Tag Graph (3D) -- Asymptote Gallery

🔗Asymptote Gallery Tagged by “Graph (3D)” #151

🔗animations-fig007

Show animations/fig0080.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Animation
Tags : #Graph (3D) | #Function (graphing) | #Animation | #Sphere | #Surface | #Path3 | #Segment

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

settings.render=0;
animation A;

int nbpts=500;
real q=2/5;
real pas=5*2*pi/nbpts;
int angle=3;
real R=3;

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

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

currentprojection=orthographic((0,5,2));
currentlight=(3,3,5);

pen p=rgb(0.1,0.1,0.58);
transform3 t=rotate(angle,(0,0,0),(1,0.25,0.25));

filldraw(box((-R-0.5,-R-0.5),(R+0.5,R+0.5)), p, 3mm+black+miterjoin);

revolution r=sphere(O,R);
draw(surface(r),p);

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],currentprojection.camera) > 0;
    front.push(test);
  }

  draw(segment(P,front,operator ..),linewidth(1mm));
  draw(segment(P,!front,operator ..),grey);
  A.add();
  restore();
}

A.movie();

🔗animations-fig008

Show animations/fig0090.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Animation
Tags : #Graph (3D) | #Function (graphing) | #Animation | #Sphere | #Surface | #Path3 | #Segment | #Projection (3D) | #Plane

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-fig001

A Möbius strip of half-width $w$ with midcircle of radius

$R$ and at height $z=0$ can be represented parametrically by :

$\backslash begin\{cases\}\%\; x=\backslash left(R+s\backslash times\backslash cos\; \backslash left(\backslash frac\{t\}\{2\}\backslash right)\backslash right)\backslash cos(t)\backslash \backslash \; y=\backslash left(R+s\backslash times\backslash cos\; \backslash left(\backslash frac\{t\}\{2\}\backslash right)\backslash right)\backslash sin(t)\backslash \backslash \; z=s\backslash times\backslash sin\; \backslash left(\backslash frac\{t\}\{2\}\backslash right)\; \backslash end\{cases\}$

for $s$ in $[-w\backslash ,;\backslash ,w]$ and $t$ in $[0\backslash ,;\backslash ,2\backslash pi]$. In this parametrization, the Möbius strip is therefore a cubic surface with equation

$-R2y+x2y+y3-2Rxz-2x2z-2y2z+yz2=0$

Source

Show graph3/fig0010.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Surface | #Level set (3D)

import graph3;
ngraph=200;
size(12cm,0);
currentprojection=orthographic(-4,-4,5);

real x(real t), y(real t), z(real t);

real R=2;
void xyzset(real s){
  x=new real(real t){return (R+s*cos(t/2))*cos(t);};
  y=new real(real t){return (R+s*cos(t/2))*sin(t);};
  z=new real(real t){return s*sin(t/2);};
}


int n=ngraph;
real w=1;
real s=-w, st=2w/n;
path3 p;
triple[][] ts;
for (int i=0; i <= n; ++i) {
  xyzset(s);
  p=graph(x,y,z,0,2pi);

  ts.push(new triple[] {});
  for (int j=0; j <= ngraph; ++j) {
    ts[i].push(point(p,j));
  }
  s += st;
}

pen[] pens={black, yellow, red, yellow, black};
draw(surface(ts, new bool[][]{}), lightgrey);
for (int i=0; i <= 4; ++i) {
  xyzset(-w+i*w/2);
  draw(graph(x,y,z,0,2pi), 2bp+pens[i]);
}

🔗graph3-fig002

Show graph3/fig0020.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Axis (3D)

import graph3;

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

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

xaxis3("$x$", OutTicks());
yaxis3("$y$", OutTicks());
zaxis3("$z$", OutTicks());

🔗graph3-fig003

Show graph3/fig0030.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Axis (3D)

import graph3;

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

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

axes3("$x$","$y$","$z$",Arrow3);

🔗graph3-fig004

Show graph3/fig0040.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Axis (3D)

import graph3;

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

defaultpen(overwrite(SuppressQuiet));

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

xaxis3("$x$", InTicks(XY()*Label));
yaxis3("$y$", InTicks(XY()*Label));
zaxis3("$z$", OutTicks, p=red, arrow=Arrow3);

🔗graph3-fig005

Show graph3/fig0050.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Axis (3D)

import graph3;

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

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

xaxis3(Label("$x$",MidPoint), OutTicks());
yaxis3("$y$", InTicks());
zaxis3("$z$",XYEquals(-2,0), OutTicks());

🔗graph3-fig006

Show graph3/fig0060.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Axis (3D)

import graph3;
usepackage("icomma");

size(8cm,0);
currentprojection=orthographic(1.5,1,1);

limits((-2,-1,-.5), (0,1,1.5));

xaxis3("$x$",
       Bounds(Both,Value),
       OutTicks(endlabel=false));

yaxis3("$y$",
       Bounds(Both,Value),
       OutTicks(Step=.5,step=.25));

zaxis3("$z$", XYEquals(-2,0), InOutTicks(Label(align=Y-X)));

dot(Label("",align=Z), (-1,0,0), red);

🔗graph3-fig007

Show graph3/fig0070.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Axis (3D) | #Triple

import graph3;

size(8cm,0);
currentprojection=orthographic(1,1,0.5);
limits((-2,-2,0),(0,2,2));

xaxis3(Label("$x$",align=Z),
       Bounds(Min,Min),
       OutTicks(endlabel=false,Step=1,step=0.5));

yaxis3("$y$", Bounds(),
       OutTicks(pTick=0.8*red, ptick=lightgrey));

zaxis3("$z$", Bounds(),
       OutTicks, p=red, arrow=Arrow3);

dot(Label("",align=Z), (-1,0,0), red);

🔗graph3-fig008

Show graph3/fig0080.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Surface | #Level set (3D) | #Contour | #Function (implicit)

// Adapted from the documentation of Asymptote.
import graph3;
import contour;
texpreamble("\usepackage{icomma}");

size3(12cm, 12cm, 8cm, IgnoreAspect);

real sinc(pair z) {
  real r=2pi*abs(z);
  return r != 0 ? sin(r)/r : 1;
}

limits((-2, -2, -0.2), (2, 2, 1.2));
currentprojection=orthographic(1, -2, 0.5);

xaxis3(rotate(90, X)*"$x$",
       Bounds(Min, Min),
       OutTicks(rotate(90, X)*Label, endlabel=false));

yaxis3("$y$", Bounds(Max, Min), InTicks(Label));
zaxis3("$z$", Bounds(Min, Min), OutTicks());

draw(lift(sinc, contour(sinc, (-2, -2), (2, 2), new real[] {0})), bp+0.8*red);
draw(surface(sinc, (-2, -2), (2, 2), nx=100, Spline), lightgray);

draw(scale3(2*sqrt(2))*unitdisk, paleyellow+opacity(0.25), nolight);
draw(scale3(2*sqrt(2))*unitcircle3, 0.8*red);

🔗graph3-fig009

Show graph3/fig0090.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Surface | #Level set (3D) | #Contour | #Function (implicit) | #Palette

size(12cm,0,false);
import graph3;
import contour;
import palette;

texpreamble("\usepackage{icomma}");

real f(pair z) {return z.x*z.y*exp(-z.x);}

currentprojection=orthographic(-2.5,-5,1);

draw(surface(f,(0,0),(5,10),20,Spline),palegray,bp+rgb(0.2,0.5,0.7));

scale(true);

xaxis3(Label("$x$",MidPoint),OutTicks());
yaxis3(Label("$y$",MidPoint),OutTicks(Step=2));
zaxis3(Label("$z=xye^{-x}$",Relative(1),align=2E),Bounds(Min,Max),OutTicks);

real[] datumz={0.5,1,1.5,2,2.5,3,3.5};

Label[] L=sequence(new Label(int i) {
    return YZ()*(Label(format("$z=%g$",datumz[i]),
                       align=2currentprojection.vector()-1.5Z,Relative(1)));
  },datumz.length);

pen fontsize=bp+fontsize(10);
draw(L,lift(f,contour(f,(0,0),(5,10),datumz)),
     palette(datumz,Gradient(fontsize+red,fontsize+black)));

🔗graph3-fig011

Show graph3/fig0110.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Surface | #Level set (3D) | #Contour | #Function (implicit) | #Palette | #Projection (3D) | #Axis (3D) | #Label (3D) | #Shading (3D) | #Shading

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

Show graph3/fig0120.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Palette | #Surface | #Projection (3D) | #Shading (3D)

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);

🔗graph3-fig013

From TeXgraph exemples.

Show graph3/fig0130.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Palette | #Surface | #Shading (3D)

settings.render=0;
import graph3;
import palette;
size(10cm,0);
currentprojection=orthographic(2,-2,2.5);

real f(pair z) {
  real u=z.x, v=z.y;
  return (u/2+v)/(2+cos(u/2)*sin(v));
}

surface s=surface(f,(0,0),(14,14),150,Spline);
draw(s,mean(palette(s.map(zpart),Gradient(yellow,red))));

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

🔗graph3-fig014

From TeXgraph exemples.

Show graph3/fig0140.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Palette | #Surface | #Shading (3D)

settings.render=0;
import graph3;
import palette;
size(15cm,0);
currentprojection=orthographic(2,-2,2.5);

real f(pair z) {
  real u=z.x, v=z.y;
  return (u/2+v)/(2+cos(u/2)*sin(v));
}

surface s=surface(f,(0,0),(14,14),50,Spline);
s.colors(palette(s.map(zpart),Gradient(yellow,red)));

draw(s);

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

🔗graph3-fig015

Show graph3/fig0150.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Palette | #Surface | #Shading (3D) | #Array | #Spherical harmonics

settings.render=0;
import graph3;
size(15cm);

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);}

pen[] pens(triple[] z)
{
  return sequence(new pen(int i) {
      real a=abs(z[i]);
      return a < 1+1e-3 ? black : interp(blue, red, 2*(a-1));
    },z.length);
}

surface s=surface(f,(0,0),(pi,2pi),100,Spline);
// Interpolate the corners, and coloring each patch with one color
// produce some artefacts
draw(s,pens(s.cornermean()));

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

🔗graph3-fig016

Show graph3/fig0160.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Palette | #Surface | #Shading (3D) | #Array | #Spherical harmonics

settings.render=0;
import graph3;
size(15cm);

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);}

pen[][] pens(triple[][] z)
{
  pen[][] p=new pen[z.length][];
  for(int i=0; i < z.length; ++i) {
    triple[] zi=z[i];
    p[i]=sequence(new pen(int j) {
	real a=abs(zi[j]);
	return a < 1+1e-3 ? black : interp(blue, red, 2*(a-1));},
      zi.length);
  }
  return p;
}

surface s=surface(f,(0,0),(pi,2pi),100,Spline);
// Here we interpolate the pens, this looks smoother, with fewer artifacts
draw(s,mean(pens(s.corners())));

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

🔗graph3-fig017

Show graph3/fig0170.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Palette | #Surface | #Shading (3D) | #Array | #Spherical harmonics

import graph3;
size(16cm, 0);

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);}

pen[][] pens(triple[][] z)
{
  pen[][] p=new pen[z.length][];
  for(int i=0; i < z.length; ++i) {
    triple[] zi=z[i];
    p[i]=sequence(new pen(int j) {
    real a=abs(zi[j]);

    return a < 1+1e-3 ? black : interp(blue, red, 2*(a-1));}, zi.length);
  }

  return p;
}

surface s=surface(f, (0, 0), (pi, 2pi), 100, Spline);
// Here we determine the colors of vertexes (vertex shading).
// Since the PRC output format does not support vertex shading of Bezier surfaces, PRC patches
// are shaded with the mean of the four vertex colors.
s.colors(pens(s.corners()));
draw(s);

if(!is3D())
  shipout(bbox(1mm, Fill(black)));

🔗graph3-fig018

The spherical harmonics $Y\_l^m(\backslash theta,\backslash varphi)$ are the angular portion of the solution to Laplace's equation in spherical coordinates where azimuthal symmetry is not present.

The spherical harmonics are defined by:

$Y\_l^m(\backslash theta,\backslash varphi)=\backslash sqrt\{\backslash frac\{2l+1\}\{4\backslash pi\}\backslash frac\{(l-m)!\}\{(l+m)!\}\}P\_\{l\}^\{m\}(\backslash cos\backslash theta)e^\{im\backslash varphi\}$

where $m=-l,\backslash ,-(l-1),\backslash ,\backslash ldots,\backslash ,0,\backslash ,\backslash ldots,\backslash ,l-1,\backslash ,l$ and $P\_l^m$ is the Legendre polynomial.

Source

Show graph3/fig0180.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Palette | #Surface | #Shading (3D) | #Spherical harmonics

import palette;
import math;
import graph3;

typedef real fct(real);
typedef pair zfct2(real,real);
typedef real fct2(real,real);

real binomial(real n, real k)
{
  return gamma(n+1)/(gamma(n-k+1)*gamma(k+1));
}

real factorial(real n) {
  return gamma(n+1);
}

real[] pdiff(real[] p)
{ // p(x)=p[0]+p[1]x+...p[n]x^n
  // retourne la dérivée de p
  real[] dif;
  for (int i : p.keys) {
    if(i != 0) dif.push(i*p[i]);
  }
  return dif;
}

real[] pdiff(real[] p, int n)
{ // p(x)=p[0]+p[1]x+...p[n]x^n
  // dérivée n-ième de p
  real[] dif={0};
  if(n >= p.length) return dif;
  dif=p;
  for (int i=0; i < n; ++i)
    dif=pdiff(dif);
  return dif;
}

fct operator *(real y, fct f)
{
  return new real(real x){return y*f(x);};
}

zfct2 operator +(zfct2 f, zfct2 g)
{// Défini f+g
  return new pair(real t, real p){return f(t,p)+g(t,p);};
}

zfct2 operator -(zfct2 f, zfct2 g)
{// Défini f-g
  return new pair(real t, real p){return f(t,p)-g(t,p);};
}

zfct2 operator /(zfct2 f, real x)
{// Défini f/x
  return new pair(real t, real p){return f(t,p)/x;};
}

zfct2 operator *(real x,zfct2 f)
{// Défini x*f
  return new pair(real t, real p){return x*f(t,p);};
}

fct fct(real[] p)
{ // convertit le tableau des coefs du poly p en fonction polynôme
  return new real(real x){
    real y=0;
    for (int i : p.keys) {
      y += p[i]*x^i;
    }
    return y;
  };
}

real C(int l, int m)
{
  if(m < 0) return 1/C(l,-m);
  real OC=1;
  int d=l-m, s=l+m;
  for (int i=d+1; i <=s ; ++i) OC *= i;
  return 1/OC;
}

int csphase=-1;
fct P(int l, int m)
{ // Polynôme de Legendre associé
  // http://mathworld.wolfram.com/LegendrePolynomial.html
  if(m < 0) return (-1)^(-m)*C(l,-m)*P(l,-m);
  real[] xl2;
  for (int k=0; k <= l; ++k) {
    xl2.push((-1)^(l-k)*binomial(l,k));
    if(k != l) xl2.push(0);
  }
  fct dxl2=fct(pdiff(xl2,l+m));
  return new real(real x){
    return (csphase)^m/(2^l*factorial(l))*(1-x^2)^(m/2)*dxl2(x);
  };
}

zfct2 Y(int l, int m)
{// http://fr.wikipedia.org/wiki/Harmonique_sph%C3%A9rique#Expression_des_harmoniques_sph.C3.A9riques_normalis.C3.A9es
  return new pair(real theta, real phi) {
    return sqrt((2*l+1)*C(l,m)/(4*pi))*P(l,m)(cos(theta))*expi(m*phi);
  };
}

real xyabs(triple z){return abs(xypart(z));}

size(16cm);
currentprojection=orthographic(0,1,1);

zfct2 Ylm;

triple F(pair z)
{
  //   real r=0.75+dot(0.25*I,Ylm(z.x,z.y));
  //   return r*expi(z.x,z.y);
  real r=abs(Ylm(z.x,z.y))^2;
  return r*expi(z.x,z.y);
}

int nb=4;
for (int l=0; l < nb; ++l) {
  for (int m=0; m <= l; ++m) {
    Ylm=Y(l,m);

    surface s=surface(F,(0,0),(pi,2pi),60);
    s.colors(palette(s.map(xyabs),Rainbow()));

    triple v=(-m,0,-l);
    draw(shift(v)*s);
    label("$Y_"+ string(l) + "^" + string(m) + "$:",shift(X/3)*v);
  }
}

🔗grid3-fig001

Show grid3/fig0100.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Grid3.asy
Tags : #Graph (3D) | #Grid (3D) | #Axis (3D)

import grid3;

size(10cm,0,IgnoreAspect);
currentprojection=orthographic(0.25, 1, 0.25);

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

grid3(
      pic=currentpicture,            // picture (default=currentpicture)

      gridroutine=XYZgrid(           // gridtype3droutine or gridtype3droutine [] (alias gridtype3droutines)
                          //                         or gridtype3droutines []:
                          //                         The routine(s) to draw the grid(s);
                          //                         the values can be as follows:
                          //                            * XYgrid : draw grid from X in direction of Y
                          //                            * YXgrid : draw grid from Y in direction of X
                          //                                etc...
                          //                            * An array of previous values XYgrid, YXgrid, ...
                          //                            * XYXgrid : draw XYgrid and YXgrid grids
                          //                            * YXYgrid : draw XYgrid and YXgrid grids
                          //                            * ZXZgrid : draw ZXgrid and XZgrid grids
                          //                            * YX_YZgrid : draw YXgrid and YZgrid grids
                          //                            * XY_XZgrid : draw XYgrid and XZgrid grids
                          //                            * YX_YZgrid : draw YXgrid and YZgrid grids
                          //                            * An array of previous values XYXgrid, YZYgrid, ...
                          //                            * XYZgrid : draw XYXgrid, ZYZgrid and XZXgrid grids.
                          pos=Relative(0)), // position (default=Relative(0)) :
      //                          this is the position of the grid relatively to
      //                          the perpendicular axe of the grid.
      //                          If 'pos' is a the real, 'pos' is a coordinate relativly to this axe.
      //                          Alias 'top=Relative(1)', 'middle=Relative(0.5)'
      //                          and 'bottom=Relative(0)' can be used as value.

      // Following arguments are similar as the function 'Ticks'.
      N=0,                // int (default=0)
      n=0,                // int (default=0)
      Step=0,             // real (default=0)
      step=0,             // real (default=0)
      begin=true,         // bool (default=true)
      end=true,           // bool (default=true)
      pGrid=grey,         // pen (default=grey)
      pgrid=lightgrey,    // pen (default=lightgrey)
      above=false         // bool (default=false)
      );

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=(0,0.5)+W), Bounds(Min,Min), OutTicks(beginlabel=false));

🔗grid3-fig002

Show grid3/fig0200.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Grid3.asy
Tags : #Graph (3D) | #Grid (3D) | #Axis (3D)

import grid3;

size(10cm,0,IgnoreAspect);
currentprojection=orthographic(0.25, 1, 0.25);

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

scale(Linear, Linear, Log(automax=false));
grid3(XZXgrid);
grid3(XYXgrid);
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=(0,0.5)+W), Bounds(Min,Min), OutTicks(beginlabel=false));

🔗grid3-fig003

Show grid3/fig0300.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Grid3.asy
Tags : #Graph (3D) | #Grid (3D) | #Axis (3D)

import grid3;

size(10cm,0,IgnoreAspect);
currentprojection=orthographic(0.25, 1, 0.25);
limits((-2,-2,0), (0,2,2));

grid3(new grid3routines [] {XYXgrid(Relative(1)), XZXgrid(0)});

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=(0,.5)+W), Bounds(Min,Min), OutTicks(beginlabel=false));

🔗grid3-fig004

Show grid3/fig0400.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Grid3.asy
Tags : #Graph (3D) | #Grid (3D) | #Axis (3D)

import grid3;

size(10cm,0,IgnoreAspect);
currentprojection=orthographic(0.25, 1, 0.25);
limits((-2,-2,0),(0,2,2));

grid3(new grid3routines [] {XYXgrid(-0.5), XYXgrid(1.5)},
      pGrid=new pen[] {red, blue},
      pgrid=new pen[] {0.5red, 0.5blue});
xaxis3(Label("$x$",position=EndPoint,align=Z), YZEquals(-2,0), OutTicks());
yaxis3(Label("$y$",position=EndPoint,align=Z), XZEquals(-2,0), OutTicks());
zaxis3(Label("$z$",position=EndPoint,align=X), XYEquals(-2,-2), OutTicks(Label("",align=-X-Y)));

🔗grid3-fig005

Show grid3/fig0500.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Grid3.asy
Tags : #Graph (3D) | #Grid (3D) | #Axis (3D)

import grid3;

size(10cm,0,IgnoreAspect);
currentprojection=orthographic(0.25,1,0.25);
limits((-2,-2,0),(0,2,2));

real Step=0.5, step=0.25;
xaxis3(Label("$x$",position=EndPoint,align=Z), YZEquals(-2,0),
       InOutTicks(Label(align=0.5*(Z-Y)),
                  Step=Step, step=step,
                  gridroutine=XYgrid,
                  pGrid=red, pgrid=0.5red));

yaxis3(Label("$y$",position=EndPoint,align=Z), XZEquals(-2,0),
       InOutTicks(Label(align=-0.5*(X-Z)), Step=Step, step=step,
                  gridroutine=YXgrid,
                  pGrid=red, pgrid=0.5red));

zaxis3("$z$", XYEquals(-1,0), OutTicks(Label(align=-0.5*(X+Y))));

🔗grid3-fig006

Show grid3/fig0600.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Grid3.asy
Tags : #Graph (3D) | #Grid (3D) | #Axis (3D)

import grid3;

size(10cm,0,IgnoreAspect);
currentprojection=orthographic(0.25,1,0.25);
limits((-2,-2,0),(0,2,2));

xaxis3(Label("$x$",position=EndPoint,align=Z), YZEquals(-2,0),
       OutTicks(Label(align=0.5*(Z-Y)),Step=0.5, gridroutine=XYgrid));

yaxis3(Label("$y$",position=EndPoint,align=-X), XZEquals(-2,0),
       InOutTicks(Label(align=0.5*(Z-X)),N=8,n=2, gridroutine=YX_YZgrid));

zaxis3("$z$", OutTicks(ZYgrid));

🔗tube-fig004

Show tube/fig0040.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Tube.asy
Tags : #Tube | #Graph (3D)

import tube;
import graph3;

size(10cm,0);
currentprojection=perspective(4,3,4);

triple f(real t){
  return t*Z+(cos(2pi*t),sin(2pi*t),0)/sqrt(1+0.5*t^2);
}

path3 p=graph(f,0,2.7,operator ..);
draw(tube(p,scale(0.2)*polygon(5)), purple);

🔗tube-fig005

Show tube/fig0050.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Tube.asy
Tags : #Tube | #Graph (3D) | #Shading (3D)

import tube;
import graph3;

size(10cm,0);
currentprojection=perspective(4,3,4);
real x(real t) {return (1/sqrt(1+0.5*t^2))*cos(2pi*t);}
real y(real t) {return (1/sqrt(1+0.5*t^2))*sin(2pi*t);}
real z(real t) {return t;}

path3 p=graph(x,y,z,0,2.7,operator ..);
path section=scale(0.2)*polygon(5);

// tube.asy defines a "colored path".
// The value of coloredtype may be coloredSegments or coloredNodes.
// Here the path scale(0.2)*polygon(5) has fixed colored SEGMENTS.
coloredpath cp=coloredpath(section,
                           // The array of pens become automatically cyclic.
                           new pen[]{0.8*red, 0.8*blue, 0.8*yellow, 0.8*purple, black},
                           colortype=coloredSegments);

// Draw the tube, each SEGMENT of the section is colored.
draw(tube(p,cp));

🔗tube-fig006

Show tube/fig0060.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Tube.asy
Tags : #Tube | #Graph (3D) | #Shading (3D)

import tube;
import graph3;

size(10cm,0);
currentprojection=perspective(4,3,4);
real x(real t) {return (1/sqrt(1+0.5*t^2))*cos(2pi*t);}
real y(real t) {return (1/sqrt(1+0.5*t^2))*sin(2pi*t);}
real z(real t) {return t;}

path3 p=graph(x,y,z,0,2.7,operator ..);
path section=scale(0.2)*polygon(5);

// Here the path scale(0.2)*polygon(5) has colored NODES.
coloredpath cp=coloredpath(section,
                           new pen[]{0.8*red, 0.8*blue, 0.8*yellow, 0.8*purple, black},
                           colortype=coloredNodes);

// Draw the tube, each NODE of the section is colored.
draw(tube(p,cp));

🔗tube-fig007

Show tube/fig0070.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Tube.asy
Tags : #Tube | #Graph (3D) | #Shading (3D)

import tube;
import graph3;

size(10cm,0);
currentprojection=perspective(4,3,4);
real x(real t) {return (1/sqrt(1+0.5*t^2))*cos(2pi*t);}
real y(real t) {return (1/sqrt(1+0.5*t^2))*sin(2pi*t);}
real z(real t) {return t;}

path3 p=graph(x,y,z,0,2.7,operator ..);
path section=scale(0.2)*polygon(5);

// Define a pen wich depends of a real t. t represent the "reltime" of the path3 p.
pen pen(real t){
  return interp(red,blue,1-2*abs(t-0.5));
}

// Here the section has colored segments (by default) depending to reltime.
draw(tube(p,coloredpath(section,pen)));

🔗tube-fig008

Show tube/fig0080.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Tube.asy
Tags : #Tube | #Graph (3D) | #Shading (3D)

import tube;
import graph3;
size(12cm,0);
currentprojection=perspective((-1,1,1));

int p=7, q=3;
real n=p/q;
real a=1, b=1;
real x(real t){return a*cos(t);}
real y(real t){return a*sin(t);}
real z(real t){return b*cos(n*t);}

real R(real t){
  real st2=(n*sin(n*t))^2;
  return a*(1+st2)^(1.5)/sqrt(1+st2+n^4*cos(n*t)^2);
  // return -a*(1+st2)^(1.5)/sqrt(1+st2+n^4*cos(n*t)^2); // Signed radius curvature
}

real mt=q*2*pi;
path3 p=graph(x,y,z,0,mt,operator ..)..cycle;

real m=R(0), M=R(0.5*pi/n);

// Define a pen depending to the radius curvature of graph(x,y,z) at reltime t
pen curvaturePen(real t){
  real r=abs(R(t*mt)-m)/(M-m);
  return interp(red,blue,r);
}

// Draw the tube, colors depend of the radius curvature R.
draw(tube(p,coloredpath(scale(0.1)*unitcircle, curvaturePen)));

🔗tube-fig009

Show tube/fig0090.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Tube.asy
Tags : #Tube | #Graph (3D) | #Shading (3D) | #Array

import tube;
import graph3;

size(10cm,0);
currentprojection=perspective(4,3,4);
real x(real t) {return (1/sqrt(1+0.5*t^2))*cos(2pi*t);}
real y(real t) {return (1/sqrt(1+0.5*t^2))*sin(2pi*t);}
real z(real t) {return t;}

path3 p=graph(x,y,z,0,2.7,operator ..);
path section=scale(0.2)*polygon(4);

// Define an array of pen wich depends of a real t. t represent the "reltime" of the path3 p.
pen[] pens(real t){
  return new pen[] {interp(blue,red,t),
      interp(orange,yellow,t),
      interp(green,orange,t),
      interp(red,purple,t)};
}

// "pen[] pens(real t)" allows to color each nodes or segments with a real parameter (the reltime)
// Note that all arrays of pens are convert to cyclical arrays.
draw(tube(p,coloredpath(section,
                        pens,
                        colortype=coloredNodes)));

🔗tube-fig021

Show tube/fig0210.asy on Github.
Generated with Asymptote 3.00-0.
Categories : Examples 3D | Tube.asy
Tags : #Tube | #Palette | #Shading (3D) | #Graph (3D)

import tube;
import graph3;
import palette;

size(12cm,0);
currentprojection=perspective(1,1,1);

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=Rainbow(15);
pens.push(black);
for (int i=pens.length-2; i >= 0 ; --i)
  pens.push(pens[i]);

path sec=subpath(Circle(0,1.5,2*pens.length),0,pens.length);
coloredpath colorsec=coloredpath(sec, pens,colortype=coloredNodes);
draw(tube(p,colorsec));

This page was generated by the Asymptote Exemples Builder
Last modified the 2025-06-30 22:08:01
©2011 Philippe Ivaldi