Summary

Reflection Symmetry example using ShapeJS

Instructions

Goto shapejs.shapeways.,com and us 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 objects inside of
// such kaleidoscope and reflections in the mirrors create infinite repeating pattern.
// Here in addition to usual flat mirrors we use spherical mirrors. "Reflections" in spherical mirrors are
// inversion in the spheres.
// If dihedral angles between spheres and planes is integer submultiple of the half turn (PI or 180 degrees)
// the reflections in such mirros form regular pattern.
// The type of pattern created by such kaleidoscope can be wildly complex.
// In this case we have 4 mirrors: 2 flat mirros and 2 spherical mirrors. The mirrors are placed in such a ways, that
// the pattern scales down near the boundary of a disk. It resembles a tiling of 2D hyperbolic plane in Poincare disk model
// with important difference that our pattern is three dimensional.
//

var voxelSize = 0.2*MM;

function getQuad_1( r, r1, alpha){
var r2 = rr/(r1Math.cos(alpha));
var x1 = Math.sqrt(r1r1 + rr);
var y2 = Math.sqrt(r2r2 + rr);

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_g(size, thickness){
var t = (thickness/2) 1.5;
var s = size/2;
//var g = createGrid(-t, t, -t, t, -s, s,voxelSize);
var b = 20MM;
var g = createGrid(-b,b,-b,b,-b,b,0.5*MM);

var boxZ = new Box(0,0,0,thickness, thickness, size);

var mm = new GridMaker();
mm.setSource(boxZ);
mm.setMaxAttributeValue(255);
mm.makeGrid(g);

var gmm = new GridMipMap(g);

gmm.setScalingType(GridMipMap.SCALING_AVERAGE);
//gmm.setScalingType(GridMipMap.SCALING_MAX);

return gmm;
}

function makePart(size, thickeness){
var union = new Union();
var boxX = new Box(0,0,0,thickeness, thickeness, size);
union.add(boxX);
return union;
}

function main(){
var a = 25MM;
var voxelSize = 0.1MM;
var cz = 20.0MM;
var cx = 5.0MM;
var cy = 5.0*MM;

var part = makePart_g(30MM, 5MM);
part.setTransform(new Rotation(new Vector3d(-1,1,0), 3*Math.PI/8));

var dt = new DataTransformer();
dt.setSource(part);

var sym = new ReflectionSymmetry(getQuad_1(25MM, 30MM, Math.PI/3));
sym.setMaxCount(50);

dt.setTransform(sym);

var maker = new GridMaker();
maker.setSource(dt);
var dest = createGrid(-a,a,-a,a,-a,a,voxelSize);
maker.makeGrid(dest);

return dest;
}