## Asymptote Generalities – fig1600

Category: Asymptote,Examples 2D,GeneralitiesPh. Ivaldi @ 13 h 39 min

 (Compiled with Asymptote version 2.14svn-r5318)

size(0,4cm);

texpreamble("\usepackage{amsmath}
\DeclareMathOperator{\e}{e}");

pair A=2*expi(pi/3);

draw((0,-2)--(0,2.5));
draw((0,0)--(1,0),linewidth(1mm),Arrow(2mm));
draw((0,0)--(3.5,0));
draw((0,0)--(0,1),linewidth(1mm),Arrow(2mm));

dot(Label("$A(z_a=2\e^{i\frac{\pi}{3}})$"),A,NE);
label(format("$\vert z_a\vert=%.1f$",length(A)),(.5,-1),E);
label(format("$\arg(z_a)\simeq%.4f$",angle(A)),(.5,-2),E);



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## Asymptote Generalities – fig1610

Category: Asymptote,Examples 2D,GeneralitiesPh. Ivaldi @ 14 h 39 min

 (Compiled with Asymptote version 2.14svn-r5318)

size(10cm,0);

texpreamble("\usepackage{amsmath}
\DeclareMathOperator{\e}{e}");

pair A=2*expi(pi/3);
pair B=expi(pi/6);
pair C=A*B;
pair D=C-B;
pair Bp=2*B;
pair E=I*D;

draw((0,-2)--(0,2.5));
draw((0,0)--(1,0),linewidth(1mm),Arrow(2mm));
draw((-3,0)--(3.5,0));
draw((0,0)--(0,1),linewidth(1mm),Arrow(2mm));

dot(Label("$A(z_a=2\e^{i\frac{\pi}{3}})$"),A);
dot(Label("$B(z_a=\e^{i\frac{\pi}{6}})$"),B);
dot(Label("$B'(z_{b'}=2z_b)$"),Bp);
dot(Label("$\overline{A}(\overline{z_a})$"),conj(A));
dot(Label("$C(z_c=z_a z_c)$"),C,NE);
dot(Label("$D(z_d=z_c-z_d)$"),D,NW);
dot(Label("$E(z_e=iz_d)$"),E,NW);



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## Asymptote Generalities – fig1620

Category: Asymptote,Examples 2D,GeneralitiesPh. Ivaldi @ 15 h 39 min

 (Compiled with Asymptote version 2.14svn-r5318)

size(6cm,0);

pair A=2expi(pi/2);

pair homography(pair z)
{
return (z^2+A)/(z+2);
}

guide image;
pair tpt;

draw(unitcircle);
for(real t=0; t<length(unitcircle);t+=.05)
{
tpt=homography(point(unitcircle,t));
image=image..tpt;
draw(point(unitcircle,t)--tpt,dotted);
}
draw(image..cycle,red);



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## Asymptote using geometry.asy – fig0010

Category: Asymptote,Examples 2D,geometry.asyPh. Ivaldi @ 6 h 02 min

 (Compiled with Asymptote version 2.14svn-r5318)

size(8cm,0);
import geometry;

/* View the definition of struct coordsys */
show(currentcoordsys);

pair a=(0,0.5), b=(1,0.5);
/* View the definition of struct point */
point A=a, B=b;

dot("$A$",A);
dot("$B$",B);



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## Asymptote using geometry.asy – fig0020

Category: Asymptote,Examples 2D,geometry.asyPh. Ivaldi @ 7 h 02 min

 (Compiled with Asymptote version 2.14svn-r5318)

size(8cm,0);
import geometry;

show(currentcoordsys);

pair a=(0,0.5), b=(1,0.5);
point A=a, B=b;

dot("$A$",A);
dot("$B$",B);

/* View the definition of coordsys cartesiansystem(pair,pair,pair) */
currentcoordsys=cartesiansystem((0.5,0.5), i=(0.7,0.7), j=(-0.7,0.7));
show("$O'$", "$\vec{u'}$", "$\vec{v'}$", currentcoordsys, xpen=invisible);

point Ap=a;
/* View the definition of point point(coordsys,explicit point) */
point Bp=point(currentcoordsys,B); // same as 'point Bp=b;'

dot("$A'$",Ap);
dot("$B'$",Bp);
dot("$M$",(Ap+Bp)/2);



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## Asymptote using geometry.asy – fig0030

Category: Asymptote,Examples 2D,geometry.asyPh. Ivaldi @ 8 h 02 min

 (Compiled with Asymptote version 2.14svn-r5318)

size(8cm,0);
import geometry;

show(currentcoordsys);

pair a=(0,0.5), b=(1,0.5);
point A=a, B=b;

dot("$A$",A);
dot("$B$",B);

/* View the definition of coordsys cartesiansystem(pair,pair,pair) */
currentcoordsys=cartesiansystem((0.5,0.5), i=(0.7,0.7), j=(-0.7,0.7));
show("$O'$", "$\vec{u'}$", "$\vec{v'}$", currentcoordsys, xpen=invisible);

point Ap=a;
/* View the definition of point point(coordsys,explicit point,real) */
point Bp=point(currentcoordsys,B); // same as 'point Bp=b;'

dot("$A'$",Ap);
dot("$B'$",Bp);
dot("$M$",(Ap+Bp)/2);

draw(Ap--Bp);

/* View the definition of point locate(pair) */
draw(locate((0,0))--Bp,blue);

/* View the definition of pair locate(point) */
draw((0,0)--locate(Bp),0.8*green);



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## Asymptote using geometry.asy – fig0040

Category: Asymptote,Examples 2D,geometry.asyPh. Ivaldi @ 9 h 02 min

 (Compiled with Asymptote version 2.14svn-r5318)

size(8cm,0);
import geometry;

coordsys R=defaultcoordsys;
show(R);

coordsys Rp=cartesiansystem((0.5,0.5), i=(0.35,0.35), j=(-0.35,0.35));
show("$O'$", "$\vec{\imath'}$", "$\vec{\jmath'}$", Rp, ipen=blue, xpen=invisible);

coordsys Rpp=cartesiansystem((-1,-0.5),
i=rotate(-90)*(0.35,0.35),
j=rotate(-90)*(-0.35,0.35));
show("$O''$", "$\vec{\imath''}$", "$\vec{\jmath''}$", Rpp, ipen=green, xpen=invisible);

pair m=(1,1);

/* View the definition of point point(coordsys,pair,real) */
dot("",point(R,m),red); // Same as 'dot("",m,red);'
dot("",point(Rp,m),blue);

point M=m;
/* View the definition of point point(coordsys,explicit point,real) */
dot("",point(Rpp,M),green); // Works also with 'point'

pair p=(-0.75,0.75);
point P=point(R,(-0.75,0.75));

dot("$P$",P,2E,4mm+red);

// There are two methods for changing
// the coordinate system of a point (or a pair)

/* View the definition of pair /(pair,coordsys) */
dot("$P'$",point(Rp,p/Rp),2S,3mm+blue); // Necessary for 'pair'
dot("$P'$",point(Rp,P/Rp),2N,3mm+blue); // but works with 'point' by casting.

/* View the definition of point changecoordsys(coordsys,point) */
dot("$P''$",changecoordsys(Rpp,P),2W,1.5mm+green); // Useful for 'point'.



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## Asymptote using geometry.asy – fig0050

Category: Asymptote,Examples 2D,geometry.asyPh. Ivaldi @ 10 h 02 min

 (Compiled with Asymptote version 2.14svn-r5318)

import geometry;
size(8cm,0);

currentcoordsys=cartesiansystem((1.25,0.75),i=(1,1),j=(-1,1));
coordsys Rp=currentcoordsys;
coordsys R=defaultcoordsys;

show("$O$", "$\vec{\imath}$", "$\vec{\jmath}$", R);
show("$O'$","$\vec{u}$","$\vec{u}$", Rp, xpen=invisible);

vector w=(0.125,0.5);
point P=(1,0.5);

dot("$P$",P);
draw(Label("$\overrightarrow{w}$",EndPoint), origin()--origin()+w, Arrow);
draw("$\overrightarrow{O'P}+\overrightarrow{w}$",
origin()--P+w, Arrow);

dot("$M$",P+w,red);

/* View the definition of pair locate(explicit vector) */
draw("$\overrightarrow{w}$", (0,0)--locate(w), W,Arrow);



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## Asymptote using geometry.asy – fig0070

Category: Asymptote,Examples 2D,geometry.asyPh. Ivaldi @ 12 h 02 min

 (Compiled with Asymptote version 2.14svn-r5318)

import geometry;
size(15cm);

currentcoordsys=cartesiansystem((0,0),i=(1,0.5),j=(-1,0.5));
coordsys R=currentcoordsys;
show(R, xpen=invisible);

point A=(2,2);
dot("A",A,SE);

point B=(3,1.5);
dot("B",B,SE);

point C=A+(4,2);
dot("C",C);

drawline(A,B,red);
drawline(A,C,blue);

/* View the definition of transform scale(real,point,point,point,point,bool) */
transform t=scale(2,A,B,A,C);
/* View the definition of transform projection(point,point,point,point,bool) */
transform proj=projection(A,B,A,C);

point M=(2,4);
point Mh=proj*M;
dot("$H_M$",Mh,SE);
dot("$M$",M);
point Mp=t*M;
dot("\small$scale(2,A,B,A,C)*M=M'$",Mp,W);
drawline(M,Mh);

point P=(1,-1);
point Ph=proj*P;
dot("$H_P$",Ph,NW);
drawline(P,Ph);
dot("$P$",P);

transform t=scale(-1,A,B,A,C);
point Pp=t*P;
dot("\small$P'=scale(-1,A,B,A,C)*P$",Pp);
draw(P--Pp);



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## Asymptote using geometry.asy – fig0080

Category: Asymptote,Examples 2D,geometry.asyPh. Ivaldi @ 13 h 02 min

 (Compiled with Asymptote version 2.14svn-r5318)

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((1.5,1.5),i=(1,0.5),j=(-1,1));
coordsys Rp=currentcoordsys;
coordsys Rs=cartesiansystem((-1.5,1.5),i=(-1,0.5),j=(-1,-1));
coordsys R=defaultcoordsys;

show("$O$","$\vec{\imath}$", "$\vec{\jmath}$", R);
show("$O'$","$\vec{u}$","$\vec{v}$", Rp, xpen=invisible);
show("$O''$","$\vec{u'}$","$\vec{v'}$", Rs, xpen=invisible);

pair w=(0.75,1.5);
draw("$\overrightarrow{w}$",(0,0)--w,Arrow);

pair P=(1,1);
dot("$P$",P);
dot("$P$",point(Rp,P/Rp),N);
dot("$P$",point(Rs,P/Rs),S);

show("$\overrightarrow{w'}$", vector(w));
show("$\overrightarrow{w''}$", vector(Rs,w));

dot("$P'$",point(Rp,P));
dot("$P''$",point(Rs,P));



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## Asymptote using geometry.asy – fig0090

Category: Asymptote,Examples 2D,geometry.asyPh. Ivaldi @ 14 h 02 min

 (Compiled with Asymptote version 2.14svn-r5318)

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((1.5,1.5),i=(1,0.5),j=(-1,1));
coordsys Rp=currentcoordsys;
coordsys Rs=cartesiansystem((-1.5,1.5),i=(-1,0.5),j=(-1,-1));
coordsys R=defaultcoordsys;

show("$O$","$\vec{\imath}$", "$\vec{\jmath}$", R);
show("$O'$","$\vec{u}$","$\vec{v}$", Rp, xpen=invisible);
show("$O''$","$\vec{u'}$","$\vec{v'}$", Rs, xpen=invisible);

pair P=(1,1);
dot("$P$",P);

draw(format("$\vert OP\vert\simeq %.2f$",abs(P)),(0,0)--P,Arrows);

point Pp=P;
dot("$P'$",Pp);
vector wp=Pp;
show(format("$\vert O'P'\vert= %.2f$",abs(Pp)), wp, Arrows);

point Ps=point(Rs,P);
dot("$P''$",Ps,S);
vector ws=Ps;
show(format("$\vert O''P''\vert\simeq %.2f$",abs(Ps)), ws, Arrows);



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## Asymptote using geometry.asy – fig0100

Category: Asymptote,Examples 2D,geometry.asyPh. Ivaldi @ 15 h 02 min

 (Compiled with Asymptote version 2.14svn-r5318)

import geometry;
size(10cm,0);

currentcoordsys=cartesiansystem((1.5,1.5),i=(1,0.5),j=(-1,1));
coordsys Rp=currentcoordsys;
coordsys R=defaultcoordsys;

show("$O$","$\vec{\imath}$", "$\vec{\jmath}$", R);
show("$O'$", "$\vec{u}$", Label("$\vec{v}$",align=NE), Rp, xpen=invisible);

pair w=(1.5,0.75);
draw("$\overrightarrow{w}$",(0,0)--w,Arrow);

pair P=(1,-1);
dot("$P$",P);

show("$\overrightarrow{w'}$", vector(w));

dot("$P'$",point(Rp,P),N);

point Ip=I;
dot("$I'$",Ip,N);
dot("$I'*P'$",Ip*point(Rp,P),S);
dot("$I*P'$",I*point(Rp,P),N);

vector wp=Ip*vector(w);
show(Label("$I'*\overrightarrow{w'}$",EndPoint), wp);

vector foo=I*vector(w);
show("$I*\overrightarrow{w'}$", foo);



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## Asymptote using geometry.asy – fig0260

Category: Asymptote,Examples 2D,geometry.asyPh. Ivaldi @ 7 h 02 min

 (Compiled with Asymptote version 2.14svn-r5318)

import geometry;

size(5cm,0);

point M=(1,1);
point N=(0.25,0.28);
point P=(0.75,0.66);

path g=origin--M;
line l=line(origin,M);
pen p=linewidth(5mm);
draw(l,p);

dot(N,p+red);
dot(N,blue);

dot(P,p+red);
dot(P,blue);

draw(box(origin,(1,1)),invisible);

/* View the definition of bool @(point,line) */
write(N@l);// Return 'false'

/* View the definition of bool onpath(picture,path,point,pen) */
write(onpath(g,N,p));// Return 'true'
write(onpath(g,P,p));// Return 'false'



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## Official Asymptote example – Hobbycontrol

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 17 h 57 min

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



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## Official Asymptote example – Hobbydir

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 18 h 57 min

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



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## Official Asymptote example – circles

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 */

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);



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## Official Asymptote example – fano

Category: Asymptote,Official Gallery One-PagerPh. Ivaldi @ 1 h 57 min

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



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