Recreate the sphere in TeX.SX logo

Question

I'm trying to recreate this

But looking in this Meta question the only code provided doesn't give that output

%!TEX TS-program = xelatex
\documentclass{minimal}
\usepackage{pst-solides3d}

\begin{document} 

\psset{viewpoint=50 20 10 rtp2xyz,Decran=50}
\psset{unit=0.75}
\begin{pspicture}(-5,-5)(5,5)
\psSolid[object=sphere,r=4,action=draw*,ngrid=9 9,resolution=720]%
\defFunction[algebraic]{helicespherique}(t)%
  {4*cos(10*t)*cos(t)}%
  {4*sin(10*t)*cos(t)}%
  {4*sin(t)}
\psSolid[object=courbe,linecolor=blue,
        resolution=720,range=pi -2 div pi 2 div,
       function=helicespherique,r=0.05]
%\gridIIID[Zmin=-4,Zmax=4](-4,4)(-4,4)
\end{pspicture}

\end{document} 

But I know nothing about PSTricks

How can I reproduce the sphere in the backround of this site?

I'm looking for code (in TikZ, MetaPost, Asymptote or PStricks) to reproduce the image. An important thing is that what's behind the ball should be in another layer (thinner or gray). Like the image from this site.

In any case, this is what I ended up with a few changes from the code

\documentclass{standalone}
\usepackage{pst-solides3d}

\begin{document} 

\psset{viewpoint=50 20 40 rtp2xyz,Decran=50}
\psset{unit=0.75}
\begin{pspicture}(-5,-5)(5,5)
\psSolid[object=sphere,r=4,fillcolor=white,ngrid=14 14,resolution=720,linewidth=.1pt,linecolor=gray]%
\defFunction[algebraic]{helicespherique}(t)%
  {4*cos(2*t)*cos(t)}%
  {4*sin(2*t)*cos(t)}%
  {4*sin(t)}
\psSolid[object=courbe,linecolor=black,
        resolution=720,range=pi -2 div pi 2 div,
       function=helicespherique,r=0.0001]
\end{pspicture}

\end{document} 

Answer 1

The (original) image was created using ePiX (available from CTAN). The source sphere.xp can be compiled using

elaps <options> sphere.xp

to produce

sphere.xp:

/* -*-ePiX-*- */
#include "epix.h"
using namespace ePiX;
const double k(2M_PI/(360sqrt(3))); // assume "degrees" mode
double exp_cos(double t) { return exp(kt)Cos(t); }
double exp_sin(double t) { return exp(kt)Sin(t); }
double minus_exp_cos(double t) { return -exp_cos(t); }
double minus_exp_sin(double t) { return -exp_sin(t); }
int main()
{
  picture(P(-1,-1), P(1,1), "2.5 x 2.5in");
begin();
  degrees(); // set angle units
  camera.at(P(1, 2.5, 3));
sphere(); // draw unit sphere's horizon
pen(Blue(1.6)); // hidden portions of loxodromes
  backplot_N(exp_cos, exp_sin, -540, 540, 180);
  backplot_N(minus_exp_cos, minus_exp_sin, -540, 540, 180);
pen(Red(1.6));
  backplot_N(exp_sin, minus_exp_cos, -540, 540, 180);
  backplot_N(minus_exp_sin, exp_cos, -540, 540, 180);
pen(Black(0.3)); // coordinate grid
for (int i=0; i<=12; ++i) {
    latitude(90-15i, 0, 360);
    longitude(30i, 0, 360);
  }
bold(Blue()); // visible portions of loxodromes
  frontplot_N(exp_cos, exp_sin, -540, 540, 360);
  frontplot_N(minus_exp_cos, minus_exp_sin, -540, 540, 360);
pen(Red());
  frontplot_N(exp_sin, minus_exp_cos, -540, 540, 360);
  frontplot_N(minus_exp_sin, exp_cos, -540, 540, 360);
end();
}

Possible outputs:

• LaTeX's picture environment; elaps sphere.xp

• PSTricks; elaps --pst sphere.xp

• TikZ; elaps --tikz sphere.xp

Answer 2

Minimal Working Solution

\documentclass[pstricks,margin=1mm]{standalone}
\usepackage{pst-solides3d}

\psset{viewpoint=50 70 50 rtp2xyz,Decran=50,linewidth=0.5\pslinewidth}

\defFunction[algebraic]{helicespherique}(t)
        {0.5*cos(10*t)*cos(t)}
        {0.5*sin(10*t)*cos(t)}
        {0.5*sin(t)}    

\begin{document}
\begin{pspicture*}(-0.5,-0.5)(0.5,0.5)
    \psSolid
    [
        object=sphere,
        fillcolor=gray,
        opacity=.25,
        strokeopacity=.25,
        ngrid=30 30,
        r=0.5,
        grid=false,
    ]
    \psSolid
    [
        object=courbe,
        linewidth=0.05pt,
        range=pi -.5 mul 0.5 pi mul,
        function=helicespherique,
        r=0.005,
        grid=false,
    ]
\end{pspicture*}
\end{document}

Answer 3

The package pst-rubans draws a spiral ribbon on objects (cylinder, cone, torus, paraboloid, sphere).

pst-rubans – Draw three-dimensional ribbons

\documentclass{article}
\usepackage{pst-rubans}
\begin{document}
\begin{center}
\begin{pspicture}(-5,-5)(5,5)
\psframe*(-5,-5)(5,5)
\psset{viewpoint=50 20 40,Decran=50,resolution=720,lightsrc=viewpoint}
\psSphericalSpiral[incolor=yellow!20,R=4,fillcolor=orange,grid,dPHI=8]
\end{pspicture}
\end{center}
\end{document} 

Answer 4

\documentclass{standalone}
\usepackage{pst-solides3d}
\begin{document} 

\psset{viewpoint=50 20 40 rtp2xyz,Decran=50,unit=0.75}
\begin{pspicture}(-5,-5)(5,5)
    \psSolid[object=sphere,r=4,ngrid=20 20,linewidth=.1pt,linecolor=black!10,
      action=draw]% don't use hidden lines
    \defFunction[algebraic]{helix}(t)%
        {4*cos(3*t)*cos(t)}%
        {4*sin(3*t)*cos(t)}%
        {4*sin(t)}
    \psSolid[object=courbe,linecolor=black,range=-0.33 1.57,
            function=helix,r=0.02]
    \psSolid[object=courbe,linecolor=black!30,range=-1.57 -0.33,
    function=helix,r=0.02]
\end{pspicture}

\end{document} 

Answer 5

Using the code with epix, please find a (non optimized) Asymptote version.

size(10cm);
import three;
import graph3;
import math;
import solids;
settings.render=0; 
settings.prc=false; // on se restreint à une vue 2d


currentprojection=orthographic(1,2.5,3);

real  k=2*pi/(360*sqrt(3));

real  exp_cos(real t) { return exp(k*t)*Cos(t); }
real  exp_sin(real t) { return exp(k*t)*Sin(t); }
real minus_exp_cos(real t) { return -exp_cos(t); }
real minus_exp_sin(real t) { return -exp_sin(t); }

triple f1(real t)
{
  real ss;
  triple ff;
  ss=exp_cos(t)^2+exp_sin(t)^2+1;
  ff=(2*exp_cos(t)/ss,2*exp_sin(t)/ss,(ss-2)/ss);
  return ff;
}


triple f2(real t)
{
  real ss;
  triple ff;
  ss=minus_exp_cos(t)^2+minus_exp_sin(t)^2+1;
  ff=(2*minus_exp_cos(t)/ss,2*minus_exp_sin(t)/ss,(ss-2)/ss);
  return ff;
}

triple f3(real t)
{
  real ss;
  triple ff;
  ss=exp_sin(t)^2+minus_exp_cos(t)^2+1;
  ff=(2*exp_sin(t)/ss,2*minus_exp_cos(t)/ss,(ss-2)/ss);
  return ff;
}


triple f4(real t)
{
  real ss;
  triple ff;
  ss=minus_exp_sin(t)^2+exp_cos(t)^2+1;
  ff=(2*minus_exp_sin(t)/ss,2*exp_cos(t)/ss,(ss-2)/ss);
  return ff;
}


revolution r=sphere(O,1);
draw(r,9,gray,longitudinalpen=nullpen,backpen=nullpen);
draw(r.silhouette());


for(int k=-2; k<5;++k) 
  draw(rotate(k*30,(0,0,1))*rotate(-90,(1,0,0))*r,1,gray,
       longitudinalpen=nullpen,backpen=nullpen);
int nbpts=280;
real step=1080/nbpts;


draw(graph(f1,-540,540,280,Spline),blue+gray);
draw(graph(f2,-540,540,280,Spline),blue+gray);
draw(graph(f3,-540,540,280,Spline),red+gray);
draw(graph(f4,-540,540,280,Spline),red+gray);


triple[] P1=new triple[nbpts];
triple[] P2=new triple[nbpts];
triple[] P3=new triple[nbpts];
triple[] P4=new triple[nbpts];

for(int i=0; i < nbpts; ++i) {
  real t=-540+i*step;
  P1[i]=f1(t);
  P2[i]=f2(t);
  P3[i]=f3(t);
  P4[i]=f4(t);

}

bool[] front1=new bool[nbpts];
bool[] front2=new bool[nbpts];
bool[] front3=new bool[nbpts];
bool[] front4=new bool[nbpts];


for(int i=0; i < nbpts; ++i) {
  front1[i]=dot(P1[i],currentprojection.camera) > 0;
  front2[i]=dot(P2[i],currentprojection.camera) > 0;
  front3[i]=dot(P3[i],currentprojection.camera) > 0;
  front4[i]=dot(P4[i],currentprojection.camera) > 0;
}
draw(segment(P1,front1,operator ..),blue+1bp);
draw(segment(P2,front2,operator ..),blue+1bp);
draw(segment(P3,front3,operator ..),red+1bp);
draw(segment(P4,front4,operator ..),red+1bp);

And the result.