newSphere.jscad

// title: New Sphere
// author: Rene K. Mueller
// description: geodesic approach to the sphere, in contrast with openscad-like

function getParameterDefinitions() {
   return [
      { name: "fn", type: "float", initial: 32, caption: "Resolution" }
   ];
}

function main(param) {
   return [
      newSphere({r: 5, fn: param.fn}),
      sphere({r:5, fn: param.fn}).translate([10,0,0])
   ];
}

function newSphere(p) {
   var r = 1, fn = 4;

   var ci = [              // hard-coded data of icosahedron (20 faces, all triangles)
      [0.850651,0.000000,-0.525731],
      [0.850651,-0.000000,0.525731],
      [-0.850651,-0.000000,0.525731],
      [-0.850651,0.000000,-0.525731],
      [0.000000,-0.525731,0.850651],
      [0.000000,0.525731,0.850651],
      [0.000000,0.525731,-0.850651],
      [0.000000,-0.525731,-0.850651],
      [-0.525731,-0.850651,-0.000000],
      [0.525731,-0.850651,-0.000000],
      [0.525731,0.850651,0.000000],
      [-0.525731,0.850651,0.000000]];
   var ti = [
      [0,9,1],
      [1,10,0],
      [6,7,0],
      [10,6,0],
      [7,9,0],
      [5,1,4],
      [4,1,9],
      [5,10,1],
      [2,8,3],
      [3,11,2],
      [2,5,4],
      [4,8,2],
      [2,11,5],
      [3,7,6],
      [6,11,3],
      [8,7,3],
      [9,8,4],
      [11,10,5],
      [10,11,6],
      [8,9,7]];
   
   if(p) {
      if(p.fn) fn = Math.floor(p.fn/6);
      if(p.r) r = p.r;
   }

   if(fn<0) fn = 1;
   
   var q = [];
   var c = [], f = [];
   var off = 0;

   for(var i=0; i<ti.length; i++) {
      var g = geodesicSubDivide([ ci[ti[i][0]], ci[ti[i][1]], ci[ti[i][2]] ],fn,off);
      c = c.concat(g.points);
      f = f.concat(g.triangles);
      off = g.off;
   }
   return polyhedron({points: c, triangles: f}).scale(r);
}


//           p3
//           /\
//          /__\     fn = 3
//      i  /\  /\
//        /__\/__\
//       /\  /\  /\
//     0/__\/__\/__\
//    p1 0   j      p2

function geodesicSubDivide(p,fn,off) {
   var p1 = p[0], p2 = p[1], p3 = p[2];
   var n = off;
   var c = [];
   var f = [];

   for(var i=0; i<fn; i++) {
      for(var j=0; j<fn-i; j++) {
         var t0 = i/fn;
         var t1 = (i+1)/fn;
         var s0 = j/(fn-i);
         var s1 = (j+1)/(fn-i);
         var s2 = fn-i-1?j/(fn-i-1):1
         var s3 = fn-i-1?(j+1)/(fn-i-1):1
         var q = [];
         
         q[0] = mix3(mix3(p1,p2,s0),p3,t0);
         q[1] = mix3(mix3(p1,p2,s1),p3,t0);
         q[2] = mix3(mix3(p1,p2,s2),p3,t1);
         
         // normalize
         for(var k=0; k<3; k++) {
            var r = Math.sqrt(q[k][0]*q[k][0]+q[k][1]*q[k][1]+q[k][2]*q[k][2]);
            for(var l=0; l<3; l++) {
               q[k][l] /= r;
            }
         }
         c.push(clone(q[0]),clone(q[1]),clone(q[2]));
         f.push([n,n+1,n+2]); n += 3;
         
         if(j<fn-i-1) {
            q[0] = mix3(mix3(p1,p2,s1),p3,t0);
            q[1] = mix3(mix3(p1,p2,s3),p3,t1);
            q[2] = mix3(mix3(p1,p2,s2),p3,t1);

            // normalize
            for(var k=0; k<3; k++) {
               var r = Math.sqrt(q[k][0]*q[k][0]+q[k][1]*q[k][1]+q[k][2]*q[k][2]);
               for(var l=0; l<3; l++) {
                  q[k][l] = q[k][l]/r;
               }
            }
            c.push(q[0],q[1],q[2]);
            f.push([n,n+1,n+2]); n += 3;
         }
      }
   } 
   return { points: c, triangles: f, off: n };
}

function mix3(a,b,f) {
   var _f = 1-f;
   var c = [];
   for(var i=0; i<3; i++) {
      c[i] = a[i]*_f+b[i]*f;
   }
   return c;
}