Summary

This is a tealight created with ShapeJS. Sized to accept standard LED lights. The code takes an image and tiles it around a sphere to make interesting patterns.

Instructions

Goto shapejs.shapeways.com and use this code. It takes one file parameter which is the image to tile around the sphere.

//
// Tealight example using polyhedra reflection
//
// author Vladimir Bulatov
// author Alan Hudson
//
var TAU = (Math.sqrt(5)+1)/2; // golden ratio
var PI = Math.PI;

// Returns plane via 3 points (v1, 0, v2)
// external normal points in the direction from where points are ordered counter clockwise
function getPlane(v1,v2){
var n = new Vector3d();
n.cross(v2,v1);
n.normalize();
return ReflectionSymmetry.getPlane(n, 0);
}

function getIcosahedralSymmetry( ){
var v5 = new Vector3d(1,0,TAU); // vertex of icosahedron
var v3 = new Vector3d(0,1/TAU,TAU); // vertex of dodecahedron
var p35 = new Vector3d(); // normal to plane via (0, v3, v5)

p35.cross(v3, v5);   p35.normalize();  var splanes = new Array();  var count = 0;  splanes[count++] = new ReflectionSymmetry.getPlane(new Vector3d(-1,0,0), 0.);  splanes[count++] = new ReflectionSymmetry.getPlane(new Vector3d(0,-1,0), 0.);  splanes[count++] = new ReflectionSymmetry.getPlane(p35, 0.);  return new ReflectionSymmetry(splanes);

}

function getSphereBend(fixedRadius, bendAmount, offset){

var center = fixedRadius*fixedRadius/bendAmount;  var radius = Math.sqrt(center*center + fixedRadius*fixedRadius);  var cp = new CompositeTransform();  cp.add(new PlaneReflection(new Vector3d(0,0,1), new Vector3d(0,0,offset)));  cp.add(new SphereInversion(new Vector3d(0,0,-center + offset), radius));  return cp;

}

function getImage(radius, thickness, path){

var s = radius/Math.sqrt(1 + 1./(TAU*TAU));  var v5 = new Vector3d(s/TAU,0,s); // vertex of icosahedron   var v3 = new Vector3d(0,s/(TAU*TAU),s); // vertex of dodecahedron   var union = new Union();  var correction = 1.1; // correction to get  var ypnt = v3.y*correction;  var xpnt = v5.x;  var image = new ImageBitmap(path, xpnt, ypnt, thickness);  var vs = 0.1*MM;  image.setBaseThickness(0);  image.setVoxelSize(vs);  image.setUseGrayscale(false);  image.setBlurWidth(vs);  image.setTransform(new Translation(xpnt/2,ypnt/2,v5.z));  union.add(image);  union.setTransform(getSphereBend(v5.x, radius - v5.z, v5.z));  var dt = new DataTransformer();  dt.setSource(union);  return dt;

}

// Create a hole for the tea light to be placed through
function getLightHole(hole,outside) {
var cyl = new Cylinder(new Vector3d(0,0,0), new Vector3d(0,-outside,0), hole);

return cyl;

}

// Create a rim around the light hole
function getRim(hole,radius,thickness) {
var cr = hole + thickness;

// Calculate intersection location of cylinder with sphere  var loc = -radius +(radius - Math.sqrt(radius * radius - cr * cr)) - thickness;  var outer = new Cylinder(new Vector3d(0,loc,0), new Vector3d(0,loc-thickness,0), hole + thickness);  var inner = new Cylinder(new Vector3d(0,loc,0), new Vector3d(0,loc-thickness,0), hole);  var rim = new Subtraction(outer,inner);  return rim;

}

function main(arg){

var radius = 31.1*MM;     var thickness = 1.0*MM;   var voxelSize = 0.2*MM;  var holeRadius = 20*MM;  // a bit larger then a typical 1.5" / 38.1mm tea light  var rimThickness = 1.25*MM;  var a = radius + 2*thickness;  var path = arg[0];  var image = getImage(radius,thickness, path,voxelSize);  var reflectedImage = new Union();  reflectedImage.add(image);  reflectedImage.setTransform(getIcosahedralSymmetry( ));  var subtract = new Subtraction(reflectedImage, getLightHole(holeRadius,a));  var rim = getRim(holeRadius,radius,rimThickness);  var tealight = new Union(subtract, rim);  var maker = new GridMaker();  maker.setSource(tealight);  var dest = createGrid(-a,a,-a,a,-a,a,voxelSize);  maker.makeGrid(dest);  return dest;

}

Reflection Tealight