The three.asy module of the Asymptote drawing software

Examples using the Asymptote module `three.asy`

🔗three-fig001

Figure three 001 Generated with Asymptote

import three;

size(12cm);
currentprojection=orthographic(1,1,1.5);
currentlight=(1,0,1);

triple P00=-X-Y+0.5*Z, P03=-X+Y, P33=X+Y, P30=X-Y;

triple[][] P={
  {P00,P00+(-0.5,0.5,-1),P03+(0,-0.5,1),P03},
  {P00+(0.5,-0.5,-1),(-0.5,-0.5,0.5),(-0.5,0.5,-1.5),P03+(0.5,0,1)},
  {P30+(-0.5,0,1),(0.5,-0.5,-1.5),(0.5,0.5,1),P33+(-0.5,0,1)},
  {P30,P30+(0,0.5,1),P33+(0,-0.5,1),P33}
};

surface s=surface(patch(P));
draw(s,15,15,yellow,meshpen=grey);
draw(sequence(new path3(int i){
      return s.s[i].external();},s.s.length), bp+red);

dot("P[0][0]",P[0][0], align=N, black);
dot("P[0][3]",P[0][3], black);
dot("P[3][3]",P[3][3], align=S, black);
dot("P[3][0]",P[3][0], align=W, black);

draw(Label("P[0][1]",align=SW,EndPoint),P[0][0]--P[0][1], Arrow3);
draw(Label("P[1][0]",align=SE,EndPoint),P[0][0]--P[1][0], Arrow3);

draw(Label("P[0][2]",align=E,EndPoint),P[0][3]--P[0][2], Arrow3);
draw(Label("P[1][3]",EndPoint),P[0][3]--P[1][3], Arrow3);

draw(Label("P[2][3]",EndPoint),P[3][3]--P[2][3], Arrow3);
draw(Label("P[3][2]",EndPoint),P[3][3]--P[3][2], Arrow3);

draw(Label("P[3][1]",EndPoint),P[3][0]--P[3][1], Arrow3);
draw(Label("P[2][0]", align=W,EndPoint),P[3][0]--P[2][0], Arrow3);


dot("P[1][1]",P[1][1], align=S);
dot("P[1][2]",P[1][2], align=E);
dot("P[2][2]",P[2][2], align=N);
dot("P[2][1]",P[2][1], align=W);

for (int i=0; i < s.s.length; ++i)
  dot(s.s[i].internal(), bp+red);

if(!is3D())
  shipout(bbox(Fill(lightgrey)));

🔗three-fig002

Figure three 002 Generated with Asymptote

import three;
import palette;

size(12cm);
currentprojection=orthographic(1,1,1.5);
currentlight=(1,0,1);

triple P00=-X-Y+0.5*Z, P03=-X+Y, P33=X+Y, P30=X-Y;

triple[][] P={
  {P00,P00+(-0.5,0.5,-1),P03+(0,-0.5,1),P03},
  {P00+(0.5,-0.5,-1),(-0.5,-0.5,0.5),(-0.5,0.5,-1.5),P03+(0.5,0,1)},
  {P30+(-0.5,0,1),(0.5,-0.5,-1.5),(0.5,0.5,1),P33+(-0.5,0,1)},
  {P30,P30+(0,0.5,1),P33+(0,-0.5,1),P33}
};

surface s=surface(patch(P));
s.colors(palette(s.map(zpart),Gradient(yellow,red)));
// s.colors(palette(s.map(zpart),Rainbow()));

draw(s);
draw(sequence(new path3(int i){
      return s.s[i].external();},s.s.length), bp+orange);


if(!is3D())
  shipout(bbox(Fill(lightgrey)));

🔗three-fig003

Figure three 003 Generated with Asymptote

import three;

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

surface sf=surface(patch(P=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(sf,surfacepen=yellow);
draw(sf.s[0].vequals(0.5),squarecap+2bp+blue,currentlight);
draw(sf.s[0].uequals(0.5),squarecap+2bp+red,currentlight);

🔗three-fig004

Figure three 004 Generated with Asymptote

import three;
size(8cm, 0);
real radius=1, theta=37, phi=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, bg);
draw(surface((0, 1.2, 0)--(0, 1.2, 1.2)--(0, 0, 1.2)--(0, 0, 0)--cycle), bg, bg);
draw(surface((1.2, 0, 0)--(1.2, 1.2, 0)--(0, 1.2, 0)--(0, 0, 0)--cycle), bg, bg);

real r=1.5;
draw(Label("$x$", 1), O--r*X, Arrow3(HookHead3));
draw(Label("$y$", 1), O--r*Y, Arrow3(HookHead3));
draw(Label("$z$", 1), O--r*Z, Arrow3(HookHead3));
label("$\rm O$",  (0, 0, 0), W);

triple pQ=radius*dir(theta, phi); // Point Q
// triple pQ=radius*expi(radians(theta), radians(phi)); // Point Q
draw(O--radius*dir(90, phi)^^O--pQ, dashed);
dot("$R*\mathrm{dir}\left(\theta, \phi\right)$", pQ);

// Arcs
draw("$\theta$", reverse(arc(O, 0.5*pQ, 0.5*Z)), N+0.3E, Arrow3(HookHead2));
draw("$\phi$", arc(O, 0.5*X, 0.5*(pQ.x, pQ.y, 0)), N+0.3E, Arrow3(HookHead2));

path3 p3=O--arc(O, radius, 0, phi, 90, phi)--cycle;
draw(surface(p3), blue+opacity(0.5));

🔗three-fig005

Figure three 005 Generated with Asymptote

import three; import math;
size(8cm,0);
currentprojection=obliqueX;

real h=2;
triple A =(0,0,h), B=(h,0,0), C=(0,h,0), D=(0,0,0);
triple Ip=midpoint(A--C), J=midpoint(A--B);
triple K=shift((0,0,-0.25*h))*A;

triple M=interp(K,J,intersect(K,J,normal(new triple[]{B,C,D}),D));
triple Np=interp(K,Ip,intersect(K,Ip,normal(new triple[]{B,C,D}),D));

dot("$A$", A, align=Z);  dot("$B$", B, align=S);
dot("$C$", C, align=S);  dot("$D$", D, align=W);
dot("$I$", Ip, align=N); dot("$J$", J, align=W);
dot("$K$", K, align=NE); dot("$M$", M, align=SE);
dot("$N$", Np, align=S);

draw(A--B--C--cycle^^B--M^^C--Np^^J--M^^Ip--Np);
draw(A--D--C^^D--B^^J--K^^K--Ip, dashed);

🔗three-fig006

Figure three 006 Generated with Asymptote

Show three/fig0060.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Three.asy
Tags : #Label (3D) | #Projection (3D) | #Plan

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)));

🔗three-fig007

Figure three 007 Generated with Asymptote

From the Asymptote forum.

Show three/fig0070.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Three.asy
Tags : #Bsp | #Wire frame | #Plan

import bsp;

typedef path3[] shape;

shape operator *(transform3 T, shape p){
  shape os;
  for(path3 g:p) os.push(T*g);
  return os;
}


path3 path(triple[] T){
  path3 P;
  for(triple i:T) P=P--i;
  return P;
}

void addshapes(face[] F, shape[] shp, pen drawpen=currentpen, pen fillpen=white)
{
  for(int i=0; i < shp.length; ++i)
    for(int j=0; j < shp[i].length; ++j) {
      path3 g=shp[i][j];
      picture pic=F.push(g);
      filldraw(pic, project(g), fillpen, drawpen);
      // filldraw(pic, g, currentlight.intensity(F[F.length-1].point)*fillpen, drawpen);
    }
}

shape cylinder(real R=1, real H=1, int n=18){
  shape Cyl;
  triple[] CTop;
  triple[] CBot;
  for(int i=0; i <= n; ++i)
    CBot.push((R*cos(2pi*i/n), R*sin(2pi*i/n), 0));
  CTop = CBot+(0, 0, H);
  for(int i=0; i < n; ++i)
    Cyl.push(CBot[i]--CBot[i+1]--CTop[i+1]--CTop[i]--cycle);

  path3 P=path(CBot)--cycle;
  Cyl.push(P);
  Cyl.push(shift(H*Z)*P);

  return Cyl;
}

shape rightslab(real x=1, real y=1, real z=1){
  shape slab;
  slab[0] = (0, 0, 0)--(1, 0, 0)--(1, 1, 0)--(0, 1, 0)--cycle;
  slab[1] = (0, 0, 0)--(1, 0, 0)--(1, 0, 1)--(0, 0, 1)--cycle;
  slab[2] = (1, 0, 0)--(1, 1, 0)--(1, 1, 1)--(1, 0, 1)--cycle;
  slab[3] = (1, 1, 0)--(0, 1, 0)--(0, 1, 1)--(1, 1, 1)--cycle;
  slab[4] = (0, 1, 0)--(0, 0, 0)--(0, 0, 1)--(0, 1, 1)--cycle;
  slab[5] = (0, 0, 1)--(1, 0, 1)--(1, 1, 1)--(0, 1, 1)--cycle;
  return scale(x, y, z)*slab;
}

size(10cm, 0);
triple cam=(1600, 200, 150);
//currentprojection=orthographic(1600, 800, 400);
currentprojection=perspective(cam); //Far away!
currentlight=rotate(-45, Z)*(cam+(0, 0, 1000));

real Blen = 180;
real Bwdt = 30;
real Bhgt = 3;
real Clen = 130;
real Cwdt = 50;
real Chgt = 50;
real cylr = 7.5;
real cylh = 37.0 ;

shape slab1 = shift(-Bwdt/2*Y-Bhgt/2*Z+Clen/2*X)*rightslab(Blen, Bwdt, Bhgt);
shape slab2 = shift(-Cwdt/2*Y-Chgt/2*Z-Clen/2*X)*rightslab(Clen, Cwdt, Chgt);
shape cyl1 = shift((Blen+Clen/2-2*cylr)*X-(cylh/2)*Z)*cylinder(R=cylr, H=cylh);

shape[] group1={slab1};
shape[] group2={slab2};
shape[] group3={cyl1};

face[] faces;
addshapes(faces, group1, drawpen=linewidth(0.25bp), fillpen=opacity(0.35)+red);
addshapes(faces, group2, drawpen=linewidth(0.25bp), fillpen=opacity(0.5)+lightblue);
addshapes(faces, group3, drawpen=linewidth(0.25bp), fillpen=opacity(0.5)+lightyellow);
add(faces);

shipout(format="pdf", bbox(3mm, white));

🔗three-fig008

Figure three 008 Generated with Asymptote

Show three/fig0080.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Three.asy
Tags : #Bsp | #Wire frame | #Line type | #Plan

import bsp;

typedef path3[] shape;

shape operator *(transform3 T, shape p){
  shape os;
  for(path3 g:p) os.push(T*g);
  return os;
}


path3 path(triple[] T){
  path3 P;
  for(triple i:T) P=P--i;
  return P;
}

void addshapes(face[] F, shape[] shp, pen drawpen=currentpen, pen fillpen=white)
{
  for(int i=0; i < shp.length; ++i)
    for(int j=0; j < shp[i].length; ++j) {
      path3 g=shp[i][j];
      picture pic=F.push(g);
      if(fillpen != nullpen) filldraw(pic,project(g),fillpen, drawpen);
      else draw(pic,project(g),drawpen);
      // filldraw(pic,g,currentlight.intensity(F[F.length-1].point)*fillpen, drawpen);
    }
}

shape cylinder(real R=1, real H=1, int n=18){
  shape Cyl;
  triple[] CTop;
  triple[] CBot;
  for(int i=0; i <= n; ++i)
    CBot.push((R*cos(2pi*i/n), R*sin(2pi*i/n),0));
  CTop = CBot+(0,0,H);
  for(int i=0; i < n; ++i)
    Cyl.push(CBot[i]--CBot[i+1]--CTop[i+1]--CTop[i]--cycle);

  path3 P=path(CBot)--cycle;
  Cyl.push(P);
  Cyl.push(shift(H*Z)*P);

  return Cyl;
}


size(10cm,0);

currentprojection=orthographic(1,1,1);

shape cyl1 = cylinder(R=1, H=2);

shape[] group={cyl1};

face[] hidden, visible;
addshapes(hidden, group, drawpen=linewidth(bp));
addshapes(visible, group, drawpen=dotted, fillpen=nullpen);
add(hidden);
add(visible);

shipout(format="pdf");

🔗three-fig009

Figure three 009 Generated with Asymptote

size(10cm,0);
import three;

currentprojection=obliqueX;

triple v1=(4,0,0),
       v2=(0,6,0),
       p0=(-2,-3,0);
path3 pl1=plane(v1,v2,p0);

path ph=transform(v1,v2,p0,currentprojection)*((0,-2){W}..(0,2){W}..cycle);
filldraw(project(pl1)^^ph,evenodd+lightgrey);

🔗three-fig010

Figure three 010 Generated with Asymptote

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);
add(f);

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);

🔗three-fig011

Figure three 011 Generated with Asymptote

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);
}

Examples using the Asymptote module three.asy