ShapeJS

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//
// 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( r, r1, alpha){

var r2 = r*r/(r1*Math.cos(alpha));
    var x1 = Math.sqrt(r1*r1 + r*r);
    var y2 = Math.sqrt(r2*r2 + 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, thickeness){

var union = new Union();

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

function main(args){

var a = 25*MM;

var voxelSize = 0.1*MM;

var cz = 20.0*MM;
    var cx = 5.0*MM;
    var cy = 5.0*MM;

var part = makePart(30*MM, 5*MM);

part.setTransform(new Rotation(new Vector3d(-1,1,0), 3*Math.PI/8));

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

var sym = new ReflectionSymmetry(getQuad(25*MM, 30*MM, Math.PI/3));

sym.set("riemannSphereRadius", a);

shape.setTransform(sym);

return new Scene(shape, new Bounds(-a,a,-a,a,-a,a,voxelSize));

}