Koch snowflake vase for OpenJsCad

koch.jscad

function circlify(v, opts) {
  var d = Math.sqrt(v[0]*v[0] + v[1]*v[1]);
  d = 1 + ((opts.radius-d)*opts.circle / d);
  v[0] *= d;
  v[1] *= d;
}

function kochs(a,b,opts) {
  if (opts.d>=3) return [];
  opts.d++;
  var c = [(a[0]+b[0])/2, (a[1]+b[1])/2];
  var x = [(b[0]-a[0])/3, (b[1]-a[1])/3];
  var s = Math.sqrt(0.75)*opts.spread;
  var y = [-x[1]*s, x[0]*s];
  var pts = [];
  var aa = [a[0]+x[0],a[1]+x[1], opts.z];
  var cc = [c[0]+y[0],c[1]+y[1], opts.z];
  var bb = [b[0]-x[0],b[1]-x[1], opts.z];
  circlify(aa, opts);
  circlify(bb, opts);
  circlify(cc, opts);
  pts = pts.concat(kochs(a,aa,opts));
  pts.push(aa);
  pts = pts.concat(kochs(aa,cc,opts));
  pts.push(cc);
  pts = pts.concat(kochs(cc,bb,opts));
  pts.push(bb);
  pts = pts.concat(kochs(bb,b,opts));
  opts.d--;
  return pts;
}

function koch(opts) {
  opts.d = 0;
  opts.rotate = opts.rotate||0;
  var sides = 3;
  var a,b;
  var pts =  [];
  for (var i=0;i<sides;i++) {
      var ang1 = opts.rotate + i*Math.PI*2/sides;
      var ang2 = opts.rotate + (i+1)*Math.PI*2/sides;
      a = [Math.sin(ang1)*opts.radius,Math.cos(ang1)*opts.radius, opts.z];
      b = [Math.sin(ang2)*opts.radius,Math.cos(ang2)*opts.radius, opts.z];
      pts.push(a);  
      pts = pts.concat(kochs(a,b,opts));
  }
  pts.push(b);
  return pts;
}

function slice_extrude(slices) {
    if (slices.length<2) return;
    var polygons = [];
    
    polygons = polygons.concat(polygon(slices[0])._toPlanePolygons({translation: [0, 0, slices[0][0][2]],
        normalVector: CSG.Vector3D.Create(0, -1, 0), flipped: true}));
    polygons = polygons.concat(polygon(slices[slices.length-1])._toPlanePolygons({translation: [0, 0, slices[slices.length-1][0][2]],
        normalVector: CSG.Vector3D.Create(0, 1, 0), flipped: false}));

    // walls
    for (var i = 0; i < slices.length-1; i++) {
        var a = slices[i];
        var b = slices[i+1];
        if (a.length!=b.length) throw new Error("All paths for slice_extrude must have the same number of points");
        var k = a.length-1;
        for (var j=0;j<a.length;j++) {
            polygons.push(new CSG.Polygon([
                new CSG.Vertex(new CSG.Vector3D(b[k])), 
                new CSG.Vertex(new CSG.Vector3D(b[j])), 
                new CSG.Vertex(new CSG.Vector3D(a[j]))]));
            polygons.push(new CSG.Polygon([
                new CSG.Vertex(new CSG.Vector3D(b[k])), 
                new CSG.Vertex(new CSG.Vector3D(a[j])), 
                new CSG.Vertex(new CSG.Vector3D(a[k]))]));
            k=j;
        }
    }

    return CSG.fromPolygons(polygons);
}



function main() { 
    var s = [];
    for (var i=0;i<1;i+=0.05) {
      var p = koch({
          rotate:i,
          radius:(4-Math.cos(i*Math.PI))*12.5,
          circle:1-i,
          z:i*100,
          spread:i});
      //s.push(translate([0,0,i*2],linear_extrude({ height: 0.1 },polygon({ points: p })))); 
      s.push(p);
    }
    return slice_extrude(s);
    //return union(pts.map(function(xy) { return CSG.cube({center:[xy[0],xy[1],0], radius: [1, 1, 1]}) }));
    return s;
}