1.1X,0.4,90,90,3,-90),Arrow3);
Figure 0181
Figure 0181: sin1x.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(200,0);

real f(real x) {return (x != 0) ? sin(1/x) : 0;}
real T(real x) {return 2/(x*pi);}

real a=-4/pi, b=4/pi;
int n=150,m=5;

xaxis("$x$",red);
yaxis(red);

draw(graph(f,a,-T(m),n)--graph(f,-m,-(m+n),n,T)--(0,f(0))--graph(f,m+n,m,n,T)--
     graph(f,T(m),b,n));

label("$\sin\frac{1}{x}$",(b,f(b)),SW);
Figure 0182
Figure 0182: sinc.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import contour;

currentprojection=orthographic(1,-2,1);
currentlight=(1,-1,0.5);

size(12cm,0);

real sinc(pair z) {
  real r=2pi*abs(z);
  return r != 0 ? sin(r)/r : 1;
}

draw(lift(sinc,contour(sinc,(-2,-2),(2,2),new real[] {0})),red);
draw(surface(sinc,(-2,-2),(2,2),Spline),lightgray+opacity(0.5));

xaxis3("$x$",Bounds,InTicks);
yaxis3("$y$",Bounds,InTicks(beginlabel=false));
zaxis3("$z$",Bounds,InTicks);
Figure 0183
Figure 0183: sinxlex.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import geometry;

size(0,100);
real theta=30;

pair A=(0,0); 
pair B=dir(theta);
pair C=(1,0);
pair D=(1,Tan(theta));
pair E=(Cos(theta),0);

filldraw(A--C{N}..B--cycle,lightgrey);
draw(B--C--D--cycle);
draw(B--E);

draw("$x$",arc(C,A,B,0.7),RightSide,Arrow,PenMargin);

dot("$A$",A,W);
dot("$B$",B,NW);
dot("$C$",C);
dot("$D$",D);
dot(("$E$"),E,S);
label("$1$",A--B,LeftSide);
Figure 0184
Figure 0184: slopefield1.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import slopefield;

size(200);

real func(real x) {return 2x;}
add(slopefield(func,(-3,-3),(3,3),20,Arrow));
draw(curve((0,0),func,(-3,-3),(3,3)),red);
Figure 0185
Figure 0185: smoothelevation.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import grid3;
import palette;

if(settings.render <= 0) settings.prc=false;

currentprojection=orthographic(1,2,13);

size(400,300,IgnoreAspect);

real f(pair z) {return cos(2*pi*z.x)*sin(2*pi*z.y);}

surface s=surface(f,(-1/2,-1/2),(1/2,1/2),20,Spline);
s.colors(palette(s.map(zpart),Rainbow()));

draw(s);

scale(true);

xaxis3(Label("$x$",0.5),Bounds,InTicks);
yaxis3(Label("$y$",0.5),Bounds,InTicks);
zaxis3(Label("$z$",0.5),Bounds,InTicks(beginlabel=false));

grid3(XYZgrid);
Figure 0186
Figure 0186: soccerball.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3; 
size(400); 
currentlight.background=palegreen;

real c=(1+sqrt(5))/2; 
 
triple[] z={(c,1,0),(-c,1,0),(-c,-1,0),(c,-1,0)}; 
triple[] x={(0,c,1),(0,-c,1),(0,-c,-1),(0,c,-1)}; 
triple[] y={(1,0,c),(1,0,-c),(-1,0,-c),(-1,0,c)}; 
 
triple[][] Q={
  {z[0],y[1],x[3],x[0],y[0],z[3]},
  {z[1],x[0],x[3],y[2],z[2],y[3]},
  {z[2],z[1],y[2],x[2],x[1],y[3]},
  {z[3],z[0],y[0],x[1],x[2],y[1]},
  {x[0],x[3],z[1],y[3],y[0],z[0]},
  {x[1],x[2],z[2],y[3],y[0],z[3]},
  {x[2],x[1],z[3],y[1],y[2],z[2]},
  {x[3],x[0],z[0],y[1],y[2],z[1]},
  {y[0],y[3],x[1],z[3],z[0],x[0]},
  {y[1],y[2],x[2],z[3],z[0],x[3]},
  {y[2],y[1],x[3],z[1],z[2],x[2]},
  {y[3],y[0],x[0],z[1],z[2],x[1]} 
}; 
 
path3 p=arc(O,Q[0][0],Q[0][1]); 
real R=abs(point(p,reltime(p,1/3))); 
 
triple[][] P;
for(int i=0; i < Q.length; ++i){
  P[i]=new triple[] ; 
  for(int j=0; j < Q[i].length; ++j){
    P[i][j]=Q[i][j]/R; 
  } 
} 
 
surface sphericaltriangle(triple center, triple A, triple B, triple C,
                          int nu=3, int nv=nu) {
  path3 tri1=arc(center,A,B); 
  path3 tri2=arc(center,A,C); 
  path3 tri3=arc(center,B,C); 
  triple tri(pair p) {
    path3 cr=arc(O,relpoint(tri2,p.x),relpoint(tri3,p.x)); 
    return relpoint(cr,p.y); 
  }; 
 
  return surface(tri,(0,0),(1-sqrtEpsilon,1),nu,nv,Spline); 
} 
 
for(int i=0; i < P.length; ++i){
  triple[] pentagon=sequence(new triple(int k) {
      path3 p=arc(O,P[i][0],P[i][k+1]); 
      return point(p,reltime(p,1/3)); 
    },5); 
  pentagon.cyclic=true; 
  draw(sequence(new path3(int k) {
        return arc(O,pentagon[k],pentagon[k+1]);},5),linewidth(2pt)); 
  triple M=unit(sum(pentagon)/5); 
  for(int i=0; i < 5; ++i){
    surface sf=sphericaltriangle(O,pentagon[i],M,pentagon[i+1]); 
    draw(sf,black); 
  } 
} 
 
for(int i=0; i < P.length; ++i){
  for(int j=1; j <= 5; ++j){
    triple K=P[i][0]; 
    triple A=P[i][j]; 
    triple B=P[i][(j % 5)+1]; 
    path3[] p={arc(O,K,A),arc(O,A,B),arc(O,B,K)}; 
    draw(subpath(p[0],reltime(p[0],1/3),reltime(p[0],2/3)),linewidth(4pt)); 
    triple[] hexagon={point(p[0],reltime(p[0],1/3)),
                      point(p[0],reltime(p[0],2/3)),
                      point(p[1],reltime(p[1],1/3)),
                      point(p[1],reltime(p[1],2/3)),
                      point(p[2],reltime(p[2],1/3)),
                      point(p[2],reltime(p[2],2/3))}; 
    hexagon.cyclic=true; 
    triple M=unit(sum(hexagon)/6); 
    for(int i=0; i < 6; ++i){
      surface sf=sphericaltriangle(O,hexagon[i],M,hexagon[i+1]); 
      draw(sf,white); 
    } 
  } 
}
Figure 0187
Figure 0187: spectrum.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
usepackage("ocg");
settings.tex="pdflatex";

// Dan Bruton algorithm
pen nm2rgb(real wl, real gamma=0.8, bool intensity=true) {
  triple rgb;
  if(wl >= 380 && wl <= 440) {rgb=((440-wl)/60,0,1);}
  if(wl >  440 && wl <= 490) {rgb=(0,(wl-440)/50,1);}
  if(wl >  490 && wl <= 510) {rgb=(0,1,(510-wl)/20);}
  if(wl >  510 && wl <= 580) {rgb=((wl-510)/70,1,0);}
  if(wl >  580 && wl <= 645) {rgb=(1,(645-wl)/65,0);}
  if(wl >  645 && wl <= 780) {rgb=(1,0,0);}
  
  real Intensity=1;
  if(intensity) {
    if(wl >= 700) {Intensity=0.3+0.7*(780-wl)/80;}
    else if(wl <= 420) {Intensity=0.3+0.7*(wl-380)/40;}
  }

  return rgb((Intensity*rgb.x)**gamma,(Intensity*rgb.y)**gamma,
             (Intensity*rgb.z)**gamma);
}

real width=1;
real height=50;

begin("spectrum");
for(real i=380 ; i <= 780 ; i += width) {
  draw((i,0)--(i,height),width+nm2rgb(wl=i,false)+squarecap);
}
begin("Extinction",false); // nested
for(real i=380 ; i <= 780 ; i += width) {
  draw((i,0)--(i,height),width+nm2rgb(wl=i,true)+squarecap);
}
end();
end();

begin("Wavelength");
xaxis(scale(0.5)*"$\lambda$(nm)",BottomTop,380,780,
      RightTicks(scale(0.5)*rotate(90)*Label(),step=2,Step=10),above=true);
end();

// From Astronomical Data Center(NASA)
// Neutral only
real[] Na={423.899, 424.208, 427.364, 427.679, 428.784, 429.101,
           432.14, 432.462, 434.149, 434.474, 439.003, 439.334, 441.989, 442.325,
           449.418, 449.766, 454.163, 454.519, 568.2633, 568.8204, 588.995,
           589.5924};
begin("Na absorption");
for(int i=0; i < Na.length; ++i) {
  draw((Na[i],0)--(Na[i],height),0.1*width+squarecap);
}
end();

begin("Na emission");
for(int i=0; i < Na.length; ++i) {
  draw((Na[i],0)--(Na[i],-height),0.1*width+nm2rgb(Na[i],false)+squarecap);
}
end();

// Neutral only
real[] Zn={388.334, 396.543, 411.321, 429.288, 429.833, 462.981,
           468.014, 472.215, 481.053 , 506.866, 506.958, 518.198, 530.865,
           531.024, 531.102, 577.21, 577.55, 577.711, 623.79, 623.917, 636.234,
           647.918, 692.832, 693.847, 694.32, 779.936};
begin("Zn absorption",false);
for(int i=0; i < Zn.length; ++i) {
  draw((Zn[i],0)--(Zn[i],height),width+squarecap);
}
end();

begin("Zn emission",false);
for(int i=0; i < Zn.length; ++i) {
  draw((Zn[i],0)--(Zn[i],-height),width+nm2rgb(Zn[i],false)+squarecap);
}
end();

shipout(bbox(2mm,Fill(white)));
Figure 0188
Figure 0188: sphere.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

size(200);
currentprojection=orthographic(5,4,3);

draw(unitsphere,green);
Figure 0189
Figure 0189: spheresilhouette.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import solids;
settings.render=0;
settings.prc=false;

size(200);

revolution r=sphere(O,1);
draw(r,1,longitudinalpen=nullpen);
draw(r.silhouette());
Figure 0190
Figure 0190: sphereskeleton.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(100); 
import solids; 

currentprojection=orthographic(5,4,2);

revolution sphere=sphere(1); 
draw(surface(sphere),green+opacity(0.2));
draw(sphere,m=7,blue);
Figure 0191
Figure 0191: sphericalharmonic.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import palette;
size(200);

currentprojection=orthographic(4,2,4);

real r(real theta, real phi) {return 1+0.5*(sin(2*theta)*sin(2*phi))^2;}

triple f(pair z) {return r(z.x,z.y)*expi(z.x,z.y);}

surface s=surface(f,(0,0),(pi,2pi),50,Spline);
s.colors(palette(s.map(abs),Gradient(yellow,red)));
draw(s);
Figure 0192
Figure 0192: spiral.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,150);
import graph;

real f(real t) {return exp(-t/(2pi));}

draw(polargraph(f,0,20*pi,operator ..));

xaxis("$x$",-infinity,1.3);
yaxis("$y$",-infinity,1);

labelx(1);
labelx("$e^{-1}$",1.0/exp(1),SE);
Figure 0193
Figure 0193: spiral3.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import palette;
 
size3(10cm);
 
currentprojection=orthographic(5,4,2);

real r(real t) {return 3exp(-0.1*t);}
real x(real t) {return r(t)*cos(t);}
real y(real t) {return r(t)*sin(t);}
real z(real t) {return t;}

path3 p=graph(x,y,z,0,6*pi,50,operator ..);

tube T=tube(p,2);
surface s=T.s;
s.colors(palette(s.map(zpart),BWRainbow()));
draw(s);
draw(T.center,thin());
Figure 0194
Figure 0194: spline.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph; 
import interpolate; 
 
size(15cm,15cm,IgnoreAspect); 
 
real a=1997, b=2002; 
int n=5; 
real[] xpt=a+sequence(n+1)*(b-a)/n; 
real[] ypt={31,36,26,22,21,24}; 
horner h=diffdiv(xpt,ypt);
fhorner L=fhorner(h);
 
scale(false,true);

pen p=linewidth(1);

draw(graph(L,a,b),dashed+black+p,"Lagrange interpolation");
draw(graph(xpt,ypt,Hermite(natural)),red+p,"natural spline");
draw(graph(xpt,ypt,Hermite(monotonic)),blue+p,"monotone spline");
xaxis("$x$",BottomTop,LeftTicks(Step=1,step=0.25));
yaxis("$y$",LeftRight,RightTicks(Step=5));

dot(pairs(xpt,ypt),4bp+gray(0.3));

attach(legend(),point(10S),30S);
Figure 0195
Figure 0195: splitpatch.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

currentprojection=orthographic(0,0,1);

triple[][] A={
  {(0,0,0),(1,0,0),(1,0,0),(2,0,0)},
  {(0,4/3,0),(2/3,4/3,2),(4/3,4/3,2),(2,4/3,0)},
  {(0,2/3,0),(2/3,2/3,0),(4/3,2/3,0),(2,2/3,0)},
  {(0,2,0),(2/3,2,0),(4/3,2,0),(2,2,0)}
};

triple[][] B={
  {(0.5,0,-1),(0.5,1,-1),(0.5,2,-1),(0.5,3,-1)},
  {(0.5,0,0),(0.5,1,0),(0.5,2,0),(0.5,3,0)},
  {(0.5,0,1),(0.5,1,1),(0.5,2,1),(0.5,3,1)},
  {(0.5,0,2),(0.5,1,2),(0.5,2,2),(0.5,3,2)}
};

split S=split(A,B,10);
//write(S.T.length);

for(int i=0; i < S.T.length; ++i)
  draw(surface(patch(S.T[i])),Pen(i));
draw(surface(patch(B)),blue);
Figure 0196
Figure 0196: spring0.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import spring;

drawspring(0,"$L$");
Figure 0197
Figure 0197: spring2.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import spring;

drawspring(40.0,"$L+x$");
Figure 0198
Figure 0198: sqrtx01.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import solids;
size(0,150);
currentprojection=perspective(1.5,0,10,Y);
pen color=green+opacity(0.75);

real f(real x){return sqrt(x);}
pair F(real x){return (x,f(x));}
triple F3(real x){return (x,f(x),0);}

path p=graph(F,0,1,n=20,operator ..);
path3 p3=path3(p);

revolution a=revolution(p3,X,0,360);
draw(surface(a),color);
draw(p3,blue);

real x=relpoint(p,0.5).x;

xaxis3(Label("$x$",1),xmax=1.5,dashed,Arrow3);
yaxis3(Label("$y$",1),Arrow3);
dot(Label("$(1,1)$"),(1,1,0));
arrow(Label("$y=\sqrt{x}$"),F3(0.7),Y,0.75cm,red);
draw(arc(1.2X,0.4,90,90,175,-40,CW),Arrow3);
draw("$r$",(x,0,0)--F3(x),red,Arrow3,PenMargin3);
Figure 0199
Figure 0199: sqrtx01y1.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import solids;
size(0,150);
currentprojection=perspective(0,1,10,up=Y);

real f(real x) {return sqrt(x);}
pair F(real x) {return (x,f(x));}
triple F3(real x) {return (x,f(x),0);}

path p=graph(F,0,1,n=25,operator ..);
path3 p3=path3(p);

revolution a=revolution(p3,Y,0,360);
draw(surface(a),green);
draw(p3,blue);

xtick((0,0,0));
xtick((1,0,0));

xaxis3(Label("$x$",1),Arrow3);
yaxis3(Label("$y$",1),ymax=1.5,dashed,Arrow3);
dot(Label("$(1,1)$"),(1,1,0));
arrow("$y=\sqrt{x}$",F3(0.5),X,0.75cm,red);
draw(arc(1.2Y,0.3,90,0,7.5,140),Arrow3);
Figure 0200
Figure 0200: square.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
draw((0,0)--(100,0)--(100,100)--(0,100)--cycle);
Figure 0201
Figure 0201: star.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(100);
import math;

int n=5;
path p;

int i=0;
do {
  p=p--unityroot(n,i);
  i=(i+2) % n;
} while(i != 0);

filldraw(p--cycle,red+evenodd);
Figure 0202
Figure 0202: strokepath.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
path g=scale(100)*unitcircle;
pen p=linewidth(1cm);

frame f;
// Equivalent to draw(f,g,p):
fill(f,strokepath(g,p),red);
shipout("strokepathframe",f);
shipped=false;

size(400);

// Equivalent to draw(g,p):
currentpicture.add(new void(frame f, transform t) {
    fill(f,strokepath(t*g,p),red);
  });
currentpicture.addPath(g,p);
Figure 0203
Figure 0203: strokeshade.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(100);
guide g=(0,0)..controls(70,30) and (-40,30)..(30,0);
latticeshade(g,stroke=true,linewidth(10),
             new pen[][] {{red,orange,yellow},{green,blue,purple}});
Figure 0204
Figure 0204: subpictures.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
picture pic1;
real size=50;
size(pic1,size);
fill(pic1,(0,0)--(50,100)--(100,0)--cycle,red);

picture pic2;
size(pic2,size);
fill(pic2,unitcircle,green);

picture pic3;
size(pic3,size);
fill(pic3,unitsquare,blue);

picture pic;
add(pic,pic1.fit(),(0,0),N);
add(pic,pic2.fit(),(0,0),10S);

add(pic.fit(),(0,0),N);
add(pic3.fit(),(0,0),10S);
Figure 0205
Figure 0205: superpath.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,100);
path unitcircle=E..N..W..S..cycle;
path g=scale(2)*unitcircle;
filldraw(unitcircle^^g,evenodd+yellow,black);
Figure 0206
Figure 0206: tanh.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(100,0);

real f(real x) {return tanh(x);}
pair F(real x) {return (x,f(x));}

xaxis("$x$");
yaxis("$y$");

draw(graph(f,-2.5,2.5,operator ..));

label("$\tanh x$",F(1.5),1.25*N);
Figure 0207
Figure 0207: teapot.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

size(20cm);

currentprojection=perspective(250,-250,250);
//currentlight=White;

triple[][][] Q={
  {
    {(39.68504,0.0,68.03150),(39.68504,-22.22362,68.03150),(22.22362,-39.68504,68.03150),(0.0,-39.68504,68.03150)},
    {(37.91339,0.0,71.75197),(37.91339,-21.23150,71.75197),(21.23150,-37.91339,71.75197),(0.0,-37.91339,71.75197)},
    {(40.74803,0.0,71.75197),(40.74803,-22.81890,71.75197),(22.81890,-40.74803,71.75197),(0.0,-40.74803,71.75197)},
    {(42.51969,0.0,68.03150),(42.51969,-23.81102,68.03150),(23.81102,-42.51969,68.03150),(0.0,-42.51969,68.03150)},
  },
  {
    {(0.0,-39.68504,68.03150),(-22.22362,-39.68504,68.03150),(-39.68504,-22.22362,68.03150),(-39.68504,0.0,68.03150)},
    {(0.0,-37.91339,71.75197),(-21.23150,-37.91339,71.75197),(-37.91339,-21.23150,71.75197),(-37.91339,0.0,71.75197)},
    {(0.0,-40.74803,71.75197),(-22.81890,-40.74803,71.75197),(-40.74803,-22.81890,71.75197),(-40.74803,0.0,71.75197)},
    {(0.0,-42.51969,68.03150),(-23.81102,-42.51969,68.03150),(-42.51969,-23.81102,68.03150),(-42.51969,0.0,68.03150)},
  },
  {
    {(-39.68504,0.0,68.03150),(-39.68504,22.22362,68.03150),(-22.22362,39.68504,68.03150),(0.0,39.68504,68.03150)},
    {(-37.91339,0.0,71.75197),(-37.91339,21.23150,71.75197),(-21.23150,37.91339,71.75197),(0.0,37.91339,71.75197)},
    {(-40.74803,0.0,71.75197),(-40.74803,22.81890,71.75197),(-22.81890,40.74803,71.75197),(0.0,40.74803,71.75197)},
    {(-42.51969,0.0,68.03150),(-42.51969,23.81102,68.03150),(-23.81102,42.51969,68.03150),(0.0,42.51969,68.03150)},
  },
  {
    {(0.0,39.68504,68.03150),(22.22362,39.68504,68.03150),(39.68504,22.22362,68.03150),(39.68504,0.0,68.03150)},
    {(0.0,37.91339,71.75197),(21.23150,37.91339,71.75197),(37.91339,21.23150,71.75197),(37.91339,0.0,71.75197)},
    {(0.0,40.74803,71.75197),(22.81890,40.74803,71.75197),(40.74803,22.81890,71.75197),(40.74803,0.0,71.75197)},
    {(0.0,42.51969,68.03150),(23.81102,42.51969,68.03150),(42.51969,23.81102,68.03150),(42.51969,0.0,68.03150)},
  },
  {
    {(42.51969,0.0,68.03150),(42.51969,-23.81102,68.03150),(23.81102,-42.51969,68.03150),(0.0,-42.51969,68.03150)},
    {(49.60629,0.0,53.14960),(49.60629,-27.77952,53.14960),(27.77952,-49.60629,53.14960),(0.0,-49.60629,53.14960)},
    {(56.69291,0.0,38.26771),(56.69291,-31.74803,38.26771),(31.74803,-56.69291,38.26771),(0.0,-56.69291,38.26771)},
    {(56.69291,0.0,25.51181),(56.69291,-31.74803,25.51181),(31.74803,-56.69291,25.51181),(0.0,-56.69291,25.51181)},
  },
  {
    {(0.0,-42.51969,68.03150),(-23.81102,-42.51969,68.03150),(-42.51969,-23.81102,68.03150),(-42.51969,0.0,68.03150)},
    {(0.0,-49.60629,53.14960),(-27.77952,-49.60629,53.14960),(-49.60629,-27.77952,53.14960),(-49.60629,0.0,53.14960)},
    {(0.0,-56.69291,38.26771),(-31.74803,-56.69291,38.26771),(-56.69291,-31.74803,38.26771),(-56.69291,0.0,38.26771)},
    {(0.0,-56.69291,25.51181),(-31.74803,-56.69291,25.51181),(-56.69291,-31.74803,25.51181),(-56.69291,0.0,25.51181)},
  },
  {
    {(-42.51969,0.0,68.03150),(-42.51969,23.81102,68.03150),(-23.81102,42.51969,68.03150),(0.0,42.51969,68.03150)},
    {(-49.60629,0.0,53.14960),(-49.60629,27.77952,53.14960),(-27.77952,49.60629,53.14960),(0.0,49.60629,53.14960)},
    {(-56.69291,0.0,38.26771),(-56.69291,31.74803,38.26771),(-31.74803,56.69291,38.26771),(0.0,56.69291,38.26771)},
    {(-56.69291,0.0,25.51181),(-56.69291,31.74803,25.51181),(-31.74803,56.69291,25.51181),(0.0,56.69291,25.51181)},
  },
  {
    {(0.0,42.51969,68.03150),(23.81102,42.51969,68.03150),(42.51969,23.81102,68.03150),(42.51969,0.0,68.03150)},
    {(0.0,49.60629,53.14960),(27.77952,49.60629,53.14960),(49.60629,27.77952,53.14960),(49.60629,0.0,53.14960)},
    {(0.0,56.69291,38.26771),(31.74803,56.69291,38.26771),(56.69291,31.74803,38.26771),(56.69291,0.0,38.26771)},
    {(0.0,56.69291,25.51181),(31.74803,56.69291,25.51181),(56.69291,31.74803,25.51181),(56.69291,0.0,25.51181)},
  },
  {
    {(56.69291,0.0,25.51181),(56.69291,-31.74803,25.51181),(31.74803,-56.69291,25.51181),(0.0,-56.69291,25.51181)},
    {(56.69291,0.0,12.75590),(56.69291,-31.74803,12.75590),(31.74803,-56.69291,12.75590),(0.0,-56.69291,12.75590)},
    {(42.51969,0.0,6.377957),(42.51969,-23.81102,6.377957),(23.81102,-42.51969,6.377957),(0.0,-42.51969,6.377957)},
    {(42.51969,0.0,4.251961),(42.51969,-23.81102,4.251961),(23.81102,-42.51969,4.251961),(0.0,-42.51969,4.251961)},
  },
  {
    {(0.0,-56.69291,25.51181),(-31.74803,-56.69291,25.51181),(-56.69291,-31.74803,25.51181),(-56.69291,0.0,25.51181)},
    {(0.0,-56.69291,12.75590),(-31.74803,-56.69291,12.75590),(-56.69291,-31.74803,12.75590),(-56.69291,0.0,12.75590)},
    {(0.0,-42.51969,6.377957),(-23.81102,-42.51969,6.377957),(-42.51969,-23.81102,6.377957),(-42.51969,0.0,6.377957)},
    {(0.0,-42.51969,4.251961),(-23.81102,-42.51969,4.251961),(-42.51969,-23.81102,4.251961),(-42.51969,0.0,4.251961)},
  },
  {
    {(-56.69291,0.0,25.51181),(-56.69291,31.74803,25.51181),(-31.74803,56.69291,25.51181),(0.0,56.69291,25.51181)},
    {(-56.69291,0.0,12.75590),(-56.69291,31.74803,12.75590),(-31.74803,56.69291,12.75590),(0.0,56.69291,12.75590)},
    {(-42.51969,0.0,6.377957),(-42.51969,23.81102,6.377957),(-23.81102,42.51969,6.377957),(0.0,42.51969,6.377957)},
    {(-42.51969,0.0,4.251961),(-42.51969,23.81102,4.251961),(-23.81102,42.51969,4.251961),(0.0,42.51969,4.251961)},
  },
  {
    {(0.0,56.69291,25.51181),(31.74803,56.69291,25.51181),(56.69291,31.74803,25.51181),(56.69291,0.0,25.51181)},
    {(0.0,56.69291,12.75590),(31.74803,56.69291,12.75590),(56.69291,31.74803,12.75590),(56.69291,0.0,12.75590)},
    {(0.0,42.51969,6.377957),(23.81102,42.51969,6.377957),(42.51969,23.81102,6.377957),(42.51969,0.0,6.377957)},
    {(0.0,42.51969,4.251961),(23.81102,42.51969,4.251961),(42.51969,23.81102,4.251961),(42.51969,0.0,4.251961)},
  },
  {
    {(-45.35433,0.0,57.40157),(-45.35433,-8.503932,57.40157),(-42.51969,-8.503932,63.77952),(-42.51969,0.0,63.77952)},
    {(-65.19685,0.0,57.40157),(-65.19685,-8.503932,57.40157),(-70.86614,-8.503932,63.77952),(-70.86614,0.0,63.77952)},
    {(-76.53543,0.0,57.40157),(-76.53543,-8.503932,57.40157),(-85.03937,-8.503932,63.77952),(-85.03937,0.0,63.77952)},
    {(-76.53543,0.0,51.02362),(-76.53543,-8.503932,51.02362),(-85.03937,-8.503932,51.02362),(-85.03937,0.0,51.02362)},
  },
  {
    {(-42.51969,0.0,63.77952),(-42.51969,8.503932,63.77952),(-45.35433,8.503932,57.40157),(-45.35433,0.0,57.40157)},
    {(-70.86614,0.0,63.77952),(-70.86614,8.503932,63.77952),(-65.19685,8.503932,57.40157),(-65.19685,0.0,57.40157)},
    {(-85.03937,0.0,63.77952),(-85.03937,8.503932,63.77952),(-76.53543,8.503932,57.40157),(-76.53543,0.0,57.40157)},
    {(-85.03937,0.0,51.02362),(-85.03937,8.503932,51.02362),(-76.53543,8.503932,51.02362),(-76.53543,0.0,51.02362)},
  },
  {
    {(-76.53543,0.0,51.02362),(-76.53543,-8.503932,51.02362),(-85.03937,-8.503932,51.02362),(-85.03937,0.0,51.02362)},
    {(-76.53543,0.0,44.64566),(-76.53543,-8.503932,44.64566),(-85.03937,-8.503932,38.26771),(-85.03937,0.0,38.26771)},
    {(-70.86614,0.0,31.88976),(-70.86614,-8.503932,31.88976),(-75.11811,-8.503932,26.57480),(-75.11811,0.0,26.57480)},
    {(-56.69291,0.0,25.51181),(-56.69291,-8.503932,25.51181),(-53.85826,-8.503932,17.00787),(-53.85826,0.0,17.00787)},
  },
  {
    {(-85.03937,0.0,51.02362),(-85.03937,8.503932,51.02362),(-76.53543,8.503932,51.02362),(-76.53543,0.0,51.02362)},
    {(-85.03937,0.0,38.26771),(-85.03937,8.503932,38.26771),(-76.53543,8.503932,44.64566),(-76.53543,0.0,44.64566)},
    {(-75.11811,0.0,26.57480),(-75.11811,8.503932,26.57480),(-70.86614,8.503932,31.88976),(-70.86614,0.0,31.88976)},
    {(-53.85826,0.0,17.00787),(-53.85826,8.503932,17.00787),(-56.69291,8.503932,25.51181),(-56.69291,0.0,25.51181)},
  },
  {
    {(48.18897,0.0,40.39370),(48.18897,-18.70866,40.39370),(48.18897,-18.70866,17.00787),(48.18897,0.0,17.00787)},
    {(73.70078,0.0,40.39370),(73.70078,-18.70866,40.39370),(87.87401,-18.70866,23.38582),(87.87401,0.0,23.38582)},
    {(65.19685,0.0,59.52755),(65.19685,-7.086619,59.52755),(68.03150,-7.086619,57.40157),(68.03150,0.0,57.40157)},
    {(76.53543,0.0,68.03150),(76.53543,-7.086619,68.03150),(93.54330,-7.086619,68.03150),(93.54330,0.0,68.03150)},
  },
  {
    {(48.18897,0.0,17.00787),(48.18897,18.70866,17.00787),(48.18897,18.70866,40.39370),(48.18897,0.0,40.39370)},
    {(87.87401,0.0,23.38582),(87.87401,18.70866,23.38582),(73.70078,18.70866,40.39370),(73.70078,0.0,40.39370)},
    {(68.03150,0.0,57.40157),(68.03150,7.086619,57.40157),(65.19685,7.086619,59.52755),(65.19685,0.0,59.52755)},
    {(93.54330,0.0,68.03150),(93.54330,7.086619,68.03150),(76.53543,7.086619,68.03150),(76.53543,0.0,68.03150)},
  },
  {
    {(76.53543,0.0,68.03150),(76.53543,-7.086619,68.03150),(93.54330,-7.086619,68.03150),(93.54330,0.0,68.03150)},
    {(79.37007,0.0,70.15748),(79.37007,-7.086619,70.15748),(99.92125,-7.086619,70.68897),(99.92125,0.0,70.68897)},
    {(82.20472,0.0,70.15748),(82.20472,-4.251961,70.15748),(97.79527,-4.251961,71.22047),(97.79527,0.0,71.22047)},
    {(79.37007,0.0,68.03150),(79.37007,-4.251961,68.03150),(90.70866,-4.251961,68.03150),(90.70866,0.0,68.03150)},
  },
  {
    {(93.54330,0.0,68.03150),(93.54330,7.086619,68.03150),(76.53543,7.086619,68.03150),(76.53543,0.0,68.03150)},
    {(99.92125,0.0,70.68897),(99.92125,7.086619,70.68897),(79.37007,7.086619,70.15748),(79.37007,0.0,70.15748)},
    {(97.79527,0.0,71.22047),(97.79527,4.251961,71.22047),(82.20472,4.251961,70.15748),(82.20472,0.0,70.15748)},
    {(90.70866,0.0,68.03150),(90.70866,4.251961,68.03150),(79.37007,4.251961,68.03150),(79.37007,0.0,68.03150)},
  },
  {
    {(0.0,0.0,89.29133),(0.0,0.0,89.29133),(0.0,0.0,89.29133),(0.0,0.0,89.29133)},
    {(22.67716,0.0,89.29133),(22.67716,-12.75590,89.29133),(12.75590,-22.67716,89.29133),(0.0,-22.67716,89.29133)},
    {(0.0,0.0,80.78740),(0.0,0.0,80.78740),(0.0,0.0,80.78740),(0.0,0.0,80.78740)},
    {(5.669294,0.0,76.53543),(5.669294,-3.174809,76.53543),(3.174809,-5.669294,76.53543),(0.0,-5.669294,76.53543)},
  },
  {
    {(0.0,0.0,89.29133),(0.0,0.0,89.29133),(0.0,0.0,89.29133),(0.0,0.0,89.29133)},
    {(0.0,-22.67716,89.29133),(-12.75590,-22.67716,89.29133),(-22.67716,-12.75590,89.29133),(-22.67716,0.0,89.29133)},
    {(0.0,0.0,80.78740),(0.0,0.0,80.78740),(0.0,0.0,80.78740),(0.0,0.0,80.78740)},
    {(0.0,-5.669294,76.53543),(-3.174809,-5.669294,76.53543),(-5.669294,-3.174809,76.53543),(-5.669294,0.0,76.53543)},
  },
  {
    {(0.0,0.0,89.29133),(0.0,0.0,89.29133),(0.0,0.0,89.29133),(0.0,0.0,89.29133)},
    {(-22.67716,0.0,89.29133),(-22.67716,12.75590,89.29133),(-12.75590,22.67716,89.29133),(0.0,22.67716,89.29133)},
    {(0.0,0.0,80.78740),(0.0,0.0,80.78740),(0.0,0.0,80.78740),(0.0,0.0,80.78740)},
    {(-5.669294,0.0,76.53543),(-5.669294,3.174809,76.53543),(-3.174809,5.669294,76.53543),(0.0,5.669294,76.53543)},
  },
  {
    {(0.0,0.0,89.29133),(0.0,0.0,89.29133),(0.0,0.0,89.29133),(0.0,0.0,89.29133)},
    {(0.0,22.67716,89.29133),(12.75590,22.67716,89.29133),(22.67716,12.75590,89.29133),(22.67716,0.0,89.29133)},
    {(0.0,0.0,80.78740),(0.0,0.0,80.78740),(0.0,0.0,80.78740),(0.0,0.0,80.78740)},
    {(0.0,5.669294,76.53543),(3.174809,5.669294,76.53543),(5.669294,3.174809,76.53543),(5.669294,0.0,76.53543)},
  },
  {
    {(5.669294,0.0,76.53543),(5.669294,-3.174809,76.53543),(3.174809,-5.669294,76.53543),(0.0,-5.669294,76.53543)},
    {(11.33858,0.0,72.28346),(11.33858,-6.349609,72.28346),(6.349609,-11.33858,72.28346),(0.0,-11.33858,72.28346)},
    {(36.85039,0.0,72.28346),(36.85039,-20.63622,72.28346),(20.63622,-36.85039,72.28346),(0.0,-36.85039,72.28346)},
    {(36.85039,0.0,68.03150),(36.85039,-20.63622,68.03150),(20.63622,-36.85039,68.03150),(0.0,-36.85039,68.03150)},
  },
  {
    {(0.0,-5.669294,76.53543),(-3.174809,-5.669294,76.53543),(-5.669294,-3.174809,76.53543),(-5.669294,0.0,76.53543)},
    {(0.0,-11.33858,72.28346),(-6.349609,-11.33858,72.28346),(-11.33858,-6.349609,72.28346),(-11.33858,0.0,72.28346)},
    {(0.0,-36.85039,72.28346),(-20.63622,-36.85039,72.28346),(-36.85039,-20.63622,72.28346),(-36.85039,0.0,72.28346)},
    {(0.0,-36.85039,68.03150),(-20.63622,-36.85039,68.03150),(-36.85039,-20.63622,68.03150),(-36.85039,0.0,68.03150)},
  },
  {
    {(-5.669294,0.0,76.53543),(-5.669294,3.174809,76.53543),(-3.174809,5.669294,76.53543),(0.0,5.669294,76.53543)},
    {(-11.33858,0.0,72.28346),(-11.33858,6.349609,72.28346),(-6.349609,11.33858,72.28346),(0.0,11.33858,72.28346)},
    {(-36.85039,0.0,72.28346),(-36.85039,20.63622,72.28346),(-20.63622,36.85039,72.28346),(0.0,36.85039,72.28346)},
    {(-36.85039,0.0,68.03150),(-36.85039,20.63622,68.03150),(-20.63622,36.85039,68.03150),(0.0,36.85039,68.03150)},
  },
  {
    {(0.0,5.669294,76.53543),(3.174809,5.669294,76.53543),(5.669294,3.174809,76.53543),(5.669294,0.0,76.53543)},
    {(0.0,11.33858,72.28346),(6.349609,11.33858,72.28346),(11.33858,6.349609,72.28346),(11.33858,0.0,72.28346)},
    {(0.0,36.85039,72.28346),(20.63622,36.85039,72.28346),(36.85039,20.63622,72.28346),(36.85039,0.0,72.28346)},
    {(0.0,36.85039,68.03150),(20.63622,36.85039,68.03150),(36.85039,20.63622,68.03150),(36.85039,0.0,68.03150)},
  },
  {
    {(0.0,0.0,0.0),(0.0,0.0,0.0),(0.0,0.0,0.0),(0.0,0.0,0.0)},
    {(40.39370,0.0,0.0),(40.39370,22.62047,0.0),(22.62047,40.39370,0.0),(0.0,40.39370,0.0)},
    {(42.51969,0.0,2.12598),(42.51969,23.81102,2.12598),(23.81102,42.51969,2.12598),(0.0,42.51969,2.12598)},
    {(42.51969,0.0,4.251961),(42.51969,23.81102,4.251961),(23.81102,42.51969,4.251961),(0.0,42.51969,4.251961)},
  },
  {
    {(0.0,0.0,0.0),(0.0,0.0,0.0),(0.0,0.0,0.0),(0.0,0.0,0.0)},
    {(0.0,40.39370,0.0),(-22.62047,40.39370,0.0),(-40.39370,22.62047,0.0),(-40.39370,0.0,0.0)},
    {(0.0,42.51969,2.12598),(-23.81102,42.51969,2.12598),(-42.51969,23.81102,2.12598),(-42.51969,0.0,2.12598)},
    {(0.0,42.51969,4.251961),(-23.81102,42.51969,4.251961),(-42.51969,23.81102,4.251961),(-42.51969,0.0,4.251961)},
  },
  {
    {(0.0,0.0,0.0),(0.0,0.0,0.0),(0.0,0.0,0.0),(0.0,0.0,0.0)},
    {(-40.39370,0.0,0.0),(-40.39370,-22.62047,0.0),(-22.62047,-40.39370,0.0),(0.0,-40.39370,0.0)},
    {(-42.51969,0.0,2.12598),(-42.51969,-23.81102,2.12598),(-23.81102,-42.51969,2.12598),(0.0,-42.51969,2.12598)},
    {(-42.51969,0.0,4.251961),(-42.51969,-23.81102,4.251961),(-23.81102,-42.51969,4.251961),(0.0,-42.51969,4.251961)},
  },
  {
    {(0.0,0.0,0.0),(0.0,0.0,0.0),(0.0,0.0,0.0),(0.0,0.0,0.0)},
    {(0.0,-40.39370,0.0),(22.62047,-40.39370,0.0),(40.39370,-22.62047,0.0),(40.39370,0.0,0.0)},
    {(0.0,-42.51969,2.12598),(23.81102,-42.51969,2.12598),(42.51969,-23.81102,2.12598),(42.51969,0.0,2.12598)},
    {(0.0,-42.51969,4.251961),(23.81102,-42.51969,4.251961),(42.51969,-23.81102,4.251961),(42.51969,0.0,4.251961)},
  }
};

draw(surface(Q),blue);
Figure 0208
Figure 0208: tensor.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);

pen[][] p={{red,green,blue,cyan},{green,blue,rgb(black),magenta}};
path G=(0,0){dir(-120)}..(1,0)..(1,1)..(0,1)..cycle;
path[] g={G,subpath(G,1,2)..(2,1)..(2,0)..cycle};
pair[][] z={{(0.5,0.5),(0.5,0.5),(0.5,0.5),(0.5,0.5)},{(2,0.5),(2,0.5),(1.5,0.5),(2,0.5)}};
tensorshade(g,p,z);
dot(g);
Figure 0209
Figure 0209: textpath.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(300);

fill(texpath(Label("test",TimesRoman())),pink);
fill(texpath(Label("test",fontcommand('.fam T\n.ps 12')),tex=false),red);

pair z=10S;

fill(texpath(Label("$ \sqrt{x^2} $",z,TimesRoman())),pink);
fill(texpath(Label("$ sqrt {x sup 2} $",z,fontcommand('.fam T\n.ps 12')),
             tex=false),red);
Figure 0210
Figure 0210: thermodynamics.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
// example file for roundedpath() in roundedpath.asy
// written by stefan knorr


// import needed packages
import roundedpath;

// function definition
picture CreateKOOS(real Scale, string legend)               // draw labeled coordinate system as picture
{
  picture ReturnPic;
  real S = 1.2*Scale;
  draw(ReturnPic, ((-S,0)--(S,0)), bar = EndArrow);         // x axis
  draw(ReturnPic, ((0,-S)--(0,S)), bar = EndArrow);         // y axis
  label(ReturnPic, "$\varepsilon$", (S,0), SW);             // x axis label
  label(ReturnPic, "$\sigma$", (0,S), SW);                  // y axis label
  label(ReturnPic, legend, (0.7S, -S), NW);                 // add label 'legend' 
  return ReturnPic;                                         // return picture
}


// some global definitions
real S = 13mm;                          // universal scale factor for the whole file
real grad = 0.25;                       // gradient for lines
real radius = 0.04;                     // radius for the rounded path'
real lw = 2;                            // linewidth
pair A = (-1, -1);                      // start point for graphs
pair E = ( 1,  1);                      // end point for graphs
path graph;                             // local graph
pen ActPen;                             // actual pen for each drawing
picture T[];                            // vector of all four diagrams
real inc = 2.8;                         // increment-offset for combining pictures

//////////////////////////////////////// 1st diagram
T[1] = CreateKOOS(S, "$T_1$");                                        // initialise T[1] as empty diagram with label $T_1$                  
graph = A;                                                            //  # pointwise definition of current path 'graph'                    
graph = graph -- (A.x + grad*1.6, A.y + 1.6);                         //  #                                                                 
graph = graph -- (E.x - grad*0.4, E.y - 0.4);                         //  #                                                                 
graph = graph -- E;                                                   //  #

graph = roundedpath(graph, radius, S);                                // round edges of 'graph' using roundedpath() in roundedpath.asy      
ActPen =  rgb(0,0,0.6) + linewidth(lw);                               // define pen for drawing in 1st diagram                              
draw(T[1],                   graph, ActPen);                          // draw 'graph' with 'ActPen' into 'T[1]' (1st hysteresis branch)     
draw(T[1], rotate(180,(0,0))*graph, ActPen);                          // draw rotated 'graph' (2nd hysteresis branch)                       

graph = (0,0) -- (grad*0.6, 0.6) -- ( (grad*0.6, 0.6) + (0.1, 0) );   // define branch from origin to hysteresis
graph = roundedpath(graph, radius, S);                                // round this path                        
draw(T[1], graph, ActPen);                                            // draw this path into 'T[1]'             


//////////////////////////////////////// 2nd diagram
T[2] = CreateKOOS(S, "$T_2$");                                        // initialise T[2] as empty diagram with label $T_2$              
graph = A;                                                            //  # pointwise definition of current path 'graph'                
graph = graph -- (A.x + grad*1.3, A.y + 1.3);                         //  #                                                             
graph = graph -- (E.x - grad*0.7 , E.y - 0.7);                        //  #                                                             
graph = graph -- E;                                                   //  #
                                                                                                
graph = roundedpath(graph, radius, S);                                // round edges of 'graph' using roundedpath() in roundedpath.asy      
ActPen =  rgb(0.2,0,0.4) + linewidth(lw);                             // define pen for drawing in 2nd diagram                              
draw(T[2],                   graph, ActPen);                          // draw 'graph' with 'ActPen' into 'T[2]' (1st hysteresis branch)     
draw(T[2], rotate(180,(0,0))*graph, ActPen);                          // draw rotated 'graph' (2nd hysteresis branch)                       

graph = (0,0) -- (grad*0.3, 0.3) -- ( (grad*0.3, 0.3) + (0.1, 0) );   // define branch from origin to hysteresis
graph = roundedpath(graph, radius, S);                                // round this path                        
draw(T[2], graph, ActPen);                                            // draw this path into 'T[2]'             


//////////////////////////////////////// 3rd diagram
T[3] = CreateKOOS(S, "$T_3$");                                        // initialise T[3] as empty diagram with label $T_3$              
graph = A;                                                            //  # pointwise definition of current path 'graph'                
graph = graph -- (A.x + grad*0.7, A.y + 0.7);                         //  #                                                             
graph = graph -- ( - grad*0.3 , - 0.3);                               //  #                                                             
graph = graph -- (0,0);                                               //  #                                                             
graph = graph -- (grad*0.6, 0.6);                                     //  #                                                             
graph = graph -- (E.x - grad*0.4, E.y - 0.4);                         //  #                                                             
graph = graph -- E;                                                   //  #                                                             
                                                                                                                                        
graph = roundedpath(graph, radius, S);                                // round edges of 'graph' using roundedpath() in roundedpath.asy  
ActPen =  rgb(0.6,0,0.2) + linewidth(lw);                             // define pen for drawing in 3rd diagram                          
draw(T[3],                   graph, ActPen);                          // draw 'graph' with 'ActPen' into 'T[3]' (1st hysteresis branch) 
draw(T[3], rotate(180,(0,0))*graph, ActPen);                          // draw rotated 'graph' (2nd hysteresis branch)                   


//////////////////////////////////////// 4th diagram
T[4] = CreateKOOS(S, "$T_4$");                                        // initialise T[4] as empty diagram with label $T_4$              
graph = A;                                                            //  # pointwise definition of current path 'graph'                
graph = graph -- (A.x + grad*0.4, A.y + 0.4);                         //  #                                                             
graph = graph -- ( - grad*0.6 , - 0.6);                               //  #                                                             
graph = graph -- (0,0);                                               //  #                                                             
graph = graph -- (grad*0.9, 0.9);                                     //  #                                                             
graph = graph -- (E.x - grad*0.1, E.y - 0.1);                         //  #                                                             
graph = graph -- E;                                                   //  #                                                             
                                                                                                                                        
graph = roundedpath(graph, radius, S);                                // round edges of 'graph' using roundedpath() in roundedpath.asy  
ActPen =  rgb(0.6,0,0) + linewidth(lw);                               // define pen for drawing in 4th diagram                          
draw(T[4],                   graph, ActPen);                          // draw 'graph' with 'ActPen' into 'T[4]' (1st hysteresis branch) 
draw(T[4], rotate(180,(0,0))*graph, ActPen);                          // draw rotated 'graph' (3nd hysteresis branch)                   


// add some labels and black dots to the first two pictures
pair SWW = (-0.8, -0.6);
label(T[1], "$\sigma_f$", (0, 0.6S), NE);                             // sigma_f
draw(T[1], (0, 0.6S), linewidth(3) + black);
label(T[2], "$\sigma_f$", (0, 0.3S), NE);                             // sigma_f
draw(T[2], (0, 0.3S), linewidth(3) + black);
label(T[1], "$\varepsilon_p$", (0.7S, 0), SWW);                       // epsilon_p
draw(T[1], (0.75S, 0), linewidth(3) + black);
label(T[2], "$\varepsilon_p$", (0.7S, 0), SWW);                       // epsilon_p
draw(T[2], (0.75S, 0), linewidth(3) + black);


// add all pictures T[1...4] to the current one
add(T[1],(0,0));
add(T[2],(1*inc*S,0));
add(T[3],(2*inc*S,0));
add(T[4],(3*inc*S,0));


// draw line of constant \sigma and all intersection points with the graphs in T[1...4]
ActPen = linewidth(1) + dashed + gray(0.5);                           // pen definition
draw((-S, 0.45*S)--((3*inc+1)*S, 0.45*S), ActPen);                    // draw backgoundline
label("$\sigma_s$", (-S, 0.45S), W);                            // label 'sigma_s'

path mark = scale(2)*unitcircle;                                  // define mark-symbol to be used for intersections
ActPen = linewidth(1) + gray(0.5);                                    // define pen for intersection mark
draw(shift(( 1 - grad*0.55 + 0*inc)*S, 0.45*S)*mark, ActPen);         //  # draw all intersections
draw(shift((-1 + grad*1.45 + 0*inc)*S, 0.45*S)*mark, ActPen);         //  #
draw(shift(( 1 - grad*0.55 + 1*inc)*S, 0.45*S)*mark, ActPen);         //  #
draw(shift(( 1 - grad*0.55 + 2*inc)*S, 0.45*S)*mark, ActPen);         //  # 
draw(shift((     grad*0.45 + 2*inc)*S, 0.45*S)*mark, ActPen);         //  # 
draw(shift((     grad*0.45 + 3*inc)*S, 0.45*S)*mark, ActPen);         //  #
Figure 0211
Figure 0211: threeviews.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

picture pic;
size(pic,200);
currentlight.viewport=false;
settings.render=4;

draw(pic,scale3(0.5)*unitsphere,green);
draw(pic,Label("$x$",1),O--X);
draw(pic,Label("$y$",1),O--Y);
draw(pic,Label("$z$",1),O--Z);

addViews(pic);
Figure 0212
Figure 0212: tile.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,90);
import patterns;

add("tile",tile());
add("filledtilewithmargin",tile(6mm,4mm,red,Fill),(1mm,1mm),(1mm,1mm));
add("checker",checker());
add("brick",brick());

real s=2.5;
filldraw(unitcircle,pattern("tile"));
filldraw(shift(s,0)*unitcircle,pattern("filledtilewithmargin"));
filldraw(shift(2s,0)*unitcircle,pattern("checker"));
filldraw(shift(3s,0)*unitcircle,pattern("brick"));
Figure 0213
Figure 0213: torus.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);
import graph3;

currentprojection=perspective(5,4,4);

//import solids;
//revolution torus=revolution(shift(3X)*Circle(O,1,Y,32),Z,90,345);
//draw(surface(torus),green);

real R=3;
real a=1;

triple f(pair t) {
  return ((R+a*cos(t.y))*cos(t.x),(R+a*cos(t.y))*sin(t.x),a*sin(t.y));
}

draw(surface(f,(radians(90),0),(radians(345),2pi),8,8,Spline),green);
Figure 0214
Figure 0214: transparency.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,150);

settings.outformat="pdf";

begingroup();
fill(shift(1.5dir(120))*unitcircle,green+opacity(0.75));
fill(shift(1.5dir(60))*unitcircle,red+opacity(0.75));
fill(unitcircle,blue+opacity(0.75));
endgroup();
Figure 0215
Figure 0215: treetest.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import drawtree;

treeLevelStep = 2cm;

TreeNode root = makeNode( "Root" );
TreeNode child1 = makeNode( root, "Child\_1" );
TreeNode child2 = makeNode( root, "Child\_2" );

TreeNode gchild1 = makeNode( child1, "Grandchild\_1" );
TreeNode gchild2 = makeNode( child1, "Grandchild\_2" );

TreeNode gchild3 = makeNode( child1, "Grandchild\_3" );
TreeNode gchild4 = makeNode( child1, "Grandchild\_4" );


TreeNode gchild11 = makeNode( child2, "Grandchild\_1" );
TreeNode gchild22 = makeNode( child2, "Grandchild\_2" );

TreeNode ggchild1 = makeNode( gchild1, "Great Grandchild\_1" );

draw( root, (0,0) );
Figure 0216
Figure 0216: trefoilknot.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import tube;
import graph3;
import palette;
currentlight=White;

size(0,8cm);
currentprojection=perspective(1,1,1,up=-Y);

int e=1;
real x(real t) {return cos(t)+2*cos(2t);}
real y(real t) {return sin(t)-2*sin(2t);}
real z(real t) {return 2*e*sin(3t);}

path3 p=scale3(2)*graph(x,y,z,0,2pi,50,operator ..)&cycle;

pen[] pens=Gradient(6,red,blue,purple);
pens.push(yellow);
for (int i=pens.length-2; i >= 0 ; --i)
  pens.push(pens[i]);

path sec=scale(0.25)*texpath("$\pi$")[0];
coloredpath colorsec=coloredpath(sec, pens,colortype=coloredNodes);
draw(tube(p,colorsec));
Figure 0217
Figure 0217: triangle.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,100);
import geometry;

triangle t=triangle(b=3,alpha=90,c=4);
  
dot((0,0));

draw(t);
draw(rotate(90)*t,red);
draw(shift((-4,0))*t,blue);
draw(reflect((0,0),(1,0))*t,green);
draw(slant(2)*t,magenta);
Figure 0218
Figure 0218: triangulate.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(200);
int np=100;
pair[] points;

real r() {return 1.2*(rand()/randMax*2-1);}

for(int i=0; i < np; ++i)
  points.push((r(),r()));

int[][] trn=triangulate(points);

for(int i=0; i < trn.length; ++i) {
  draw(points[trn[i][0]]--points[trn[i][1]]);
  draw(points[trn[i][1]]--points[trn[i][2]]);
  draw(points[trn[i][2]]--points[trn[i][0]]);
}

for(int i=0; i < np; ++i)
  dot(points[i],red);
Figure 0219
Figure 0219: triceratops.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import obj;

size(15cm);
currentprojection=orthographic(0,2,5,up=Y);

// A compressed version of the required data file may be obtained from:
// http://www.cs.technion.ac.il/~irit/data/Viewpoint/galleon.obj.gz

draw(obj("triceratops.obj",brown));
Figure 0220
Figure 0220: trumpet.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
size(200,0);

triple f(pair t) {
  return(10*sin(t.y),cos(t.x)*(cos(t.y)+log(abs(tan(t.y/2)))),
         sin(t.x)*(cos(t.y)+log(abs(tan(t.y/2)))));
}

surface s=surface(f,(0,pi/2),(2pi,pi-0.1),7,15,Spline);
draw(s,olive);
Figure 0221
Figure 0221: tvgen.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
/* tvgen - draw pm5544-like television test cards.
 * Copyright (C) 2007, 2009, Servaas Vandenberghe.
 *
 * The tvgen code below is free software: you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public License as
 * published by the Free Software Foundation, either version 3 of the
 * License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with tvgen: see the file COPYING.  If not, write to the
 * Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
 * Boston, MA 02110-1301, USA.
 *
 * tvgen-1.1/tvgen.asy
 * This asy script generates pm5544-like television test cards.  The image 
 * parameters were derived from a 1990 recording.  The basic parameters 
 * conform to itu-r bt.470, bt.601, and bt.709.  There is no unique image 
 * since local variants exist and parameters have varied over time.  
 */
//papertype="a4";
import plain;
int verbose=settings.verbose/*+2*/;  /* uncomment for debug info */

/* tv dot coordinates --> PS points */
pair tvps(real col, real row, real xd, real yd, int Nv) { 
  real psx, psy; 
  psx=col*xd; psy=(Nv-row)*yd; 
  return (psx,psy); 
}
path tvrect(int lc, int tr, int rc, int br, real xd, real yd, int Nv) {
  real lx, ty, rx, by; 
  pair[] z; 
  
  lx=lc*xd; ty=(Nv-tr)*yd; 
  rx=rc*xd; by=(Nv-br)*yd; 
  /* bl br tr tl */
  z[0]=(lx, by);
  z[1]=(rx, by); 
  z[2]=(rx, ty); 
  z[3]=(lx, ty); 
  
  return z[0]--z[1]--z[2]--z[3]--cycle; 
}

/********************* image aspect ratio markers ********************/
void rimarkers(real rimage, int Nh, int Nhc, int os, int Nvc, int Nsy, pen pdef, real xd, real yd, int Nv) {
  int[] ridefN={ 4, 16 };
  int[] ridefD={ 3,  9 };
  int i;

  for(i=0; i<2; ++i) {
    real rid=ridefN[i]/ridefD[i];

    if(rimage>rid) {
      int off, offa, offb;

      /* Nhdef=Nh/rimage*rid */
      off=round(Nh/rimage*rid/2);
      offa=off+os;
      offb=off-os;
      // write(offa,offb);

      if(2*offa<Nh) {
        int hy, tr, br;
        path zz;
        
        hy=floor(Nsy/3);
        tr=Nvc-hy;
        br=Nvc+hy;
        
        zz=tvrect(Nhc+offb, tr, Nhc+offa, br, xd,yd,Nv);
        //dot(zz);
        fill(zz, p=pdef);
        zz=tvrect(Nhc-offa, tr, Nhc-offb, br, xd,yd,Nv);
        fill(zz, p=pdef);
      }
    }
  } /* for i */
  return;
}

/************* cross hatch: line pairing, center interlace test *************/
void centerline(int[] coff, int[] coffa, int[] coffb, int Nhc, int divsx,
                int os, int[] rcrowc, int Nvc, int divsy,
                pair ccenter, real[] rcoff, pair[] rcright, pair[] rcleft,
                pen pdef, real xd, real yd, int Nv) {
  pair[] z;
  int col;
  pen pblack=pdef+gray(0.0), pwhite=pdef+gray(1.0);
  
  z[0]=rcright[divsy];

  col=Nhc+coff[0];
  z[1]=tvps(col,rcrowc[divsy], xd,yd,Nv);
  z[2]=tvps(col,rcrowc[divsy-1], xd,yd,Nv);
  col=Nhc-coff[0];
  z[3]=tvps(col,rcrowc[divsy-1], xd,yd,Nv);
  z[4]=tvps(col,rcrowc[divsy], xd,yd,Nv);

  z[5]=rcleft[divsy]; 
  z[6]=rcleft[divsy+1];

  z[7]=tvps(col,rcrowc[divsy+1], xd,yd,Nv);
  z[8]=tvps(col,rcrowc[divsy+2], xd,yd,Nv);
  col=Nhc+coff[0];
  z[9]=tvps(col,rcrowc[divsy+2], xd,yd,Nv);
  z[10]=tvps(col,rcrowc[divsy+1], xd,yd,Nv);

  z[11]=rcright[divsy+1]; 
  fill(z[1]--z[2]--z[3]--z[4] //--z[5]--z[6]
       --arc(ccenter, z[5], z[6])
       --z[7]--z[8]--z[9]--z[10] //--z[11]--z[0]
       --arc(ccenter,z[11], z[0])
       --cycle, p=pblack);

  int i, maxoff, rows, tr, br;
  path zz;

  maxoff=floor(rcoff[divsy]);

  /* center cross: vertical and horizontal centerline */
  rows=min(Nvc-rcrowc[divsy-1], rcrowc[divsy+2]-Nvc);
  tr=Nvc-rows;
  br=Nvc+rows;
  //write("centerline long: rows tr br ", rows, tr, br);
  zz=tvrect(Nhc-os, tr, Nhc+os, br, xd,yd,Nv);
  fill(zz, p=pwhite);
  zz=tvrect(Nhc-maxoff,Nvc-1, Nhc+maxoff,Nvc+1, xd,yd,Nv);
  fill(zz, p=pwhite);

  /* vertical short lines */
  rows=min(Nvc-rcrowc[divsy], rcrowc[divsy+1]-Nvc);
  tr=Nvc-rows;
  br=Nvc+rows;
  if(verbose>1)
    write("centerline: rows tr br ", rows, tr, br);
  for(i=0; i<=divsx; ++i) {
    int off;
    
    off=coff[i];
    if(off<maxoff) {
      int offa, offb;
      path zzv;
      offa=coffa[i];
      offb=coffb[i];

      zzv=tvrect(Nhc+offb, tr, Nhc+offa, br, xd,yd,Nv); 
      fill(zzv, p=pwhite);
      zzv=tvrect(Nhc-offa, tr, Nhc-offb, br, xd,yd,Nv); 
      fill(zzv, p=pwhite);
    }
  }
  return;
}

/************************ topbw **************************************/
void topbw(int[] coff, int Nhc, int os, int urow, int trow, int brow, 
           pair ccenter, pair rclt, pair rclb, pair rcrt, pair rcrb, 
           pen pdef, real xd, real yd, int Nv) {
  pen pblack=pdef+gray(0.0), pwhite=pdef+gray(1.0);
  pair[] ze;
  path zext, zref, zint;
  int off, col, cr;

  off=ceil((coff[2]+coff[3])/2);
  ze[0]=tvps(Nhc+off,trow, xd,yd,Nv);
  ze[1]=rcrt;
  ze[2]=rclt;
  ze[3]=tvps(Nhc-off,trow, xd,yd,Nv);
  ze[4]=tvps(Nhc-off,brow, xd,yd,Nv);
  col=Nhc-coff[2]-os;
  ze[5]=tvps(col,brow, xd,yd,Nv);
  ze[6]=tvps(col,trow, xd,yd,Nv);
  cr=col+3*os;    /* reflection test black pulse */
  zref=tvrect(col,trow, cr,brow, xd,yd,Nv);
  ze[7]=tvps(cr,trow, xd,yd,Nv);
  ze[8]=tvps(cr,brow, xd,yd,Nv);
  ze[9]=tvps(Nhc+off,brow, xd,yd,Nv);
  //dot(ze);

  zext=ze[0] // --ze[1]--ze[2]
    --arc(ccenter, ze[1], ze[2])
    --ze[3]--ze[4]--ze[5]--ze[6]--ze[7]--ze[8]--ze[9]--cycle;

  off=ceil((coff[1]+coff[2])/2);
  zint=tvrect(Nhc-off,urow, Nhc+off,trow, xd,yd,Nv); 

  /* paths are completely resolved; no free endpoint conditions */
  fill(zext^^reverse(zint), p=pwhite);
  fill(zint, p=pblack);
  fill(zref, p=pblack);

  fill(arc(ccenter,rclt,rclb)--ze[4]--ze[3]--cycle, p=pblack);
  fill(arc(ccenter,rcrb,rcrt)--ze[0]--ze[9]--cycle, p=pblack);
  return;
}

/************************ testtone **************************************/
/* x on circle -> return y>=0 
 * in:
 *   x     x-coordinate relative to origin
 *   crad  circle radius in y units, true size=crad*yd
 */
real testcircx(real x, real crad, real xd, real yd) {
  real relx, phi, y;

  relx=x*xd/yd/crad;
  if(relx>1) {
    phi=0;
  } else {
    phi=acos(relx);
  }
  y=crad*sin(phi);         // or (x*xd)^2+(y*yd)^2=(crad*yd)^2

  return y;
}
/* y on circle -> return x>=0 */
real testcircy(real y, real crad, real xd, real yd) {
  real rely, phi, x;

  rely=y/crad;
  if(rely>1) {
    phi=pi/2;
  } else {
    phi=asin(rely);
  }
  x=crad*cos(phi)*yd/xd;         // or (x*xd)^2+(y*yd)^2=(crad*yd)^2

  return x;
}

/* brow>trow && xb>xt */
void testtone(real Tt, int trow, int brow, 
              real ccol, real crow, real crad,
              pen pdef, real xd, real yd, int Nv) {
  int blocks, i;
  real yt, xt, yb, xb, Ttt=Tt/2;
  pair ccenter;

  yt=crow-trow;
  xt=testcircy(yt, crad, xd, yd);
  yb=crow-brow;
  xb=testcircy(yb, crad, xd, yd);
  //write('#xt yt\t',xt,yt); write('#xb yb\t',xb,yb);

  ccenter=tvps(ccol,crow, xd,yd,Nv);

  blocks=floor(2*xb/Tt);

  for(i=-blocks-1; i<=blocks; ++i) {
    real tl, tr;
    path zz;

    tl=max(-xb,min(i*Ttt,xb));      /* limit [-xb..xb] */
    tr=max(-xb,min((i+1)*Ttt,xb));

    if(tl<-xt && tr<=-xt || tr>xt && tl>=xt) {   /* top full circle */
      pair[] z;
      real yl, yr;

      yl=testcircx(tl, crad, xd, yd);
      yr=testcircx(tr, crad, xd, yd);

      z[0]=tvps(ccol+tl,brow, xd,yd,Nv);
      z[1]=tvps(ccol+tr,brow, xd,yd,Nv);
      z[2]=tvps(ccol+tr,crow-yr, xd,yd,Nv);
      z[3]=tvps(ccol+tl,crow-yl, xd,yd,Nv);

      zz=z[0]--z[1]--arc(ccenter,z[2],z[3])--cycle;
    } else if(tl<-xt) {       /* tl in circel, tr not, partial */
      pair[] z;
      real yl;

      yl=testcircx(tl, crad, xd, yd);

      z[0]=tvps(ccol+tl,brow, xd,yd,Nv);
      z[1]=tvps(ccol+tr,brow, xd,yd,Nv);
      z[2]=tvps(ccol+tr,trow, xd,yd,Nv);
      z[3]=tvps(ccol-xt,trow, xd,yd,Nv);
      z[4]=tvps(ccol+tl,crow-yl, xd,yd,Nv);

      zz=z[0]--z[1]--z[2]--arc(ccenter,z[3],z[4])--cycle;
    } else if(tr>xt) { /* tr in circle, tl not, partial */
      pair[] z;
      real yr;

      yr=testcircx(tr, crad, xd, yd);

      z[0]=tvps(ccol+tl,brow, xd,yd,Nv);
      z[1]=tvps(ccol+tr,brow, xd,yd,Nv);
      z[2]=tvps(ccol+tr,crow-yr, xd,yd,Nv);
      z[3]=tvps(ccol+xt,trow, xd,yd,Nv);
      z[4]=tvps(ccol+tl,trow, xd,yd,Nv);
      zz=z[0]--z[1]--arc(ccenter,z[2],z[3])--z[4]--cycle;
    } else { /* full block */
      pair[] z;

      z[0]=tvps(ccol+tr,trow, xd,yd,Nv);
      z[1]=tvps(ccol+tl,trow, xd,yd,Nv);
      z[2]=tvps(ccol+tl,brow, xd,yd,Nv);
      z[3]=tvps(ccol+tr,brow, xd,yd,Nv);
      zz=z[0]--z[1]--z[2]--z[3]--cycle;
    } 

    if(tl<tr) {
      if(i%2 == 0) {
        fill(zz, p=pdef+gray(0.0));
      } else {
        fill(zz, p=pdef+gray(0.75));
      }
    }
  }
  return;
}

/************************ color bars *************************************/
void colorbars(int[] coff, int Nhc, int trow, int crow, int brow, 
               pair ccenter, pair rclt, pair rclb, pair rcrt, pair rcrb, 
               pen pdef, real xd, real yd, int Nv) {
  real cI=0.75;
  real[] cR={ cI,  0,  0,  cI, cI,  0 };
  real[] cG={ cI, cI, cI,   0,  0,  0 };
  real[] cB={  0, cI,  0,  cI,  0, cI };
  int cmax=2, poff, rows, i;

  rows=brow-trow;
  poff=0;
  for(i=0; i<=cmax; ++i) {
    int off;
    int ii=2*i, il=cmax-i, ir=i+cmax+1;
    path zzl, zzr;
  
    off=ceil((coff[1+ii]+coff[2+ii])/2);
    if(i!=0 && i<cmax) {
      zzr=tvrect(Nhc+poff,trow, Nhc+off,brow, xd,yd,Nv); 
      zzl=tvrect(Nhc-off,trow, Nhc-poff,brow, xd,yd,Nv); 
    } else {
      if(i==0) {
        int col, pcol;
        pair[] zl, zr;

        col=Nhc+off;
        pcol=Nhc+poff;
        zr[0]=tvps(col,trow, xd,yd,Nv);
        zr[1]=tvps(pcol,trow, xd,yd,Nv);
        zr[2]=tvps(pcol,crow, xd,yd,Nv);
        zr[3]=tvps(Nhc+coff[0],crow, xd,yd,Nv);
        zr[4]=tvps(Nhc+coff[0],brow, xd,yd,Nv);
        zr[5]=tvps(col,brow, xd,yd,Nv);
        zzr=zr[0]--zr[1]--zr[2]--zr[3]--zr[4]--zr[5]--cycle;

        col=Nhc-off;
        pcol=Nhc-poff;
        zl[0]=tvps(pcol,trow, xd,yd,Nv);
        zl[1]=tvps(col,trow, xd,yd,Nv);
        zl[2]=tvps(col,brow, xd,yd,Nv);
        zl[3]=tvps(Nhc-coff[0],brow, xd,yd,Nv);
        zl[4]=tvps(Nhc-coff[0],crow, xd,yd,Nv);
        zl[5]=tvps(pcol,crow, xd,yd,Nv);
        zzl=zl[0]--zl[1]--zl[2]--zl[3]--zl[4]--zl[5]--cycle;
      } else {
        int pcol;
        pair[] zl, zr;

        pcol=Nhc+poff;
        zr[0]=tvps(pcol,brow, xd,yd,Nv);
        zr[1]=rcrb;
        zr[2]=rcrt;
        zr[3]=tvps(pcol,trow, xd,yd,Nv);
        zzr=zr[0]--arc(ccenter,zr[1],zr[2])--zr[3]--cycle;

        pcol=Nhc-poff;
        zl[0]=tvps(pcol,trow, xd,yd,Nv);
        zl[1]=rclt;
        zl[2]=rclb;
        zl[3]=tvps(pcol,brow, xd,yd,Nv);
        zzl=zl[0]--arc(ccenter,zl[1],zl[2])--zl[3]--cycle;
      }
    }
    fill(zzr, p=pdef+rgb(cR[ir], cG[ir], cB[ir]));
    fill(zzl, p=pdef+rgb(cR[il], cG[il], cB[il]));

    poff=off;
  }
  return;
}

/************************ test frequencies ****************************/
/* in
 *   theta  rad
 *   freq   1/hdot
 *   step   hdot
 * out
 *   new phase theta
 */
real addphase(real theta, real freq, real step) {
  real cycles, thetaret;
  int coverflow;

  cycles=freq*step;
  coverflow=floor(abs(cycles));  
  if(coverflow>1) {
    thetaret=0;
  } else {
    real dpi=2*pi;

    cycles-=coverflow*sgn(cycles);
    thetaret=theta+cycles*dpi;       /* cycles=(-1 .. 1) */

    if(thetaret>pi) { 
      thetaret-=dpi; 
    } else if(thetaret<-pi) { 
      thetaret-=dpi; 
    }
  }

  //write("addphase: ", step, theta, thetaret);
  return thetaret;
}

void testfreqs(real[] ftones, int[] coff, int Nhc, int trow,int crow,int brow, 
               pair ccenter, pair rclt, pair rclb, pair rcrt, pair rcrb, 
               pen pdef, real xd, real yd, int Nv) {
  int[] divc;
  real[] divfl, divfr;
  int i, divs, coffmax, off, divnext;
  real fl, fr, thr, thl;

  /* Segment info for PAL continental test card
   * segment i extends from [divc[i] .. divc[i+1]) with frequency divf[i]
   */
  divs=2;     // the number of segments on the right, total=2*divs+1
  divc[0]=0;
  for(i=0; i<=divs; ++i) {
    int ii=i*2, il=divs-i, ir=divs+i;

    divc[i+1]=ceil((coff[ii]+coff[ii+1])/2);  /* xdot distance to center */

    divfl[i]=ftones[divs-i];
    divfr[i]=ftones[divs+i];
  }
  coffmax=divc[divs+1];

  int trowlim=coff[0];
  int tr;

  tr=crow;

  divnext=0;
  fl=0;
  fr=0;
  thl=0;
  thr=0;
  // draw a vertical line at off..off+1
  for(off=0; off<coffmax; ++off) {
    real ampl, ampr;
    int col;
    path zz;

    if(off==trowlim) {
      tr=trow;
    }

    if(off == divc[divnext]) {  
      /* switch frequency: cycles=0.5*fcur+0.5*fnext */
      thl=addphase(thl, fl, -0.5);
      thr=addphase(thr, fr,  0.5);
      fl=divfl[divnext];
      fr=divfr[divnext];
      thl=addphase(thl, fl, -0.5);
      thr=addphase(thr, fr,  0.5);

      ++divnext;
      // thl=pi; thr=pi;
      //write(off, fl, fr);
    } else {
      thl=addphase(thl, fl, -1);
      thr=addphase(thr, fr,  1);
      // thl=0; thr=0;
    }

    ampl=(1+sin(thl))/2;
    ampr=(1+sin(thr))/2;
    //write(off, thr, ampr);

    col=Nhc-off-1;
    zz=tvrect(col,tr, col+1,brow, xd,yd,Nv); 
    fill(zz, p=pdef+gray(ampl));
    col=Nhc+off;
    zz=tvrect(col,tr, col+1,brow, xd,yd,Nv); 
    fill(zz, p=pdef+gray(ampr));
  }

  pair[] z;
  z[0]=tvps(Nhc-coffmax,trow, xd,yd,Nv);
  z[1]=tvps(Nhc-coffmax,brow, xd,yd,Nv);
  fill(z[0]--arc(ccenter,rclt,rclb)--z[1]--cycle, p=pdef+gray(0.0));
  z[0]=tvps(Nhc+coffmax,brow, xd,yd,Nv);
  z[1]=tvps(Nhc+coffmax,trow, xd,yd,Nv);
  fill(z[0]--arc(ccenter,rcrb,rcrt)--z[1]--cycle, p=pdef+gray(0.0));
  return;
}

/************************ gray bars **************************************/
void graybars(int[] coff, int Nhc, int trow, int brow, 
              pair ccenter, pair rclt, pair rclb, pair rcrt, pair rcrb, 
              pen pdef, real xd, real yd, int Nv) {
  int[] gs={0, 51, 102, 153, 204, 255};
  int cmax=2, poff, rows, i;

  rows=brow-trow;
  poff=0;
  for(i=0; i<=cmax; ++i) {
    int off;
    int ii=2*i, il=cmax-i, ir=i+cmax+1;
    path zzl, zzr;
  
    off=ceil((coff[1+ii]+coff[2+ii])/2);
    if(i<cmax) {
      zzl=tvrect(Nhc-off,trow, Nhc-poff,brow, xd,yd,Nv); 
      zzr=tvrect(Nhc+poff,trow, Nhc+off,brow, xd,yd,Nv); 
    } else {
      int pcol;
      pair zlt, zlb, zrt, zrb;

      pcol=Nhc-poff;
      zlt=tvps(pcol,trow, xd,yd,Nv);
      zlb=tvps(pcol,brow, xd,yd,Nv);
      zzl=zlt--arc(ccenter,rclt,rclb)--zlb--cycle;

      pcol=Nhc+poff;
      zrb=tvps(pcol,brow, xd,yd,Nv);
      zrt=tvps(pcol,trow, xd,yd,Nv);
      zzr=zrb--arc(ccenter,rcrb,rcrt)--zrt--cycle;
    }
    fill(zzl, p=pdef+gray(gs[il]/255));
    fill(zzr, p=pdef+gray(gs[ir]/255));

    poff=off;
  }
  return;
}

/************************ bottom bw **************************************/
void bottombw(int off, int Nhc, int trow, int brow, 
              pair ccenter, pair rclt, pair rclb, pair rcrt, pair rcrb, 
              pen pdef, real xd, real yd, int Nv) {
  int rows;
  pair zt, zb;
  path zz;

  rows=brow-trow;
  zz=tvrect(Nhc-off,trow, Nhc+off,brow, xd,yd,Nv); 
  fill(zz, p=pdef+gray(0.0));

  zt=tvps(Nhc-off,trow, xd,yd,Nv);
  zb=tvps(Nhc-off,brow, xd,yd,Nv);
  fill(zt--arc(ccenter,rclt,rclb)--zb--cycle, p=pdef+gray(1.0));

  zb=tvps(Nhc+off,brow, xd,yd,Nv);
  zt=tvps(Nhc+off,trow, xd,yd,Nv);
  fill(zb--arc(ccenter,rcrb,rcrt)--zt--cycle, p=pdef+gray(1.0));
  return;
}

/************************ bottom circle **************************************/
void bottomcirc(int off, int Nhc, int trow, real cx, real cy, real crad, 
                pair ccenter, pair rclt, pair rcrt,
                pen pdef, real xd, real yd, int Nv) {
  real cI=0.75;
  real xl, yl, xr, yr, phil, phir;
  pair ccleft, ccright;
  pair[] z;

  xl=Nhc-off-cx;
  phil=acos(xl*xd/yd/crad);
  yl=crad*sin(phil);         // or (x*xd)^2+(y*yd)^2=(crad*yd)^2
  ccleft=tvps(cx+xl,cy+yl, xd,yd,Nv);
  //write(xl,yl);

  xr=Nhc+off-cx;
  phir=acos(xr*xd/yd/crad);
  yr=crad*sin(phir); 
  ccright=tvps(cx+xr,cy+yr, xd,yd,Nv);

  //dot(ccright); dot(ccleft);
  // red center
  z[0]=tvps(Nhc-off,trow, xd,yd,Nv);
  z[1]=ccleft;
  z[2]=ccright;
  z[3]=tvps(Nhc+off,trow, xd,yd,Nv);
  fill(z[0]--arc(ccenter,z[1],z[2])--z[3]--cycle, p=pdef+rgb(cI,0,0));

  // yellow
  z[0]=tvps(Nhc-off,trow, xd,yd,Nv);
  z[1]=rclt;
  z[2]=ccleft;
  fill(z[0]--arc(ccenter,z[1],z[2])--cycle, p=pdef+rgb(cI,cI,0));
  z[0]=tvps(Nhc+off,trow, xd,yd,Nv);
  z[1]=ccright;
  z[2]=rcrt;
  fill(z[0]--arc(ccenter,z[1],z[2])--cycle, p=pdef+rgb(cI,cI,0));

  return;
}

/****************************** PAL ears ***********************************
 * left  y      R       G       B 
 *      0.55    98      162     140
 *      0.5     103     128     191
 *      0.5     152     128     64
 *      0.45    157     93      115
 * right
 *      0.6     153     168     76
 *      0.4     102     87      179
 *
 * in: dright=  -1 left ear, +1 right ear
 */
void palears(int[] coff, int[] coffa, int[] coffb, int Nhc, 
             int[] rcrowt, int[] rcrowb, int Nvc, int divsy, int dright,
             pen pdef, real xd, real yd, int Nv) {
  /* the amplitude of (u,v) as seen on a vectorscope, 
   * max 0.296 Vn for 100% saturation in W and V ears.
   * cvbs:   0.7*( y +/- |u+jv| ) = -0.24 .. 0.93 V 
   * maxima: ebu 75/0 bars 0.70, bbc 100/25 0.88, 100/0 bars 0.93
   * burst:  0.150 Vcvbs, 21.4 IRE or 0.214 V normalized.
   * luma:   modulated for monochrome compatibility, 1990 version.
   * choice: set amplitude of subcarrier equal to amplitude of colorburst.
   */
  real cI=0.214;

  /* (u,v) for zero G-y, phase of -34.5 degrees */
  real wr=0.299, wb=0.114, wg=1-wr-wb;     /* wg=0.587, y=wr*R+wg*G+wb*B */
  real wu=0.493, wv=0.877;                 /* u=wu*(B-y) v=wv*(R-y) */
  real colu=wu*wg/wb, colv=-wv*wg/wr;      /* for w=(G-y)/0.696 == 0 */

  /* ears:     U==0   W==0   W==0  U==0 */
  real[] cyl={ 0.55,   0.5,   0.5, 0.45 };
  real[] cul={   0,   colu, -colu,    0 };
  real[] cvl={  -1,   colv, -colv,    1 };

  /* ears:     V==0   W==0  W==0   V==0 */
  real[] cyr={ 0.60,   0.5,  0.5,  0.40 };
  real[] cur={  -1,   colu, -colu,    1 };
  real[] cvr={   0,   colv, -colv,    0 };

  real[] cy, cu, cv;
  pair[] z;
  path[] zz;
  int lcol, ccol, cicol, rcol, i;

  if(dright>0) {
    cy=cyr; cu=cur; cv=cvr;
  } else {
    cy=cyl; cu=cul; cv=cvl;
  }

  lcol=Nhc+dright*coffa[5];
  ccol=Nhc+dright*coff[6];
  cicol=Nhc+dright*coffa[6];
  rcol=Nhc+dright*coffb[7];

  int urow, trow, crow, brow, arow;
  urow=rcrowb[divsy-5];
  trow=rcrowt[divsy-3];
  crow=Nvc;
  brow=rcrowb[divsy+4];
  arow=rcrowt[divsy+6];

  z[0]=tvps(ccol,urow, xd,yd,Nv);
  z[1]=tvps(ccol,trow, xd,yd,Nv);
  z[2]=tvps(cicol,trow, xd,yd,Nv);
  z[3]=tvps(cicol,crow, xd,yd,Nv);
  z[4]=tvps(rcol,crow, xd,yd,Nv);
  z[5]=tvps(rcol,urow, xd,yd,Nv);
  zz[0]=z[0]--z[1]--z[2]--z[3]--z[4]--z[5]--cycle;

  zz[1]=tvrect(lcol,urow, ccol,trow, xd,yd,Nv);
  zz[2]=tvrect(lcol,brow, ccol,arow, xd,yd,Nv);

  z[0]=tvps(ccol,arow, xd,yd,Nv);
  z[1]=tvps(ccol,brow, xd,yd,Nv);
  z[2]=tvps(cicol,brow, xd,yd,Nv);
  z[3]=tvps(cicol,crow, xd,yd,Nv);
  z[4]=tvps(rcol,crow, xd,yd,Nv);
  z[5]=tvps(rcol,arow, xd,yd,Nv);
  zz[3]=z[0]--z[1]--z[2]--z[3]--z[4]--z[5]--cycle;

  for(i=0; i<4; ++i) {
    real y, u, v, A, ph, By, Ry, Gy, R, G, B;

    y=cy[i];
    u=cu[i];
    v=cv[i];

    A=hypot(u,v);
    ph= (u!=0 || v!=0) ? atan2(v,u) : 0.0;
    if(v>=0) {
      if(ph<0) ph=ph+pi;
    } else {
      if(ph>0) ph=ph-pi;
    }
    if(A>0) {
      u=u/A*cI;
      v=v/A*cI;
    }

    By=u/wu;
    Ry=v/wv;
    Gy=(-wr*Ry-wb*By)/wg;
    //write(y,Gy,A,ph*180/pi);

    R=Ry+y;
    G=Gy+y;
    B=By+y;
    if(verbose > 1)
      write(y,round(R*255),round(G*255),round(B*255));

    fill(zz[i], p=pdef+rgb(R,G,B));
  }
  return;
}

/****************************** NTSC bars ***********************************
 * amplitude equals color burst smpte (pm: -V +U)
 *         y   campl  sat       R    G    B 
 * left   0.5  0.21   70%  -I?
 * right  0.5  0.17   60%  +Q?
 */
void ntscbars(int[] coff, int[] coffa, int[] coffb, int Nhc, 
              int[] rcrowt, int[] rcrowb, int Nvc, int divsy, int dright,
              pen pdef, real xd, real yd, int Nv) {
  /* The amplitude of (i,q) as seen on a vectorscope, 
   * max 0.292 Vn for 100% saturation in I==0 ears.
   * burst:    0.143 Vcvbs, 20 IRE or 0.200 V normalized.
   * pedestal: (yp,up,vp)=(p,0,0)+(1-p)*(y,u,v), p=0.075.
   * choice:   equal amplitude for colorburst and subcarrier.
   */
  real campl=0.200/0.925;

  /* wg=0.587, y=wr*R+wg*G+wb*B */
  real wr=0.299, wb=0.114, wg=1-wr-wb;
  /* iT : iq -> RyBy : rotation+scaling */
  real iT11=0.95, iT12=0.62, iT21=-1.11, iT22=1.71;

  /* bars        -2    -1    0     1       2 */
  real[] cyl={ 0.50, 0.50,   0, 0.50,   0.50 };
  real[] cil={    0,    0,   0,   -1,      1 };
  real[] cql={   -1,    1,   0,    0,      0 };
  int[]  offil={  6,    7,   5,    7,      6 };

  real cy, ci, cq;
  int dri, dris, offi, lcol, rcol, i;

  if(dright>=0) {
    dris=1;
  } else {
    dris=-1;
  }
  if(dright<-2 || dright>2) {
    dri=2;
  } else {
    dri=2+dright;
  }

  cy=cyl[dri]; ci=cil[dri]; cq=cql[dri];
  offi=offil[dri];
  lcol=Nhc+dris*coffa[offi];
  rcol=Nhc+dris*coffb[offi+1];

  real A, By, Ry, Gy, R, G, B;

  A=hypot(ci,cq);
  if(A>0) {
    ci=ci/A*campl;
    cq=cq/A*campl;
  }
  Ry=iT11*ci+iT12*cq;
  By=iT21*ci+iT22*cq;
  Gy=(-wr*Ry-wb*By)/wg;
  //write(cy,Ry,Gy,By);

  R=Ry+cy;
  G=Gy+cy;
  B=By+cy;
  if(verbose > 1)
    write(cy,ci,cq,round(R*255),round(G*255),round(B*255));

  for(i=-divsy; i<=divsy; ++i) {
    path zz;
    int brow, trow;
    
    if(i>-divsy) {
      trow=rcrowb[divsy+i];
    } else {
      trow=floor((rcrowb[divsy+i]+rcrowt[divsy+i+1])/2);
    } 

    if(divsy>i) {
      brow=rcrowt[divsy+i+1];
    } else {
      brow=floor((rcrowb[divsy+i]+rcrowt[divsy+i+1])/2);
    }

    zz=tvrect(lcol,brow, rcol,trow, xd,yd,Nv);
    fill(zz, p=pdef+rgb(R,G,B));
  }
  
  return;
}


/****************************** main ***********************************/
/* Conversion to bitmap:
 *   EPSPNG='gs -dQUIET -dNOPAUSE -dBATCH -sDEVICE=png16m'
 *   asy -u bsys=2 -u colortv=1 -u os=1 -a Z tvgen
 *   $EPSPNG -r132x144 -g720x576 -sOutputFile=tvgen.png tvgen.eps
 *
 * asy -u bsys=2 -u colortv=1 -u os=1 tvgen
 */
int bsys=2, colortv=1, os=1;

/* bsys: broadcast system
 * bsys  im aspect  Nh
 *    0    4/3       704  guaranteed analog broadcast itu-r bt.470
 *    1    4/3       720  new broadcast, most TV station logos and animations
 *    2    15/11     720  total aperture analog 4/3, 1.37 film DVDs
 *    3    20/11     720  total aperture analog 16/9, 1.85 film DVDs 
 *    4    4/3       768  bsys=0, square dot analog broadcast 
 *    5    4/3       768  bsys=1, square dot cable TV info channel
 *    6    131/96    786  bsys=2, total square dot broadcast camera 
 *    7    16/9      720  new broadcast 16/9, SD from HD-1440 or itu-r bt.709
 *    8    4/3       704  525 analog broadcast itu-r bt.470 711*485
 *    9    4/3       720  525 new broadcast
 *   10    15/11     720  525 total aperture analog broadcast
 *   11    16/9     1920  1250, 1080 square dot at 12.5 frames/second
 *   12    4/3      1600  1250, 1200 square dot at 12.5 frames/second
 * 
 * colortv:
 *   set 0 for monochrome crosshatch, 1 for pal ears, 2 for ntsc bars 
 *
 * os: horizontal oversampling, typical values for 13.5MHz:
 *    2   4/3 704*576, 15/11 720*576
 *    4   4/3 720*480
 *    5   4/3 704*480, 15/11 720*480, 4/3 768*576 14.4MHz
 *    8   4/3 720*576, 20/11 720*576
 *   12   704->768 rerastering
 *   16   720->768 rerastering
 */
access settings;
usersetting();

if(bsys<0 || bsys>12 || colortv<0 || colortv>3 || os<=0 || os>16) {
  write('Error: bad user input: bsys, colortv, os=\t', bsys, colortv, os);
  abort('Bad option  -u bsys=N  ?');
}

int[] bNdot=
  {   12,  16,  12,  16,     1,   1,    1,  64,   10,   8,  10,    1,    1 };
int[] bDdot=
  {   11,  15,  11,  11,     1,   1,    1,  45,   11,   9,  11,    1,    1 };
int[] bNh=
  {  704, 720, 720, 720,   768, 768,  786, 720,  704, 720, 720, 1920, 1600 };
int[] bNv=
  {  576, 576, 576, 576,   576, 576,  576, 576,  480, 480, 480, 1080, 1200 };
real[] bfs=
  { 13.5,13.5,13.5,13.5, 14.75,14.4,14.75,13.5, 13.5,13.5,13.5,   36,   30 };
int[] bNsy=
  {   42,  42,  42,  42,    42,  42,   42,  42,   34,  34,  34,   78,   90 };
int[] bNsh=
  {    0,   0,   0,   0,     0,   0,    0,   0,    0,   0,   0,    0,    0 };

/* active lines for a 625 line frame
 *   The number of active video lines decreased around 1997.  
 *     old:  3 run in + 575 visible + 3 run out = 581 lines
 *     new:  6 teletext and WSS + 575 visible 
 *   Hence the image center shifted down by 3 lines.  Thus
 *     old TV + new testcard = bottom is cut off,
 *     new TV + old testcard = top is cut off.
 *
 *   To generate the old testcard either use Nv=582 Nsh=0 or Nv=576 Nsh=3.
 *
 * aspect ratio
 *   rimage=xsize/ysize  rimage=rdot*Nh/Nv
 *   Nh=704 dots
 *   Nv=576 lines
 *   rd=ri*Nv/Nh=4/3*9/11=12/11
 *
 *   Nv: 480=2^5*3*5 576=2^6*3^2  
 *   Nh: 704=2^6*11 720=2^4*3^2*5
 *
 * horizontal line distance for pre 1997 test pattern
 *   top  8 lines, 13 squares of Ny=43 lines, bottom  9 lines
 *   top 12 lines, 13 squares of Ny=42 lines, bottom 18 lines
 *   pairs are from odd even field
 *   Interlace test: Ny must be odd for a cross-hatch without centerline.
 *
 * squares: ly=Nsy, lx=rd*Nsx, lx=ly ==> Nsx=Nsy/rd={ 39.4, 38.5 }
 *   x line width 230 ns -> 3 dots
 *   bottom 2.9us red -> 39.15 dots
 *
 * resolution DPI from image aspect ratio 
 *   Rv=Nv/ly,   ly=4in
 *   ri=Ni/Di,   Ni={4,15,16} Di={3,11,9}
 *   lx=ri*ly
 *
 *   Rh=Nh/lx=Di*(Nh/(Ni*ly))
 *   ==> ri=4/Di  => Nh=k*16
 *       ri=15/Di => Nh=k*60
 *       ri=16/Di => Nh=k*64
 *
 * resolution DPI from dot aspect ratio, general algorithm, 
 *
 *     rd=Nd/Dd=ldx/ldy
 *
 *   assume 1 dot = Nd x Dd square subdots at a resolution of k, in dpi, then
 *
 *     ldx=Nd/k, ldy=Dd/k  ==>  Rh=k/Nd, Rv=k/Dd
 *
 *   choosing k=m*Nd*Dd for integer Rh and Rv gives
 *
 *     ldx=1/(m*Dd), ldy=1/(m*Nd), Rh=m*Dd, Rv=m*Nd
 *
 *   and 
 *
 *     lx=Nh*ldx=Nh/(m*Dd), ly=Nv*ldy=Nv/(m*Nd)
 *
 *   so choose m for the intended height Ly, in inch, as
 *
 *     m=round(Nv/(Ly*Nd))
 *
 *   which limits Ly<=Nv/Nd since Rv>=Nd.
 */
//cm=72/2.540005;
real Ly, ly, lx, ysize, xsize, rimage, xd, yd, pwidth;
int Nd, Dd, m, Nh, Nv, Nshift, Na, Nsy;
real fs, Ttone;

Nd=bNdot[bsys];
Dd=bDdot[bsys]*os;
Nh=bNh[bsys]*os;
Nv=bNv[bsys];

Ly=4;                    // 4 inch vertical size
m=floor(0.5+Nv/(Ly*Nd));
if(m<1) m=1;
ly=Nv/(m*Nd);
lx=Nh/(m*Dd);

ysize=ly*1inch;
xsize=lx*1inch;
rimage=xsize/ysize;
if(verbose > 1)
  write('#Nd Dd m ri:\t', Nd, Dd, m, rimage);
//size(xsize,ysize,Aspect);  // should not have any effect

Nsy=bNsy[bsys];       // grating size in lines 42,43, 34,35
Nshift=bNsh[bsys];    // shift image up: pre 1997 =3, 2007 =0 
fs=1e6*bfs[bsys]*os; 
Na=0;          // add 1,0,-1 to height of hor center squares for even Na+Nsy

Ttone=fs/250e3;       // period of ft=250 kHz, fs/ft=54
real[] ftones={0.8e6/fs, 1.8e6/fs, 2.8e6/fs, 3.8e6/fs, 4.8e6/fs};

xd=xsize/Nh;
yd=ysize/Nv;
pwidth=min(abs(xd),abs(yd));

pen pdefault=squarecap+linewidth(pwidth);
pen pblack=pdefault+gray(0.0);
pen pwhite=pdefault+gray(1.0);

/**** calculate grating repeats and size in tv dots ****/
// horizontal lines
int divsy, rdisty, Nvc, Nt, Nb;

Nvc=floor(Nv/2)-Nshift;
divsy=floor(((Nv-Na-2)/Nsy-1)/2);   // (Nv-Na-2)/2-Nsy/2 dots for Nsy lengths
rdisty=Na+Nsy*(1+2*divsy);
Nt=Nvc-ceil(rdisty/2);
Nb=Nv-Nt-rdisty;
if(verbose > 1)
  write('#divsy t b: \t',divsy,Nt,Nb);

/* Nsyc: center square height 
 *   line pairing test: verify distance of center to top and bot 
 *   distance is odd ==> top=even/odd, cent=odd/even, bot=even/odd
 *
 * Nsyc odd: not possible
 *
 * Nsyc even:
 *   Nsyc/2 odd  --> OK
 *   Nsyc/2 even --> stagger the raster one line upwards
 *
 * rcrowt   top dist of hor line
 * rcrowc   true center for color info, distance to top of image.
 * rcrowb   bot dist of hor line
 *
 * Nt=Nvc-(offu+divsy*Nsy);
 * Nb=Nv-( Nvc-(offd-divsy*Nsy) );
 * ==> Nt+Nb=Nv-Nsyc-2*divsy*Nsy
 */
int Nsyc, offu, offd, Nyst=0, i;
int[] rcrowt, rcrowc, rcrowb;

Nsyc=Nsy+Na;
offu=floor(Nsyc/2);
offd=offu-Nsyc;
if(Nsyc%2 != 0) {
  Nyst=1;
} else if(Nsyc%4 == 0) {
  Nyst=1; /* stagger */
}
for(i=0; i<=divsy; ++i) {  
  int iu, id, ou, od, ru, rd;

  iu=divsy-i;
  id=divsy+i+1;

  ou=offu+Nsy*i;
  od=offd-Nsy*i;
  if(verbose > 1)
    write(ou,od);
  rcrowc[iu]=Nvc-ou;
  rcrowc[id]=Nvc-od;
  
  ru=Nvc-(ou+Nyst);
  rd=Nvc-(od+Nyst);

  rcrowt[iu]=ru-1;
  rcrowb[iu]=ru+1;

  rcrowt[id]=rd-1;
  rcrowb[id]=rd+1;
}
Nt=floor((rcrowt[0]+rcrowb[0])/2);
Nb=Nv-Nt-Nsyc-2*Nsy*divsy;
if(verbose > 1)
  write('#st t b: \t',Nyst,Nt,Nb);

/* vertical lines
 * (Nh-2*os)/2-Nsx/2 dots available for divisions of Nsx dots.
 * At least 5 dots margin left and right ==> use -10*os
 */
real lsq, Nsx;
int divsx, Nhc, Nl;

lsq=Nsy*yd;
Nsx=lsq/xd;
divsx=floor(((Nh-10*os)/Nsx-1)/2);  
Nhc=round(Nh/2);
Nl=Nhc-round((1+2*divsx)*Nsx/2);
if(verbose > 1)
  write('#Nsx divsx Nl:\t',Nsx,divsx,Nl);

/**** draw gray background ****/
{ 
  path zz;
  //zz=tvrect(0,0, Nh,Nv, xd,yd,Nv);
  /* keep white canvas for castellations */
  zz=tvrect(Nl,Nt, Nh-Nl,Nv-Nb, xd,yd,Nv);
  fill(zz, p=pdefault+gray(0.5));
  //dot(zz);
}
/**** draw center circle ****/
real cx, cy, crad;
pair ccenter;
path ccirc;
cx=Nh/2;
cy=Nv/2-Nshift;
crad=6*Nsy;
if(Nv%2 != 0) { 
  crad+=0.5; 
}
ccenter=tvps(cx,cy, xd,yd,Nv);
ccirc=circle(ccenter, crad*yd);
if(colortv<=0) {
  draw(ccirc, p=pwhite+linewidth(2*yd));
}

/****** draw 2*divsy+2 horizontal lines **********************************/
real[] rcang, rcoff;
pair[] rcright, rcleft;
int i, iend=2*divsy+1;
for(i=0; i<=iend; ++i) {
  real y, phi, x;
  path zzh;
  pair zd;

  zzh=tvrect(0,rcrowt[i], Nh,rcrowb[i], xd,yd,Nv); 
  fill(zzh, p=pwhite); 

  y=cy-rcrowc[i];
  //write(roff);
  if(abs(y)<crad) {
    phi=asin(y/crad);
  } else {
    phi=pi/2;
  }
  rcang[i]=phi;
  x=(crad*cos(phi))*yd/xd;
  rcoff[i]=x;
  zd=tvps(cx+x,cy-y, xd,yd,Nv);
  rcright[i]=zd;
  //dot(zd);
  zd=tvps(cx-x,cy-y, xd,yd,Nv);
  rcleft[i]=zd;
}

/****** draw 2*divsx+2 vertical lines ***************************/
int[] coff, coffa, coffb;
int poffa=0, ccenterwhite=divsx%2;
for(i=0; i<=divsx; ++i) {
  real cdist=(1+2*i)*Nsx;
  int off, offa, offb;
  path zzv;
  
  off=round(cdist/2);
  //write(cdist,off);
  offa=off+os;
  offb=off-os;

  coff[i]=off;
  coffa[i]=offa;
  coffb[i]=offb;

  //write(Nhc-offa);
  zzv=tvrect(Nhc+offb,0, Nhc+offa,Nv, xd,yd,Nv); 
  fill(zzv, p=pwhite); 
  zzv=tvrect(Nhc-offa,0, Nhc-offb,Nv, xd,yd,Nv); 
  fill(zzv, p=pwhite); 

  /** top castellations, must end with black **/
  if(i%2 == ccenterwhite) { 
    int j, jnum;

    if(poffa == 0) {
      poffa=-offb;
      jnum=1;
    } else {
      jnum=2;
    }

    for(j=0; j<jnum; ++j) {
      int lc, rc;
      path zzc;
      
      if(j==0) {
        lc=Nhc+poffa;
        rc=Nhc+offb;
      } else {
        lc=Nhc-offb;
        rc=Nhc-poffa;
      }

      zzc=tvrect(lc,0, rc,Nt-1, xd,yd,Nv); 
      fill(zzc, p=pblack); 
      zzc=tvrect(lc,Nv-Nb+1, rc,Nv, xd,yd,Nv); 
      fill(zzc, p=pblack); 
    }
  }

  poffa=offa;
}
//write(coff);

/** left and right castellations **/
/* The bottom right red rectangle tests for a non causal color FIR 
 * filter in the receiver.  The last 2..4 dots then typically appear 
 * colorless, green, or cyan.  
 *
 * This comes from the fact that the chroma subcarrier is of lower 
 * bandwidth than luma and thus continues after the last active sample.  
 * These trailing (y,u,v) samples result from a signal to zero 
 * transition and depend on the transmit and receive filters.  Samples 
 * from VHS, system B/G/D/K, system I, or a DVD player output are 
 * different.  Nevertheless, a sharpening filter uses this data and so 
 * adds false color to the last dots.  
 */
int lc, rc;
iend=2*divsy+1;
lc=Nhc-coffa[divsx];
rc=Nhc+coffa[divsx];
for(i=1; i<=iend; ++i) {
  pen pcast;
  if(i == iend && colortv>0) {
    pcast=pdefault+rgb(0.75,0.0,0);
  } else {
    pcast=pblack;
  }
  if(i%2 == 1) {
    int tr, br;
    path zzc;
    
    tr=rcrowb[i-1];
    br=rcrowt[i];    
    zzc=tvrect( 0,tr, lc,br, xd,yd,Nv);
    fill(zzc, p=pblack); 
    zzc=tvrect(rc,tr, Nh,br, xd,yd,Nv); 
    fill(zzc, p=pcast);
  }
}

/****** markers for 4/3 aspect ratio ******/
if(rimage>4/3)
  rimarkers(rimage, Nh, Nhc, os, Nvc, Nsy, pwhite, xd, yd, Nv);

/****** line pairing center ******/
centerline(coff, coffa, coffb, Nhc, divsx, os, rcrowc, Nvc, divsy,
           ccenter, rcoff, rcright, rcleft, pdefault, xd, yd, Nv);

if(colortv>0) {
  /* topbw structure */
  topbw(coff, Nhc, os, rcrowc[divsy-5], rcrowc[divsy-4], rcrowc[divsy-3], 
        ccenter, rcleft[divsy-4], rcleft[divsy-3], rcright[divsy-4],
        rcright[divsy-3], pdefault, xd, yd, Nv);

  /* 250 kHz */
  testtone(Ttone, rcrowc[divsy-3], rcrowc[divsy-2], 
           cx, cy, crad, pdefault, xd, yd, Nv);

  /* color bars */ 
  colorbars(coff, Nhc, rcrowc[divsy-2], rcrowc[divsy-1], rcrowc[divsy], 
            ccenter, rcleft[divsy-2], rcleft[divsy], rcright[divsy-2],
            rcright[divsy], pdefault, xd, yd, Nv);

  /* test frequencies */
  testfreqs(ftones, coff, Nhc, rcrowc[divsy+1], rcrowc[divsy+2],
            rcrowc[divsy+3], ccenter, rcleft[divsy+1], rcleft[divsy+3],
            rcright[divsy+1],rcright[divsy+3], pdefault, xd, yd, Nv);

  /* gray bars */
  graybars(coff, Nhc, rcrowc[divsy+3], rcrowc[divsy+4], ccenter,
           rcleft[divsy+3], rcleft[divsy+4],
           rcright[divsy+3], rcright[divsy+4], pdefault, xd,yd,Nv);

  /* PAL ears */
  if(colortv==1) {
    palears(coff,coffa,coffb, Nhc, rcrowt, rcrowb, Nvc, divsy, -1, 
            pdefault, xd, yd, Nv);
    palears(coff,coffa,coffb, Nhc, rcrowt, rcrowb, Nvc, divsy, 1, 
            pdefault, xd, yd, Nv);
  } else if(colortv==2) {
    ntscbars(coff,coffa,coffb, Nhc, rcrowt, rcrowb, Nvc, divsy, -1, 
             pdefault, xd, yd, Nv);
    ntscbars(coff,coffa,coffb, Nhc, rcrowt, rcrowb, Nvc, divsy, 1, 
             pdefault, xd, yd, Nv);
    ntscbars(coff,coffa,coffb, Nhc, rcrowt, rcrowb, Nvc, divsy, -2, 
             pdefault, xd, yd, Nv);
    ntscbars(coff,coffa,coffb, Nhc, rcrowt, rcrowb, Nvc, divsy, 2, 
             pdefault, xd, yd, Nv);
  }

  /* bottom wh - black - wh */
  bottombw(round((coff[2]+coff[3])/2), Nhc, rcrowc[divsy+4], rcrowc[divsy+5], 
           ccenter, rcleft[divsy+4], rcleft[divsy+5],
           rcright[divsy+4], rcright[divsy+5], pdefault, xd, yd, Nv);

  /* bottom yellow red circle */
  bottomcirc(coff[0], Nhc, rcrowc[divsy+5], cx, cy, crad, 
             ccenter, rcleft[divsy+5], rcright[divsy+5], pdefault, xd, yd, Nv);
}

/********************** set id *********************/
{ /* dpi */
  pair rpos=tvps(Nhc,round((rcrowc[divsy-4]+rcrowc[divsy-5])/2), xd,yd,Nv);
  string iRhor, iRver, ires;
  real Rh, Rv;

  Rh=Nh/xsize*inch;
  Rv=Nv/ysize*inch;
  iRhor=format("%.4gx", Rh);
  iRver=format("%.4gdpi", Rv);
  ires=insert(iRver,0, iRhor);

  /* size info */
  int rowbot=round((rcrowc[divsy+4]+rcrowc[divsy+5])/2);
  pair tpos=tvps(Nhc,rowbot, xd,yd,Nv);
  string ihor, iver, itot, iasp, ifm;
  real asp, fm;

  ihor=format("%ix",Nh);
  iver=format("%i ",Nv);
  itot=insert(iver,0, ihor);
  asp=xsize/ysize;
  iasp=format("%.3g ",asp);
  fm=fs/1e6;
  ifm=format("%.4gMHz",fm);
  itot=insert(iasp,0, itot);
  itot=insert(ifm,0, itot);

  /* size of square */
  int rowNsy=round((rcrowc[divsy+5]+rcrowc[divsy+6])/2);
  pair Npos=tvps(Nhc+round((coff[4]+coff[5])/2),rowNsy, xd,yd,Nv);
  string iNsy=format("%i",Nsy);

  pen pbw;
  if(colortv>0) { 
    pbw=pdefault+gray(1.0); 
  } else { 
    pbw=pdefault+gray(0.0); 
  }
  label(ires, rpos, p=pbw);
  label(itot, tpos, p=pbw);
  label(iNsy, Npos, p=pbw);
  if(verbose > 1)
    write('#res:\t', ires, itot, iNsy);
}
Figure 0222
Figure 0222: twistedtubes.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;  
import palette; 
 
size(300,300,keepAspect=true);  
 
real w=0.4;

real f(triple t) {return sin(t.x);} 
triple f1(pair t) {return (cos(t.x)-2cos(w*t.y),sin(t.x)-2sin(w*t.y),t.y);}
triple f2(pair t) {return (cos(t.x)+2cos(w*t.y),sin(t.x)+2sin(w*t.y),t.y);}
triple f3(pair t) {return (cos(t.x)+2sin(w*t.y),sin(t.x)-2cos(w*t.y),t.y);}
triple f4(pair t) {return (cos(t.x)-2sin(w*t.y),sin(t.x)+2cos(w*t.y),t.y);}

surface s1=surface(f1,(0,0),(2pi,10),8,8,Spline); 
surface s2=surface(f2,(0,0),(2pi,10),8,8,Spline); 
surface s3=surface(f3,(0,0),(2pi,10),8,8,Spline); 
surface s4=surface(f4,(0,0),(2pi,10),8,8,Spline); 

pen[] Rainbow=Rainbow();
s1.colors(palette(s1.map(f),Rainbow)); 
s2.colors(palette(s2.map(f),Rainbow)); 
s3.colors(palette(s3.map(f),Rainbow)); 
s4.colors(palette(s4.map(f),Rainbow)); 

draw(s1); 
draw(s2);
draw(s3);
draw(s4);
Figure 0223
Figure 0223: unitcircle.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,150);

pair z0=0;
pair z1=1;
real theta=30;
pair z=dir(theta);

draw(circle(z0,1));
filldraw(z0--arc(z0,1,0,theta)--cycle,lightgrey);
dot(z0);
dot(Label,z1);
dot("$(x,y)=(\cos\theta,\sin\theta)$",z);
arrow("area $\frac{\theta}{2}$",dir(0.5*theta),2E);
draw("$\theta$",arc(z0,0.7,0,theta),LeftSide,Arrow,PenMargin);
Figure 0224
Figure 0224: unitcircle3.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;

size(100);

path3 g=(1,0,0)..(0,1,0)..(-1,0,0)..(0,-1,0)..cycle;
draw(g);
draw(O--Z,red+dashed,Arrow3);
draw(((-1,-1,0)--(1,-1,0)--(1,1,0)--(-1,1,0)--cycle));
dot(g,red);
Figure 0225
Figure 0225: unitoctant.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

currentprojection=orthographic(5,4,2);

size(0,150);
patch s=octant1;
draw(surface(s),green+opacity(0.5));
draw(s.external(),blue);

triple[][] P=s.P;

for(int i=0; i < 4; ++i)
  dot(P[i],red);

axes3("$x$","$y$",Label("$z$",align=Z));
triple P00=P[0][0];
triple P10=P[1][0];
triple P01=P[0][1];
triple P02=P[0][2];
triple P11=P[1][1];
triple P12=P[1][2];
triple Q11=XYplane(xypart(P11));
triple Q12=XYplane(xypart(P12));

draw(P11--Q11,dashed);
draw(P12--Q12,dashed);
draw(O--Q12--Q11--(Q11.x,0,0));
draw(Q12--(Q12.x,0,0));

label("$(1,0,0)$",P00,-2Y);
label("$(1,a,0)$",P10,-Z);
label("$(1,0,a)$",P01,-2Y);
label("$(a,0,1)$",P02,Z+X-Y);
label("$(1,a,a)$",P11,3X);
label("$(a,a^2,1)$",P12,7X+Y);
Figure 0226
Figure 0226: upint.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
import lowupint;

size(100,0);

real a=-0.8, b=1.2;
real c=-1.0/sqrt(3.0);

partition(a,b,c,max);

arrow("$f(x)$",F(0.5*(a+b)),NNE,red);
label("$\cal{U}$",(0.5*(a+b),f(0.5*(a+b))/2));
Figure 0227
Figure 0227: vectorfield.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(100);

pair a=(0,0);
pair b=(2pi,2pi);

path vector(pair z) {return (0,0)--(sin(z.x),cos(z.y));}

add(vectorfield(vector,a,b));
Figure 0228
Figure 0228: vectorfield3.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size(12cm,0);

currentprojection=orthographic(1,-2,1);
currentlight=(1,-1,0.5);

real f(pair z) {return abs(z)^2;}

path3 gradient(pair z) {
  static real dx=sqrtEpsilon, dy=dx;
  return O--((f(z+dx)-f(z-dx))/2dx,(f(z+I*dy)-f(z-I*dy))/2dy,0);
}

pair a=(-1,-1);
pair b=(1,1);

triple F(pair z) {return (z.x,z.y,0);}

add(vectorfield(gradient,F,a,b,red));

draw(surface(f,a,b,Spline),gray+opacity(0.5));

xaxis3(XY()*"$x$",OutTicks(XY()*Label));
yaxis3(XY()*"$y$",InTicks(YX()*Label));
zaxis3("$z$",OutTicks);
Figure 0229
Figure 0229: vectorfieldsphere.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;

size(12cm);

currentprojection=orthographic(1,-2,1);
currentlight=(1,-1,0.5);

triple f(pair z) {return expi(z.x,z.y);}

path3 vector(pair z) {
  triple v=f(z);
  return O--(v.y,v.z,v.x);
}

add(vectorfield(vector,f,(0,0),(pi,2pi),10,0.25,red));

draw(unitsphere,gray+opacity(0.5));
Figure 0230
Figure 0230: venn.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,150);

pen colour1=red;
pen colour2=green;

pair z0=(0,0);
pair z1=(-1,0);
pair z2=(1,0);
real r=1.5;
path c1=circle(z1,r);
path c2=circle(z2,r);
fill(c1,colour1);
fill(c2,colour2);

picture intersection;
fill(intersection,c1,colour1+colour2);
clip(intersection,c2);

add(intersection);

draw(c1);
draw(c2);

label("$A$",z1);
label("$B$",z2);

pair z=(0,-2);
real m=3;
margin BigMargin=Margin(0,m*dot(unit(z1-z),unit(z0-z)));

draw(Label("$A\cap B$",0),conj(z)--z0,Arrow,BigMargin);
draw(Label("$A\cup B$",0),z--z0,Arrow,BigMargin);
draw(z--z1,Arrow,Margin(0,m));
draw(z--z2,Arrow,Margin(0,m));

shipout(bbox(0.25cm));
currentpicture.uptodate=true;
Figure 0231
Figure 0231: vertexshading.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import three;
//settings.prc=false;

size(200);

currentprojection=perspective(4,5,5);

draw(surface(unitcircle3,new pen[] {red,green,blue,white}));
draw(surface(shift(Z)*unitsquare3,
             new pen[] {red,green+opacity(0.5),blue,black}));
Figure 0232
Figure 0232: washermethod.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import solids;
size(0,150);
currentprojection=perspective(0,0,11,up=Y);

pen color1=green+opacity(0.25);
pen color2=red;
real alpha=250;

real f(real x) {return 2x^2-x^3;}
pair F(real x) {return (x,f(x));}
triple F3(real x) {return (x,f(x),0);}

ngraph=12;
path[] p={graph(F,0.7476,1.8043,Spline)--cycle,
          graph(F,0.7,0.7476,Spline)--graph(F,1.7787,1.8043,Spline)--cycle,
          graph(F,0,0.7,Spline)--graph(F,1.8043,2,Spline)--cycle};

pen[] pn=new pen[] {color1,color2,color1};

for(int i=0; i < p.length; ++i) {
  revolution a=revolution(path3(p[i]),Y,0,alpha);
  draw(surface(a),pn[i]);

  surface s=surface(p[i]);
  draw(s,pn[i]);
  draw(rotate(alpha,Y)*s,pn[i]);
}

draw((4/3,0,0)--F3(4/3),dashed);
xtick("$\frac{4}{3}$",(4/3,0,0));

xaxis3(Label("$x$",1),Arrow3);
yaxis3(Label("$y$",1),ymax=1.25,dashed,Arrow3);
arrow("$y=2x^2-x^3$",F3(1.6),X+Y,0.75cm,red);
draw(arc(1.1Y,0.3,90,0,7.5,180),Arrow3);
Figure 0233
Figure 0233: wedge.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import solids;
size(0,150);
currentprojection=perspective(8,10,2);
currentlight=White;

draw(circle(O,4,Z));
draw(shift(-4Z)*scale(4,4,8)*unitcylinder,green+opacity(0.2));

triple F(real x){return (x,sqrt(16-x^2),sqrt((16-x^2)/3));}
path3 p=graph(F,0,4,operator ..);
path3 q=reverse(p)--rotate(180,(0,4,4/sqrt(3)))*p--cycle;
draw(surface(q--cycle),red);

real t=2;
path3 triangle=(t,0,0)--(t,sqrt(16-t^2),0)--F(t)--cycle;
draw(surface(triangle),blue);

xaxis3("$x$",Arrow3,PenMargin3(0,0.25));
yaxis3("$y$",Arrow3,PenMargin3(0,0.25));
zaxis3("$z$",dashed,Arrow3);
Figure 0234
Figure 0234: westnile.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;

size(9cm,8cm,IgnoreAspect);
string data="westnile.csv";

file in=line(csv(input(data)));

string[] columnlabel=in;

real[][] A=dimension(in,0,0);
A=transpose(A);
real[] number=A[0], survival=A[1];

path g=graph(number,survival);
draw(g);

scale(true);

xaxis("Initial no.\ of mosquitoes per bird ($S_{M_0}/N_{B_0}$)",
      Bottom,LeftTicks);
xaxis(Top);
yaxis("Susceptible bird survival",Left,RightTicks(trailingzero));
yaxis(Right);

real a=number[0];
real b=number[number.length-1];

real S1=0.475;
path h1=(a,S1)--(b,S1);
real M1=interp(a,b,intersect(h1,g)[0]);

real S2=0.9;
path h2=(a,S2)--(b,S2);
real M2=interp(a,b,intersect(h2,g)[0]);

labelx("$M_1$",M1);
labelx("$M_2$",M2);

draw((a,S2)--(M2,S2)--(M2,0),Dotted);
draw((a,S1)--(M1,S1)--(M1,0),dashed);

pen p=fontsize(10pt);

real y3=0.043;
path reduction=(M1,y3)--(M2,y3);
draw(reduction,Arrow,TrueMargin(0,0.5*(linewidth(Dotted)+linewidth())));

arrow(shift(-20,5)*Label(minipage("\flushleft{\begin{itemize}\item[1.]
Estimate proportion of birds surviving at end of season\end{itemize}}",100),
                         align=NNE),
      (M1,S1),NNE,1cm,p,Arrow(NoFill));

arrow(shift(-24,5)*Label(minipage("\flushleft{\begin{itemize}\item[2.]
Read off initial mosquito abundance\end{itemize}}",80),align=NNE),
      (M1,0),NE,2cm,p,Arrow(NoFill));

arrow(shift(20,0)*Label(minipage("\flushleft{\begin{itemize}\item[3.]
Determine desired bird survival for next season\end{itemize}}",90),align=SW),
      (M2,S2),SW,arrowlength,p,Arrow(NoFill));

arrow(shift(8,-15)*Label(minipage("\flushleft{\begin{itemize}\item[4.]
Calculate required proportional reduction in mosquitoes\end{itemize}}",90),
                         align=NW),
      point(reduction,0.5),NW,1.5cm,p,Arrow(NoFill));
Figure 0235
Figure 0235: workcone.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import solids;
size(0,150);
currentprojection=orthographic(0,-30,5);

real r=4;
real h=10;
real s=8;
real x=r*s/h;

real sr=5;
real xr=r*sr/h;

real s1=sr-0.1;
real x1=r*s1/h;

real s2=sr+0.2;
real x2=r*s2/h;

path3 p=(0,0,0)--(x,0,s);
revolution a=revolution(p,Z);
draw(surface(a,4),lightblue+opacity(0.5));

path3 q=(x,0,s)--(r,0,h);
revolution b=revolution(q,Z);
draw(surface(b),white+opacity(0.5));

draw((-r-1,0,0)--(r+1,0,0));
draw((0,0,0)--(0,0,h+1),dashed);

path3 w=(x1,0,s1)--(x2,0,s2)--(0,0,s2);
revolution b=revolution(w,Z);
draw(surface(b),blue+opacity(0.5));
draw(circle((0,0,s2),x2));
draw(circle((0,0,s1),x1));

draw("$x$",(xr,0,0)--(xr,0,sr),red,Arrow3,PenMargin3);
draw("$r$",(0,0,sr)--(xr,0,sr),N,red);
draw((string) r,(0,0,h)--(r,0,h),N,red);
draw((string) h,(r,0,0)--(r,0,h),red,Arrow3,PenMargin3);
draw((string) s,(-x,0,0)--(-x,0,s),W,red,Arrow3,Bar3,PenMargin3);
Figure 0236
Figure 0236: xsin1x.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph;
size(300,0);

real f(real x) {return (x != 0.0) ? x * sin(1.0 / x) : 0.0;}
pair F(real x) {return (x,f(x));}

xaxis("$x$",red);
yaxis(red);
draw(graph(f,-1.2/pi,1.2/pi,1000));
label("$x\sin\frac{1}{x}$",F(1.1/pi),NW);
Figure 0237
Figure 0237: xxsq01.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import solids;
size(0,150);
currentprojection=perspective(0,0,10,up=Y);

pen color=green;
real alpha=250;

real f(real x) {return x^2;}
pair F(real x) {return (x,f(x));}
triple F3(real x) {return (x,f(x),0);}

path p=graph(F,0,1,n=10,operator ..)--cycle;
path3 p3=path3(p);

revolution a=revolution(p3,X,-alpha,0);
draw(surface(a),color);

surface s=surface(p);
draw(s,color);
draw(rotate(-alpha,X)*s,color);

draw(p3,blue);

xaxis3(Label("$x$",1),xmax=1.25,dashed,Arrow3);
yaxis3(Label("$y$",1),Arrow3);
dot(Label("$(1,1)$"),(1,1,0),X+Y);
arrow("$y=x$",(0.7,0.7,0),Y,0.75cm,red);
arrow("$y=x^2$",F3(0.7),X,0.75cm,red);
draw(arc(1.1X,0.3,90,90,3,-90),Arrow3);
Figure 0238
Figure 0238: xxsq01x-1.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import graph3;
import solids;
size(300);
currentprojection=perspective(0,2,10,up=Y);
currentlight=(0.25,-0.25,5);

pen color=green;

real f(real x) {return x^2;}
pair F(real x) {return (x,f(x));}
triple F3(real x) {return (x,f(x),0);}

path p=graph(F,0,1,n=10,operator ..)--cycle;
path3 p3=path3(p);

revolution a=revolution(-X,p3,Y,0,180);
draw(surface(a),color);
surface s=surface(p);
draw(s,color);
transform3 t=shift(-2X)*rotate(180,Y);
draw(t*s,color);
draw(p3);
draw(t*p3);

draw((-1,0,0)--(-1,1,0),dashed);
xaxis3(Label("$x$",1),Arrow3);
yaxis3(Label("$y$",1),Arrow3);
dot(Label("$(1,1)$"),(1,1,0));
dot(Label("$(-1,1)$"),(-1,1,0),W);
arrow("$y=x^{2}$",F3(0.7),X,1cm,red); 
arrow("$y=x$",(0.3,0.3,0),X,1.5cm,red); 
draw(circle((-1,1,0),2,Y),dashed);
draw((-1,1,0)--(1,1,0),dashed);
draw(shift(-X)*arc(0.02Y,0.3,90,0,0,0,CW),Arrow3);
Figure 0239
Figure 0239: xxsq01y.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
import solids;
size(0,150);
currentprojection=perspective(0,0,10,up=Y);
pen color=green;
real alpha=240;

real f(real x) {return x^2;}
pair F(real x) {return (x,f(x));}
triple F3(real x) {return (x,f(x),0);}

path p=graph(F,0,1,n=10,operator ..)--cycle;
path3 p3=path3(p);

draw(surface(revolution(p3,Y,0,alpha)),color);

surface s=surface(p);
draw(s,color);
draw(rotate(alpha,Y)*s,color);

draw(p3,blue);

xaxis3(Label("$x$",1),Arrow3);
yaxis3(Label("$y$",1),ymax=1.25,dashed,Arrow3);

dot("$(1,1)$",(1,1,0),X);
arrow("$y=x^{2}$",F3(0.7),X,0.75cm,red); 
arrow("$y=x$",(0.8,0.8,0),Y,1cm,red); 

real r=0.4;
draw((r,f(r),0)--(r,r,0),red);
draw("$r$",(0,(f(r)+r)*0.5,0)--(r,(f(r)+r)*0.5,0),N,red,Arrows3,PenMargins3);
draw(arc(1.1Y,0.3,90,0,7.5,180),Arrow3);
Figure 0240
Figure 0240: yingyang.asy
(Compiled with Asymptote version 1.87svn-r4652) 
/* This code comes from The Official Asymptote Gallery */
    
size(0,25cm);
guide center=(0,1){W}..tension 0.8..(0,0){(1,-.5)}..tension 0.8..{W}(0,-1); 

draw((0,1)..(-1,0)..(0,-1));
filldraw(center{E}..{N}(1,0)..{W}cycle);
unfill(circle((0,0.5),0.125));
fill(circle((0,-0.5),0.125));
Back Home Official Asymptote WEB Site

Dernière modification/Last modified: Sun Sep 20 18:48:08 CEST 2009
Philippe Ivaldi

Valide XHTML