Reflection Symmetry

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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; }