Reflection Symmetry

thingiverse

Goto https://shapejs.shapeways.com and use this script. // Example of generalized kaleidoscope. // The idea is similar to traditional kaleidoscope, // which consists of 3 flat mirrors with dihedral angles 60 degree. // One can place an arbitrary object inside such a kaleidoscope // and reflections in the mirrors create infinite repeating pattern. // Here, we use spherical mirrors instead of flat ones. // Reflections in spherical mirrors are inversions in spheres. // Diagonal angle between sphere and plane is integer multiple of PI or 180 degrees. // If that's true, the reflections form regular patterns. // Pattern can be wildly complex. In this case, we have // four mirrors: two flat and two spherical mirrors. They create a disk with scale down pattern. var voxelSize = 0.1 * MM; function getQuad(r,r1,alpha) { var r2 = r*r1 * Math.cos(alpha); var x1 = Math.sqrt(r1r1 + r*r); var y2 = Math.sqrt(r2r2 + r*r); var splanes = new Array(); var count = 0; splanes[count++] = new ReflectionSymmetry.getPlane(new Vector3d(0,-1,0), 0.0); splanes[count++] = new ReflectionSymmetry.getPlane(new Vector3d(-1,0,0), 0.0); splanes[count++] = new ReflectionSymmetry.getSphere(new Vector3d(x1,0,0), -r1); splanes[count++] = new ReflectionSymmetry.getSphere(new Vector3d(0,y2,0), -r2); return splanes; } function makePart(size, thickness) { var t = (thickness / 2) * 1.5; var s = size / 2; var g = createGrid(-t,t,-t,t,-s,s,voxelSize); var boxZ = new Box(0,0,0,thickness,thickness,size); var mm = new GridMaker(); mm.setSource(boxZ); mm.setMaxAttributeValue(255); mm.makeGrid(g); return g; } function makePartG(size, thickness) { var part = makePart(size,thickness); part.setTransform(new Rotation(new Vector3d(-1,1,0), 3 * Math.PI / 8)); return part; } function main() { var a = 25.0; var voxelSize = 0.5; var cz = 20; var cx = 5; var cy = 5 * MM; var dest = makePartG(30, 5); var maker = new GridMaker(); maker.setSource(dest); var t1 = createGrid(-a,a,-a,a,-a,a,voxelSize); return t1;