Tag Projection (3D) -- Asymptote Gallery

🔗Asymptote Gallery Tagged by “Projection (3D)” #163

🔗animations-fig008

size(16cm);
import graph3;
import animation;
import solids;

currentlight.background=black;
settings.render=0;
animation A;
A.global=false;

int nbpts=500;
real q=2/5;
real pas=5*2*pi/nbpts;
int angle=4;
real R=0.5;
pen p=rgb(0.1,0.1,0.58);
triple center=(1,1,1);
transform3 T=rotate(angle,center,center+X+0.25*Y+0.3*Z);

real x(real t){return center.x+R*cos(q*t)*cos(t);}
real y(real t){return center.y+R*cos(q*t)*sin(t);}
real z(real t){return center.z+R*sin(q*t);}

currentprojection=orthographic(1,1,1);
currentlight=(0,center.y-0.5,2*(center.z+R));

triple U=(center.x+1.1*R,0,0), V=(0,center.y+1.1*R,0);
path3 xy=plane(U,V,(0,0,0));
path3 xz=rotate(90,X)*xy;
path3 yz=rotate(-90,Y)*xy;

triple[] P;
path3 curve;
real t=-pi;
for (int i=0; i < nbpts; ++i) {
  t+=pas;
  triple M=(x(t),y(t),z(t));
  P.push(M);
  curve = curve..M;
}

curve=curve..cycle;

draw(surface(xy), grey);
draw(surface(xz), grey);
draw(surface(yz), grey);

triple xyc=(center.x,center.y,0);
path3 cle=shift(xyc)*scale3(R)*unitcircle3;
surface scle=surface(cle);
draw(scle, black);
draw(rotate(90,X)*scle, black);
draw(rotate(-90,Y)*scle, black);

draw(surface(sphere(center,R)), p);

triple vcam=1e5*currentprojection.camera-center;
for (int phi=0; phi<360; phi+=angle) {
  bool[] back,front;
  save();

  for (int i=0; i<nbpts; ++i) {
    P[i]=T*P[i];
    bool test=dot(P[i]-center,vcam) > 0;
    front.push(test);
  }

  curve=T*curve;
  draw(segment(P,front,operator ..), paleyellow);
  draw(segment(P,!front,operator ..),0.5*(paleyellow+p));
  draw((planeproject(xy)*curve)^^
       (planeproject(xz)*curve)^^
       (planeproject(yz)*curve), paleyellow);

  A.add();
  restore();
}

A.movie();

🔗graph3-fig011

Figure graph3 011 Generated with Asymptote

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);

pen[] pens=mean(palette(s.map(zpart),Gradient(yellow,red)));

// 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)));

🔗graph3-fig012

Figure graph3 012 Generated with Asymptote

import graph3;
import palette;

real sinc(real x){return x != 0 ? sin(x)/x : 1;}

real f(pair z){
  real value = (sinc(pi*z.x)*sinc(pi*z.y))**2;
  return value^0.25;
}

currentprojection=orthographic(0,0,1);

size(10cm,0);

surface s=surface(f,(-5,-5),(5,5),100,Spline);
s.colors(palette(s.map(zpart),Gradient((int)2^11 ... new pen[]{black,white})));

draw(planeproject(unitsquare3)*s,nolight);

🔗solids-fig001

Figure solids 001 Generated with Asymptote

import solids;
import three;
currentprojection=orthographic(1,2,2);

size(6cm,0);

material m = material(
  diffusepen=yellow,
  emissivepen=black,
  specularpen=orange,
  shininess=0.25,
  metallic=0.5,
  fresnel0=0.07
);

draw(surface(sphere(1)), m);

🔗solids-fig002

Figure solids 002 Generated with Asymptote

import solids;
currentlight=light(paleyellow, specularfactor=3, (2,4,6));

size(6cm,0);
draw(sphere(1,n=4*nslice), linewidth(bp), m=10);
draw(surface(sphere(1,n=4*nslice)), orange);

🔗solids-fig003

Figure solids 003 Generated with Asymptote

// Author: John Bowman.
size(6cm, 0);
import solids;
currentprojection=orthographic(0, 10, 5);

nslice=4*nslice;

revolution r=sphere(O, 1);
draw(surface(r), lightgrey+opacity(0.75));

skeleton s;
r.transverse(s, reltime(r.g, 0.6), currentprojection);
r.transverse(s, reltime(r.g, 0.5), currentprojection);
draw(s.transverse.back, linetype("8 8", 8));
draw(s.transverse.front);

r.longitudinal(s, currentprojection);
draw(s.longitudinal.front);
draw(s.longitudinal.back, linetype("8 8", 8));

🔗solids-fig004

Figure solids 004 Generated with Asymptote

import solids;
size(6cm,0);

currentprojection=orthographic(100,150,30);

real r=1;

skeleton s;
revolution sph=sphere(O,r);
draw(surface(sph), palegray);

path3 cle=rotate(90,X)*scale3(r)*unitcircle3;

triple cam=unit(currentprojection.camera);
real a=degrees(xypart(cam),false)-90;
real b=-sgn(cam.z)*aCos(sqrt(cam.x^2+cam.y^2)/abs(cam));
cle=rotate(b,cross(Z,cam))*rotate(a,Z)*cle;
draw(cle,4pt+red);

🔗solids-fig005

Figure solids 005 Generated with Asymptote

import solids;
size(6cm,0);
currentlight=light(diffuse=yellow, specular=blue, specularfactor=5, (5,-5,10));
// currentprojection=orthographic(100,100,30);
real r=2;

skeleton s;
revolution sph=sphere(O,r);
draw(surface(sph),red);

triple cam=unit(currentprojection.camera);
revolution cle=revolution(O,r*(rotate(90,Z)*cam),cam);
draw(cle, 8pt+black);

🔗solids-fig006

Figure solids 006 Generated with Asymptote

// Author: John Bowman
import three;
size(6cm,0);
currentprojection=perspective(10,100,50);
real a=2.5;

draw(scale3(a)*unitsphere,lightyellow);
draw(align(unit(currentprojection.vector()))*scale3(a)*unitcircle3,2bp+red);

🔗solids-fig008

Figure solids 008 Generated with Asymptote

import solids;
import palette;
size(14cm,0);
currentlight=light(
  gray(0.4),
  specularfactor=3,
  (-0.5,-0.25,0.45),
  (0.5,-0.5,0.5),(0.5,0.5,0.75)
);

nslice=4*nslice;
surface s=surface(sphere(O,1));
draw(s,lightgrey);

path3 pl=plane((1,0,0),(0,1,0),(0,0,-1));
surface pls=shift(3,3,-1e-3)*scale(-6,-6,1)*surface(pl);
draw(pls,0.7*red);

real dist(triple z){return abs(z-Z);}

surface shade;
for (int i=0; i < currentlight.position.length; ++i) {
  shade=planeproject(pl,currentlight.position[i])*s;
  draw(shade,mean(palette((shade.map(dist)),
                          Gradient(black,gray(0.6)))),
       nolight);
}

🔗solids-fig013

Figure solids 013 Generated with Asymptote

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);

🔗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-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);
}