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// The ray tracer code in this file is written by Adam Burmister. It
// is available in its original form from:
//
//
// It has been modified slightly by Google to work as a standalone
// benchmark, but the all the computational code remains
// untouched. This file also contains a copy of parts of the Prototype
// JavaScript framework which is used by the ray tracer.
var RayTrace = new BenchmarkSuite('RayTrace', [739989], [
new Benchmark('RayTrace', true, false, 600, renderScene)
]);
// Variable used to hold a number that can be used to verify that
// the scene was ray traced correctly.
var checkNumber;
// ------------------------------------------------------------------------
// ------------------------------------------------------------------------
// The following is a copy of parts of the Prototype JavaScript library:
// Prototype JavaScript framework, version 1.5.0
// (c) 2005-2007 Sam Stephenson
//
// Prototype is freely distributable under the terms of an MIT-style license.
var Class = {
create: function() {
return function() {
this.initialize.apply(this, arguments);
}
}
};
Object.extend = function(destination, source) {
for (var property in source) {
destination[property] = source[property];
}
return destination;
};
// ------------------------------------------------------------------------
// ------------------------------------------------------------------------
// The rest of this file is the actual ray tracer written by Adam
// Burmister. It's a concatenation of the following files:
//
// flog/color.js
// flog/light.js
// flog/vector.js
// flog/ray.js
// flog/scene.js
// flog/material/basematerial.js
// flog/material/solid.js
// flog/material/chessboard.js
// flog/shape/baseshape.js
// flog/shape/sphere.js
// flog/shape/plane.js
// flog/intersectioninfo.js
// flog/camera.js
// flog/background.js
// flog/engine.js
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
Flog.RayTracer.Color = Class.create();
Flog.RayTracer.Color.prototype = {
red : 0.0,
green : 0.0,
blue : 0.0,
initialize : function(r, g, b) {
if(!r) r = 0.0;
if(!g) g = 0.0;
if(!b) b = 0.0;
this.red = r;
this.green = g;
this.blue = b;
},
add : function(c1, c2){
var result = new Flog.RayTracer.Color(0,0,0);
result.red = c1.red + c2.red;
result.green = c1.green + c2.green;
result.blue = c1.blue + c2.blue;
return result;
},
addScalar: function(c1, s){
var result = new Flog.RayTracer.Color(0,0,0);
result.red = c1.red + s;
result.green = c1.green + s;
result.blue = c1.blue + s;
result.limit();
return result;
},
subtract: function(c1, c2){
var result = new Flog.RayTracer.Color(0,0,0);
result.red = c1.red - c2.red;
result.green = c1.green - c2.green;
result.blue = c1.blue - c2.blue;
return result;
},
multiply : function(c1, c2) {
var result = new Flog.RayTracer.Color(0,0,0);
result.red = c1.red * c2.red;
result.green = c1.green * c2.green;
result.blue = c1.blue * c2.blue;
return result;
},
multiplyScalar : function(c1, f) {
var result = new Flog.RayTracer.Color(0,0,0);
result.red = c1.red * f;
result.green = c1.green * f;
result.blue = c1.blue * f;
return result;
},
divideFactor : function(c1, f) {
var result = new Flog.RayTracer.Color(0,0,0);
result.red = c1.red / f;
result.green = c1.green / f;
result.blue = c1.blue / f;
return result;
},
limit: function(){
this.red = (this.red > 0.0) ? ( (this.red > 1.0) ? 1.0 : this.red ) : 0.0;
this.green = (this.green > 0.0) ? ( (this.green > 1.0) ? 1.0 : this.green ) : 0.0;
this.blue = (this.blue > 0.0) ? ( (this.blue > 1.0) ? 1.0 : this.blue ) : 0.0;
},
distance : function(color) {
var d = Math.abs(this.red - color.red) + Math.abs(this.green - color.green) + Math.abs(this.blue - color.blue);
return d;
},
blend: function(c1, c2, w){
var result = new Flog.RayTracer.Color(0,0,0);
result = Flog.RayTracer.Color.prototype.add(
Flog.RayTracer.Color.prototype.multiplyScalar(c1, 1 - w),
Flog.RayTracer.Color.prototype.multiplyScalar(c2, w)
);
return result;
},
brightness : function() {
var r = Math.floor(this.red*255);
var g = Math.floor(this.green*255);
var b = Math.floor(this.blue*255);
return (r * 77 + g * 150 + b * 29) >> 8;
},
toString : function () {
var r = Math.floor(this.red*255);
var g = Math.floor(this.green*255);
var b = Math.floor(this.blue*255);
return "rgb("+ r +","+ g +","+ b +")";
}
}
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
Flog.RayTracer.Light = Class.create();
Flog.RayTracer.Light.prototype = {
position: null,
color: null,
intensity: 10.0,
initialize : function(pos, color, intensity) {
this.position = pos;
this.color = color;
this.intensity = (intensity ? intensity : 10.0);
},
toString : function () {
return 'Light [' + this.position.x + ',' + this.position.y + ',' + this.position.z + ']';
}
}
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
Flog.RayTracer.Vector = Class.create();
Flog.RayTracer.Vector.prototype = {
x : 0.0,
y : 0.0,
z : 0.0,
initialize : function(x, y, z) {
this.x = (x ? x : 0);
this.y = (y ? y : 0);
this.z = (z ? z : 0);
},
copy: function(vector){
this.x = vector.x;
this.y = vector.y;
this.z = vector.z;
},
normalize : function() {
var m = this.magnitude();
return new Flog.RayTracer.Vector(this.x / m, this.y / m, this.z / m);
},
magnitude : function() {
return Math.sqrt((this.x * this.x) + (this.y * this.y) + (this.z * this.z));
},
cross : function(w) {
return new Flog.RayTracer.Vector(
-this.z * w.y + this.y * w.z,
this.z * w.x - this.x * w.z,
-this.y * w.x + this.x * w.y);
},
dot : function(w) {
return this.x * w.x + this.y * w.y + this.z * w.z;
},
add : function(v, w) {
return new Flog.RayTracer.Vector(w.x + v.x, w.y + v.y, w.z + v.z);
},
subtract : function(v, w) {
if(!w || !v) throw 'Vectors must be defined [' + v + ',' + w + ']';
return new Flog.RayTracer.Vector(v.x - w.x, v.y - w.y, v.z - w.z);
},
multiplyVector : function(v, w) {
return new Flog.RayTracer.Vector(v.x * w.x, v.y * w.y, v.z * w.z);
},
multiplyScalar : function(v, w) {
return new Flog.RayTracer.Vector(v.x * w, v.y * w, v.z * w);
},
toString : function () {
return 'Vector [' + this.x + ',' + this.y + ',' + this.z + ']';
}
}
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
Flog.RayTracer.Ray = Class.create();
Flog.RayTracer.Ray.prototype = {
position : null,
direction : null,
initialize : function(pos, dir) {
this.position = pos;
this.direction = dir;
},
toString : function () {
return 'Ray [' + this.position + ',' + this.direction + ']';
}
}
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
Flog.RayTracer.Scene = Class.create();
Flog.RayTracer.Scene.prototype = {
camera : null,
shapes : [],
lights : [],
background : null,
initialize : function() {
this.camera = new Flog.RayTracer.Camera(
new Flog.RayTracer.Vector(0,0,-5),
new Flog.RayTracer.Vector(0,0,1),
new Flog.RayTracer.Vector(0,1,0)
);
this.shapes = new Array();
this.lights = new Array();
this.background = new Flog.RayTracer.Background(new Flog.RayTracer.Color(0,0,0.5), 0.2);
}
}
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
if(typeof(Flog.RayTracer.Material) == 'undefined') Flog.RayTracer.Material = {};
Flog.RayTracer.Material.BaseMaterial = Class.create();
Flog.RayTracer.Material.BaseMaterial.prototype = {
gloss: 2.0, // [0...infinity] 0 = matt
transparency: 0.0, // 0=opaque
reflection: 0.0, // [0...infinity] 0 = no reflection
refraction: 0.50,
hasTexture: false,
initialize : function() {
},
getColor: function(u, v){
},
wrapUp: function(t){
t = t % 2.0;
if(t < -1) t += 2.0;
if(t >= 1) t -= 2.0;
return t;
},
toString : function () {
return 'Material [gloss=' + this.gloss + ', transparency=' + this.transparency + ', hasTexture=' + this.hasTexture +']';
}
}
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
Flog.RayTracer.Material.Solid = Class.create();
Flog.RayTracer.Material.Solid.prototype = Object.extend(
new Flog.RayTracer.Material.BaseMaterial(), {
initialize : function(color, reflection, refraction, transparency, gloss) {
this.color = color;
this.reflection = reflection;
this.transparency = transparency;
this.gloss = gloss;
this.hasTexture = false;
},
getColor: function(u, v){
return this.color;
},
toString : function () {
return 'SolidMaterial [gloss=' + this.gloss + ', transparency=' + this.transparency + ', hasTexture=' + this.hasTexture +']';
}
}
);
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
Flog.RayTracer.Material.Chessboard = Class.create();
Flog.RayTracer.Material.Chessboard.prototype = Object.extend(
new Flog.RayTracer.Material.BaseMaterial(), {
colorEven: null,
colorOdd: null,
density: 0.5,
initialize : function(colorEven, colorOdd, reflection, transparency, gloss, density) {
this.colorEven = colorEven;
this.colorOdd = colorOdd;
this.reflection = reflection;
this.transparency = transparency;
this.gloss = gloss;
this.density = density;
this.hasTexture = true;
},
getColor: function(u, v){
var t = this.wrapUp(u * this.density) * this.wrapUp(v * this.density);
if(t < 0.0)
return this.colorEven;
else
return this.colorOdd;
},
toString : function () {
return 'ChessMaterial [gloss=' + this.gloss + ', transparency=' + this.transparency + ', hasTexture=' + this.hasTexture +']';
}
}
);
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
if(typeof(Flog.RayTracer.Shape) == 'undefined') Flog.RayTracer.Shape = {};
Flog.RayTracer.Shape.Sphere = Class.create();
Flog.RayTracer.Shape.Sphere.prototype = {
initialize : function(pos, radius, material) {
this.radius = radius;
this.position = pos;
this.material = material;
},
intersect: function(ray){
var info = new Flog.RayTracer.IntersectionInfo();
info.shape = this;
var dst = Flog.RayTracer.Vector.prototype.subtract(ray.position, this.position);
var B = dst.dot(ray.direction);
var C = dst.dot(dst) - (this.radius * this.radius);
var D = (B * B) - C;
if(D > 0){ // intersection!
info.isHit = true;
info.distance = (-B) - Math.sqrt(D);
info.position = Flog.RayTracer.Vector.prototype.add(
ray.position,
Flog.RayTracer.Vector.prototype.multiplyScalar(
ray.direction,
info.distance
)
);
info.normal = Flog.RayTracer.Vector.prototype.subtract(
info.position,
this.position
).normalize();
info.color = this.material.getColor(0,0);
} else {
info.isHit = false;
}
return info;
},
toString : function () {
return 'Sphere [position=' + this.position + ', radius=' + this.radius + ']';
}
}
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
if(typeof(Flog.RayTracer.Shape) == 'undefined') Flog.RayTracer.Shape = {};
Flog.RayTracer.Shape.Plane = Class.create();
Flog.RayTracer.Shape.Plane.prototype = {
d: 0.0,
initialize : function(pos, d, material) {
this.position = pos;
this.d = d;
this.material = material;
},
intersect: function(ray){
var info = new Flog.RayTracer.IntersectionInfo();
var Vd = this.position.dot(ray.direction);
if(Vd == 0) return info; // no intersection
var t = -(this.position.dot(ray.position) + this.d) / Vd;
if(t <= 0) return info;
info.shape = this;
info.isHit = true;
info.position = Flog.RayTracer.Vector.prototype.add(
ray.position,
Flog.RayTracer.Vector.prototype.multiplyScalar(
ray.direction,
t
)
);
info.normal = this.position;
info.distance = t;
if(this.material.hasTexture){
var vU = new Flog.RayTracer.Vector(this.position.y, this.position.z, -this.position.x);
var vV = vU.cross(this.position);
var u = info.position.dot(vU);
var v = info.position.dot(vV);
info.color = this.material.getColor(u,v);
} else {
info.color = this.material.getColor(0,0);
}
return info;
},
toString : function () {
return 'Plane [' + this.position + ', d=' + this.d + ']';
}
}
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
Flog.RayTracer.IntersectionInfo = Class.create();
Flog.RayTracer.IntersectionInfo.prototype = {
isHit: false,
hitCount: 0,
shape: null,
position: null,
normal: null,
color: null,
distance: null,
initialize : function() {
this.color = new Flog.RayTracer.Color(0,0,0);
},
toString : function () {
return 'Intersection [' + this.position + ']';
}
}
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
Flog.RayTracer.Camera = Class.create();
Flog.RayTracer.Camera.prototype = {
position: null,
lookAt: null,
equator: null,
up: null,
screen: null,
initialize : function(pos, lookAt, up) {
this.position = pos;
this.lookAt = lookAt;
this.up = up;
this.equator = lookAt.normalize().cross(this.up);
this.screen = Flog.RayTracer.Vector.prototype.add(this.position, this.lookAt);
},
getRay: function(vx, vy){
var pos = Flog.RayTracer.Vector.prototype.subtract(
this.screen,
Flog.RayTracer.Vector.prototype.subtract(
Flog.RayTracer.Vector.prototype.multiplyScalar(this.equator, vx),
Flog.RayTracer.Vector.prototype.multiplyScalar(this.up, vy)
)
);
pos.y = pos.y * -1;
var dir = Flog.RayTracer.Vector.prototype.subtract(
pos,
this.position
);
var ray = new Flog.RayTracer.Ray(pos, dir.normalize());
return ray;
},
toString : function () {
return 'Ray []';
}
}
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
Flog.RayTracer.Background = Class.create();
Flog.RayTracer.Background.prototype = {
color : null,
ambience : 0.0,
initialize : function(color, ambience) {
this.color = color;
this.ambience = ambience;
}
}
/* Fake a Flog.* namespace */
if(typeof(Flog) == 'undefined') var Flog = {};
if(typeof(Flog.RayTracer) == 'undefined') Flog.RayTracer = {};
Flog.RayTracer.Engine = Class.create();
Flog.RayTracer.Engine.prototype = {
canvas: null, /* 2d context we can render to */
initialize: function(options){
this.options = Object.extend({
canvasHeight: 100,
canvasWidth: 100,
pixelWidth: 2,
pixelHeight: 2,
renderDiffuse: false,
renderShadows: false,
renderHighlights: false,
renderReflections: false,
rayDepth: 2
}, options || {});
this.options.canvasHeight /= this.options.pixelHeight;
this.options.canvasWidth /= this.options.pixelWidth;
/* TODO: dynamically include other scripts */
},
setPixel: function(x, y, color){
var pxW, pxH;
pxW = this.options.pixelWidth;
pxH = this.options.pixelHeight;
if (this.canvas) {
this.canvas.fillStyle = color.toString();
this.canvas.fillRect (x * pxW, y * pxH, pxW, pxH);
} else {
if (x === y) {
checkNumber += color.brightness();
}
// print(x * pxW, y * pxH, pxW, pxH);
}
},
renderScene: function(scene, canvas){
checkNumber = 0;
/* Get canvas */
if (canvas) {
this.canvas = canvas.getContext("2d");
} else {
this.canvas = null;
}
var canvasHeight = this.options.canvasHeight;
var canvasWidth = this.options.canvasWidth;
for(var y=0; y < canvasHeight; y++){
for(var x=0; x < canvasWidth; x++){
var yp = y * 1.0 / canvasHeight * 2 - 1;
var xp = x * 1.0 / canvasWidth * 2 - 1;
var ray = scene.camera.getRay(xp, yp);
var color = this.getPixelColor(ray, scene);
this.setPixel(x, y, color);
}
}
if (checkNumber !== 2321) {
throw new Error("Scene rendered incorrectly");
}
},
getPixelColor: function(ray, scene){
var info = this.testIntersection(ray, scene, null);
if(info.isHit){
var color = this.rayTrace(info, ray, scene, 0);
return color;
}
return scene.background.color;
},
testIntersection: function(ray, scene, exclude){
var hits = 0;
var best = new Flog.RayTracer.IntersectionInfo();
best.distance = 2000;
for(var i=0; i<scene.shapes.length; i++){
var shape = scene.shapes[i];
if(shape != exclude){
var info = shape.intersect(ray);
if(info.isHit && info.distance >= 0 && info.distance < best.distance){
best = info;
hits++;
}
}
}
best.hitCount = hits;
return best;
},
getReflectionRay: function(P,N,V){
var c1 = -N.dot(V);
var R1 = Flog.RayTracer.Vector.prototype.add(
Flog.RayTracer.Vector.prototype.multiplyScalar(N, 2*c1),
V
);
return new Flog.RayTracer.Ray(P, R1);
},
rayTrace: function(info, ray, scene, depth){
// Calc ambient
var color = Flog.RayTracer.Color.prototype.multiplyScalar(info.color, scene.background.ambience);
var oldColor = color;
var shininess = Math.pow(10, info.shape.material.gloss + 1);
for(var i=0; i<scene.lights.length; i++){
var light = scene.lights[i];
// Calc diffuse lighting
var v = Flog.RayTracer.Vector.prototype.subtract(
light.position,
info.position
).normalize();
if(this.options.renderDiffuse){
var L = v.dot(info.normal);
if(L > 0.0){
color = Flog.RayTracer.Color.prototype.add(
color,
Flog.RayTracer.Color.prototype.multiply(
info.color,
Flog.RayTracer.Color.prototype.multiplyScalar(
light.color,
L
)
)
);
}
}
// The greater the depth the more accurate the colours, but
// this is exponentially (!) expensive
if(depth <= this.options.rayDepth){
// calculate reflection ray
if(this.options.renderReflections && info.shape.material.reflection > 0)
{
var reflectionRay = this.getReflectionRay(info.position, info.normal, ray.direction);
var refl = this.testIntersection(reflectionRay, scene, info.shape);
if (refl.isHit && refl.distance > 0){
refl.color = this.rayTrace(refl, reflectionRay, scene, depth + 1);
} else {
refl.color = scene.background.color;
}
color = Flog.RayTracer.Color.prototype.blend(
color,
refl.color,
info.shape.material.reflection
);
}
// Refraction
/* TODO */
}
/* Render shadows and highlights */
var shadowInfo = new Flog.RayTracer.IntersectionInfo();
if(this.options.renderShadows){
var shadowRay = new Flog.RayTracer.Ray(info.position, v);
shadowInfo = this.testIntersection(shadowRay, scene, info.shape);
if(shadowInfo.isHit && shadowInfo.shape != info.shape /*&& shadowInfo.shape.type != 'PLANE'*/){
var vA = Flog.RayTracer.Color.prototype.multiplyScalar(color, 0.5);
var dB = (0.5 * Math.pow(shadowInfo.shape.material.transparency, 0.5));
color = Flog.RayTracer.Color.prototype.addScalar(vA,dB);
}
}
// Phong specular highlights
if(this.options.renderHighlights && !shadowInfo.isHit && info.shape.material.gloss > 0){
var Lv = Flog.RayTracer.Vector.prototype.subtract(
info.shape.position,
light.position
).normalize();
var E = Flog.RayTracer.Vector.prototype.subtract(
scene.camera.position,
info.shape.position
).normalize();
var H = Flog.RayTracer.Vector.prototype.subtract(
E,
Lv
).normalize();
var glossWeight = Math.pow(Math.max(info.normal.dot(H), 0), shininess);
color = Flog.RayTracer.Color.prototype.add(
Flog.RayTracer.Color.prototype.multiplyScalar(light.color, glossWeight),
color
);
}
}
color.limit();
return color;
}
};
function renderScene(){
var scene = new Flog.RayTracer.Scene();
scene.camera = new Flog.RayTracer.Camera(
new Flog.RayTracer.Vector(0, 0, -15),
new Flog.RayTracer.Vector(-0.2, 0, 5),
new Flog.RayTracer.Vector(0, 1, 0)
);
scene.background = new Flog.RayTracer.Background(
new Flog.RayTracer.Color(0.5, 0.5, 0.5),
0.4
);
var sphere = new Flog.RayTracer.Shape.Sphere(
new Flog.RayTracer.Vector(-1.5, 1.5, 2),
1.5,
new Flog.RayTracer.Material.Solid(
new Flog.RayTracer.Color(0,0.5,0.5),
0.3,
0.0,
0.0,
2.0
)
);
var sphere1 = new Flog.RayTracer.Shape.Sphere(
new Flog.RayTracer.Vector(1, 0.25, 1),
0.5,
new Flog.RayTracer.Material.Solid(
new Flog.RayTracer.Color(0.9,0.9,0.9),
0.1,
0.0,
0.0,
1.5
)
);
var plane = new Flog.RayTracer.Shape.Plane(
new Flog.RayTracer.Vector(0.1, 0.9, -0.5).normalize(),
1.2,
new Flog.RayTracer.Material.Chessboard(
new Flog.RayTracer.Color(1,1,1),
new Flog.RayTracer.Color(0,0,0),
0.2,
0.0,
1.0,
0.7
)
);
scene.shapes.push(plane);
scene.shapes.push(sphere);
scene.shapes.push(sphere1);
var light = new Flog.RayTracer.Light(
new Flog.RayTracer.Vector(5, 10, -1),
new Flog.RayTracer.Color(0.8, 0.8, 0.8)
);
var light1 = new Flog.RayTracer.Light(
new Flog.RayTracer.Vector(-3, 5, -15),
new Flog.RayTracer.Color(0.8, 0.8, 0.8),
100
);
scene.lights.push(light);
scene.lights.push(light1);
var imageWidth = 100; // $F('imageWidth');
var imageHeight = 100; // $F('imageHeight');
var pixelSize = "5,5".split(','); // $F('pixelSize').split(',');
var renderDiffuse = true; // $F('renderDiffuse');
var renderShadows = true; // $F('renderShadows');
var renderHighlights = true; // $F('renderHighlights');
var renderReflections = true; // $F('renderReflections');
var rayDepth = 2;//$F('rayDepth');
var raytracer = new Flog.RayTracer.Engine(
{
canvasWidth: imageWidth,
canvasHeight: imageHeight,
pixelWidth: pixelSize[0],
pixelHeight: pixelSize[1],
"renderDiffuse": renderDiffuse,
"renderHighlights": renderHighlights,
"renderShadows": renderShadows,
"renderReflections": renderReflections,
"rayDepth": rayDepth
}
);
raytracer.renderScene(scene, null, 0);
}