## Asymptote using graph3.asy – fig0110

Category: Asymptote,Examples 3D,graph3.asyPh. Ivaldi @ 13 h 11 min

 (Compiled with Asymptote version 2.14svn-r5318)

import graph3;
import palette;
import contour;
size(14cm,0);
currentprojection=orthographic(-1,-1.5,0.75);
currentlight=(-1,0,5);

real a=1, b=1;
real f(pair z) { return a*(6+sin(z.x/b)+sin(z.y/b));}
real g(pair z){return f(z)-6a;}

// The axes
limits((0,0,4a),(14,14,8a));
xaxis3(Label("$x$",MidPoint),OutTicks());
yaxis3(Label("$y$",MidPoint),OutTicks(Step=2));
ticklabel relativelabel()
{
return new string(real x) {return (string)(x-6a);};
}
zaxis3(Label("$z$",Relative(1),align=2E),Bounds(Min,Max),OutTicks(relativelabel()));

// The surface
surface s=surface(f,(0,0),(14,14),100,Spline);

// Draw the surface
draw(s,pens);
// Project the surface onto the XY plane.
draw(planeproject(unitsquare3)*s,pens,nolight);

// Draw contour for "datumz"
real[] datumz={-1.5, -1, 0, 1, 1.5};
guide[][] pl=contour(g,(0,0),(14,14),datumz);
for (int i=0; i < pl.length; ++i)
for (int j=0; j < pl[i].length; ++j)
draw(path3(pl[i][j]));

// Draw the contours on the surface
draw(lift(f,pl));

if(!is3D())
shipout(bbox(3mm,Fill(black)));



## Asymptote using three.asy – fig0060

Category: Asymptote,Examples 3D,three.asyPh. Ivaldi @ 19 h 50 min

 (Compiled with Asymptote version 2.14svn-r5318)

settings.render=0;
import three;
size(4cm,0);

currentprojection=perspective((45,45,30));
path3 YZ=plane((0,4,0),(0,0,4));

draw("$x$",project(O--X),Arrow);
draw("$y$",project(O--Y),Arrow);
draw("$z$",project(O--Z),Arrow);
draw(YZ);

label(scale(5)*project("A",Y,Z,(0,1,1)));



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## Asymptote using three.asy – fig0100

Category: Asymptote,Examples 3D,three.asyPh. Ivaldi @ 23 h 50 min

 (Compiled with Asymptote version 2.14svn-r5318)

size(12cm,0);
import bsp;

currentprojection=orthographic(1,1.5,1);

path3 xy=plane((1,0,0),(0,1,0),(0,0,0));
path3 xz=rotate(90,X)*xy;
path3 yz=rotate(-90,Y)*xy;

face[] f;
filldraw(f.push(xy),project(xy),grey);
filldraw(f.push(xz),project(xz),grey);
filldraw(f.push(yz),project(yz),grey);

draw(Label("$x$",EndPoint), O--(1,0,0), Arrow3);
draw(Label("$y$",EndPoint), O--(0,1,0), Arrow3);
draw(Label("$z$",EndPoint), O--(0,0,1), Arrow3);
dot(O);

path[] ph=texpath("$\displaystyle\int_{-\infty}^{+\infty}e^{-\alpha x^2}\,dx= \sqrt{\frac{\pi}{\alpha}}$");
ph =shift((0.5,0.5))*rotate(-45)*scale(1/abs(min(ph)-max(ph)))*ph;

filldraw(project(path3(ph,XYplane)),0.8*yellow);
filldraw(project(path3(ph,ZXplane)),0.8*yellow);
filldraw(project(path3(ph,YZplane)),0.8*yellow);



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## Asymptote using three.asy – fig0110

Category: Asymptote,Examples 3D,three.asyPh. Ivaldi @ 0 h 50 min

 (Compiled with Asymptote version 2.14svn-r5318)

import three;
size(10cm,0);
currentprojection=orthographic(1,1.5,1);

path3 xy=XY*unitsquare3, xz=ZX*unitsquare3, yz=YZ*unitsquare3;

draw(xy^^xz^^yz, grey);
path3 p3xy=path3(texpath("$\pi$")[0],XYplane);
p3xy=shift((0.5,0.5,0))*scale3(1/abs(min(p3xy)-max(p3xy)))*p3xy;

surface s=surface(p3xy,planar=true);
draw(s, surfacepen=blue, meshpen=orange+3pt);

transform3 Txz=planeproject(xz,(0,-1,1));
draw(Txz*s, red);

transform3 Tyz=planeproject(yz,(-1,0,1));
draw(Tyz*s, green);

path3 p3xz=Txz*p3xy;
path3 p3yz=Tyz*p3xy;

int lg=length(p3xy);
triple p;
for(int i=0;i<=lg;++i) {
p=point(p3xy,i);
draw(p--point(p3xz,i), yellow);
draw(p--point(p3yz,i), orange);
}



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## Asymptote using solids.asy – fig0130

Category: Asymptote,Examples 3D,solids.asyPh. Ivaldi @ 14 h 56 min

 (Compiled with Asymptote version 2.14svn-r5318)

import solids;
size(8cm,0);
currentprojection=orthographic((2, 1, 2));

revolution r=cylinder((0, 0, 0), 1, -10, X);

draw(r);
draw("$x$",O--X,Arrow3);
draw("$y$",O--Y,Arrow3);
draw("$z$",O--Z,Arrow3);

label(XY()*(scale(2.5)*"This is not a cylinder"), (-5,0,1), align=Z);



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## Official Asymptote example – Klein

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 19 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
/* 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,

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,"bottle",render(merge=true));

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;

begingroup3("parametrization");
draw(surface(xscale(-0.38)*yscale(-0.18)*lo,s,0,1.7,h,bottom=false),
"[0,pi]");
draw(surface(xscale(0.26)*yscale(0.1)*rotate(90)*hi,s,4.9,1.4,h,bottom=false),
"[pi,2pi]");
endgroup3();

begingroup3("boundary");
draw(s.uequals(0),blue+dashed);
draw(s.uequals(pi),blue+dashed);
endgroup3();

add(new void(frame f, transform3 t, picture pic, projection P) {
draw(f,invert(box(min(f,P),max(f,P)),P),"frame");
});



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## Official Asymptote example – curvedlabel3

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 5 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
/* 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));



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## Official Asymptote example – fin

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 6 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
/* 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);

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);



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## Official Asymptote example – label3

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 15 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
/* This code comes from The Official Asymptote Gallery */

import three;

currentprojection=perspective(0,0,1,up=Y);

label(scale(4)*"$\displaystyle\int_{-\infty}^{+\infty} e^{-\alpha x^2}\,dx= \sqrt{\frac{\pi}{\alpha}}$",O,blue,Embedded);



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## Official Asymptote example – label3solid

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 16 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
/* This code comes from The Official Asymptote Gallery */

import three;

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

draw(scale3(4)*extrude("$\displaystyle\int_{-\infty}^{+\infty} e^{-\alpha x^2}\,dx=\sqrt{\frac{\pi}{\alpha}}$",2Z),blue);



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## Official Asymptote example – logo3

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 14 h 57 min

 (Compiled with Asymptote version 2.14svn-r5318)
/* This code comes from The Official Asymptote Gallery */

import three;

size(560,320,IgnoreAspect);
size3(140,80,15);
currentprojection=perspective(-2,20,10,up=Y);
currentlight=White;

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);
path B=(0,y1){dir(88.3)}::{dir(20)}(b,0);
real c=0.5*a;
pair z=(0,2.5);
transform t=scale(1,15);
transform T=inverse(scale(t.yy,t.xx));
path[] g=shift(0,1.979)*scale(0.01)*t*
texpath(Label("{\it symptote}",z,0.25*E+0.169S,fontsize(24pt)));
pair w=(0,1.7);
pair u=intersectionpoint(A,w-1--w);

real h=0.25*linewidth();
real hy=(T*(h,h)).x;
g.push(t*((a,hy)--(b,hy)..(b+hy,0)..(b,-hy)--(a,-hy)..(a-hy,0)..cycle));
g.push(T*((h,y1)--(h,y2)..(0,y2+h)..(-h,y2)--(-h,y1)..(0,y1-h)..cycle));
g.push(shift(0,w.y)*t*((u.x,hy)--(w.x,hy)..(w.x+hy,0)..(w.x,-hy)--(u.x,-hy)..(u.x-hy,0)..cycle));
real f=0.75;
g.push(point(A,0)--shift(-f*hy,f*h)*A--point(A,1)--shift(f*hy,-f*h)*reverse(A)--cycle);
g.push(point(B,0)--shift(f*hy,-f*h)*B--point(B,1)--shift(-f*hy,f*h)*reverse(B)--cycle);

triple H=-0.1Z;
material m=material(lightgray,shininess=1.0);

for(path p : g)
draw(extrude(p,H),m);

surface s=surface(g);
draw(s,red,nolight);
draw(shift(H)*s,m);



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## Official Asymptote example – billboard

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 1 h 13 min

 (Compiled with Asymptote version 2.14svn-r5318)
/* This code comes from The Official Asymptote Gallery */

import three;

size(100);

currentprojection=perspective(1,-2,1);

draw(unitbox);

label("Billboard",X,red,Billboard);
label("Embedded",Y,blue,Embedded);



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