fractals.js

//----------------------------------------------------------------------------
//
// Global Variables
//
var canvas = null;

var numLevels = 0;

var fractalSelected = 0;

var gl = null; // WebGL context

var shaderProgram = null;

var triangleVertexPositionBuffer = null;
	
var triangleVertexNormalBuffer = null;		//NEW

// The GLOBAL transformation parameters

var globalAngleYY = 0.0;

var globalTz = 0.0;

// The local transformation parameters

// The translation vector

var tx = 0.0;

var ty = 0.0;

var tz = 0.0;

// The rotation angles in degrees

var angleXX = -22.5;

var angleYY = 16.0;

var angleZZ = 0.0;

// The scaling factors

var sx = 0.5;

var sy = 0.5;

var sz = 0.5;

// GLOBAL Animation controls

var globalRotationYY_ON = 1;

var globalRotationYY_DIR = 1;

var globalRotationYY_SPEED = 1;

// Local Animation controls

var rotationXX_ON = 0;

var rotationXX_DIR = 1;

var rotationXX_SPEED = 1;
 
var rotationYY_ON = 0;

var rotationYY_DIR = 1;

var rotationYY_SPEED = 1;
 
var rotationZZ_ON = 0;

var rotationZZ_DIR = 1;

var rotationZZ_SPEED = 1;
 
// To allow choosing the way of drawing the model triangles

var primitiveType = null;
 
// To allow choosing the projection type

var projectionType = 0;

// NEW --- The viewer position

// It has to be updated according to the projection type

var pos_Viewer = [ 0.0, 0.0, 0.0, 1.0 ];

// NEW --- Point Light Source Features

// Directional --- Homogeneous coordinate is ZERO

var pos_Light_Source = [ 0.0, 0.0, 1.0, 0.0 ];

// White light

var int_Light_Source = [ 1.0, 1.0, 1.0 ];

// Low ambient illumination

var ambient_Illumination = [ 0.3, 0.3, 0.3 ];

// NEW --- Model Material Features

// Ambient coef.

var kAmbi = [ 0.2, 0.2, 0.2 ];

// Diffuse coef.

var kDiff = [ 0.2, 0.48, 0.72 ]; // COLOR

// Specular coef.

var kSpec = [ 0.0, 0.0, 0.0 ];

// Phong coef.

var nPhong = 100;

// Initial model has just ONE TRIANGLE

var vertices = [ ];

var normals = [ ];


//----------------------------------------------------------------------------
//
// The WebGL code
//

//----------------------------------------------------------------------------
//
//  Rendering
//

// Handling the Vertex Coordinates and the Vertex Normal Vectors

function initBuffers() {	
	
	switch(fractalSelected) {
		case 0 : 
			computeSierpinskiGasket();
			break;
	
		case 1 : 
			computeKochSnowflake();
			break;
		
		case 2 :
			computeMosely();
			break;

		case 3 : 
			computeMengerSponge();
			break;
		
		case 4 :
			computeJerusalemCube();
			break;
			
		case 5 :
			computeCantorDust();
			break;
	}
	
	triangleVertexPositionBuffer = gl.createBuffer();
	gl.bindBuffer(gl.ARRAY_BUFFER, triangleVertexPositionBuffer);
	gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(vertices), gl.STATIC_DRAW);
	triangleVertexPositionBuffer.itemSize = 3;
	triangleVertexPositionBuffer.numItems = vertices.length / 3;			

	// Associating to the vertex shader
	
	gl.vertexAttribPointer(shaderProgram.vertexPositionAttribute, 
			triangleVertexPositionBuffer.itemSize, 
			gl.FLOAT, false, 0, 0);
	
	// Vertex Normal Vectors
		
	triangleVertexNormalBuffer = gl.createBuffer();
	gl.bindBuffer(gl.ARRAY_BUFFER, triangleVertexNormalBuffer);
	gl.bufferData(gl.ARRAY_BUFFER, new Float32Array(normals), gl.STATIC_DRAW);
	triangleVertexNormalBuffer.itemSize = 3;
	triangleVertexNormalBuffer.numItems = normals.length / 3;			

	// Associating to the vertex shader
	
	gl.vertexAttribPointer(shaderProgram.vertexNormalAttribute, 
			triangleVertexNormalBuffer.itemSize, 
			gl.FLOAT, false, 0, 0);	
}

//----------------------------------------------------------------------------

//  Drawing the model

function drawModel( angleXX, angleYY, angleZZ, 
					sx, sy, sz,
					tx, ty, tz,
					mvMatrix,
					primitiveType ) {

	// The the global model transformation is an input
	
	// Concatenate with the particular model transformations
	
    // Pay attention to transformation order !!
    
	mvMatrix = mult( mvMatrix, translationMatrix( tx, ty, tz ) );
						 
	mvMatrix = mult( mvMatrix, rotationZZMatrix( angleZZ ) );
	
	mvMatrix = mult( mvMatrix, rotationYYMatrix( angleYY ) );
	
	mvMatrix = mult( mvMatrix, rotationXXMatrix( angleXX ) );
	
	mvMatrix = mult( mvMatrix, scalingMatrix( sx, sy, sz ) );
						 
	// Passing the Model View Matrix to apply the current transformation
	
	var mvUniform = gl.getUniformLocation(shaderProgram, "uMVMatrix");
	
	gl.uniformMatrix4fv(mvUniform, false, new Float32Array(flatten(mvMatrix)));
    
    // Multiplying the reflection coefficents
    
    var ambientProduct = mult( kAmbi, ambient_Illumination );
    
    var diffuseProduct = mult( kDiff, int_Light_Source );
    
    var specularProduct = mult( kSpec, int_Light_Source );
    
	// Associating the data to the vertex shader
	
	// This can be done in a better way !!

	// Vertex Coordinates and Vertex Normal Vectors
	
	initBuffers();
	
	// Partial illumonation terms and shininess Phong coefficient
	
	gl.uniform3fv( gl.getUniformLocation(shaderProgram, "ambientProduct"), 
		flatten(ambientProduct) );
    
    gl.uniform3fv( gl.getUniformLocation(shaderProgram, "diffuseProduct"),
        flatten(diffuseProduct) );
    
    gl.uniform3fv( gl.getUniformLocation(shaderProgram, "specularProduct"),
        flatten(specularProduct) );

	gl.uniform1f( gl.getUniformLocation(shaderProgram, "shininess"), 
		nPhong );

	//Position of the Light Source
	
	gl.uniform4fv( gl.getUniformLocation(shaderProgram, "lightPosition"),
        flatten(pos_Light_Source) );

	// Drawing 
	
	// primitiveType allows drawing as filled triangles / wireframe / vertices
	
	if( primitiveType == gl.LINE_LOOP ) {
		
		// To simulate wireframe drawing!
		
		// No faces are defined! There are no hidden lines!
		
		// Taking the vertices 3 by 3 and drawing a LINE_LOOP
		
		var i;
		
		for( i = 0; i < triangleVertexPositionBuffer.numItems / 3; i++ ) {
		
			gl.drawArrays( primitiveType, 3 * i, 3 ); 
		}
	}	
	else {
				
		gl.drawArrays(primitiveType, 0, triangleVertexPositionBuffer.numItems); 
		
	}	
}

//----------------------------------------------------------------------------

//  Drawing the 3D scene

function drawScene() {
	
	var pMatrix;
	
	var mvMatrix = mat4();
	
	// Clearing the frame-buffer and the depth-buffer
	
	gl.clear(gl.COLOR_BUFFER_BIT | gl.DEPTH_BUFFER_BIT);
	
	// Computing the Projection Matrix
	
	if( projectionType == 0 ) {
		
		// For now, the default orthogonal view volume
		
		pMatrix = ortho( -1.0, 1.0, -1.0, 1.0, -1.0, 1.0 );
		
		// Global transformation !!
		
		globalTz = 0.0;
		
		// NEW --- The viewer is on the ZZ axis at an indefinite distance
		
		pos_Viewer[0] = pos_Viewer[1] = pos_Viewer[3] = 0.0;
		
		pos_Viewer[2] = 1.0;  
		
		// TO BE DONE !
		
		// Allow the user to control the size of the view volume
	}
	else {	

		// A standard view volume.
		
		// Viewer is at (0,0,0)
		
		// Ensure that the model is "inside" the view volume
		
		pMatrix = perspective( 45, 1, 0.05, 15 );
		
		// Global transformation !!
		
		globalTz = -2.5;

		// NEW --- The viewer is on (0,0,0)
		
		pos_Viewer[0] = pos_Viewer[1] = pos_Viewer[2] = 0.0;
		
		pos_Viewer[3] = 1.0;  
		
		// TO BE DONE !
		
		// Allow the user to control the size of the view volume
	}
	
	// Passing the Projection Matrix to apply the current projection
	
	var pUniform = gl.getUniformLocation(shaderProgram, "uPMatrix");
	
	gl.uniformMatrix4fv(pUniform, false, new Float32Array(flatten(pMatrix)));
	
	// NEW --- Passing the viewer position to the vertex shader
	
	gl.uniform4fv( gl.getUniformLocation(shaderProgram, "viewerPosition"),
        flatten(pos_Viewer) );
	
	// GLOBAL TRANSFORMATION FOR THE WHOLE SCENE
	
	mvMatrix = translationMatrix( 0, 0, globalTz );
	
	// Instantianting the current model
		
	drawModel( angleXX, angleYY, angleZZ, 
	           sx, sy, sz,
	           tx, ty, tz,
	           mvMatrix,
	           primitiveType );
}

//----------------------------------------------------------------------------
//
//  NEW --- Animation
//

// Animation --- Updating transformation parameters

var lastTime = 0;

function animate() {
	
	var timeNow = new Date().getTime();
	
	if( lastTime != 0 ) {
		
		var elapsed = timeNow - lastTime;
		
		// Global rotation
		
		if( globalRotationYY_ON ) {

			globalAngleYY += globalRotationYY_DIR * globalRotationYY_SPEED * (90 * elapsed) / 1000.0;
	    }

		// Local rotations
		
		if( rotationXX_ON ) {

			angleXX += rotationXX_DIR * rotationXX_SPEED * (90 * elapsed) / 1000.0;
	    }

		if( rotationYY_ON ) {

			angleYY += rotationYY_DIR * rotationYY_SPEED * (90 * elapsed) / 1000.0;
	    }

		if( rotationZZ_ON ) {

			angleZZ += rotationZZ_DIR * rotationZZ_SPEED * (90 * elapsed) / 1000.0;
	    }
	}
	
	lastTime = timeNow;
}


//----------------------------------------------------------------------------

// Timer

function tick() {
	
	requestAnimFrame(tick);
	
	drawScene();
	
	animate();
}




//----------------------------------------------------------------------------
//
//  User Interaction
//

function outputInfos(){
    
}

function updateColor(color) {

	color = '#' + color;

	var r = hexToR(color);
	var g = hexToG(color);
	var b = hexToB(color);

	r /= 255;
	g /= 255;
	b /= 255;

	kDiff = [r, g, b];
}

// Hex to RGB Parser
// Retired from: http://www.javascripter.net/faq/hextorgb.htm

function hexToR(h) {return parseInt((cutHex(h)).substring(0,2),16)}
function hexToG(h) {return parseInt((cutHex(h)).substring(2,4),16)}
function hexToB(h) {return parseInt((cutHex(h)).substring(4,6),16)}
function cutHex(h) {return (h.charAt(0)=="#") ? h.substring(1,7):h}

//----------------------------------------------------------------------------

//----------------------------------------------------------------------------

// Handling mouse events

// Adapted from www.learningwebgl.com


var mouseDown = false;

var lastMouseX = null;

var lastMouseY = null;

function handleMouseDown(event) {
    
    mouseDown = true;
  
    lastMouseX = event.clientX;
  
    lastMouseY = event.clientY;
}

function handleMouseUp(event) {

    mouseDown = false;
}

function handleMouseMove(event) {

    if (!mouseDown) {
      
      return;
    } 
  
    // Rotation angles proportional to cursor displacement
    
    var newX = event.clientX;
  
    var newY = event.clientY;

    var deltaX = newX - lastMouseX;
    
    angleYY += radians( 10 * deltaX  );

    var deltaY = newY - lastMouseY;
    
    angleXX += radians( 10 * deltaY  );
    
    lastMouseX = newX;
    
    lastMouseY = newY;
}

function setEventListeners() {

	// Dropdown list
	
	var list = document.getElementById("rendering-mode-selection");
	
	list.addEventListener("click", function(){
				
		// Getting the selection
		
		var mode = list.selectedIndex;
				
		switch(mode){
			
			case 0 : primitiveType = gl.TRIANGLES;
				break;
			
			case 1 : primitiveType = gl.LINE_LOOP;
				break;
			
			case 2 : primitiveType = gl.POINTS;
				break;
		}
	});

	var projectionList = document.getElementById("projection-selection");
	
	projectionList.addEventListener("click", function(){
				
		// Getting the selection
		
		var p = projectionList.selectedIndex;
		
		switch(p){
			
			case 0 : projectionType = 0;
				break;
			
			case 1 : projectionType = 1;
				break;
		}  
	});
	
	var fractalList = document.getElementById("fractal-selection");
	
	fractalList.addEventListener("click", function(){
				
		// Getting the selection
		
		var mode = fractalList.selectedIndex;
				
		switch(mode){
			
			case 0 : 
				fractalSelected = 0;
				computeSierpinskiGasket();
				break;
			
			case 1 : 
				fractalSelected = 1;
				computeKochSnowflake();
				break;
			
			case 2 :
				fractalSelected = 2;
				computeMosely();
				break;

			case 3 : 
				fractalSelected = 3;
				computeMengerSponge();
				break;
			
			case 4 :
				fractalSelected = 4;
				computeJerusalemCube();
				break;
			
			case 5 :
				fractalSelected = 5;
				computeCantorDust();
				break;
		}
		
	});   

	// Button events
	
	document.getElementById("XX-on-off-button").onclick = function(){
		
		// Switching on / off
		
		if( rotationXX_ON ) {
			
			rotationXX_ON = 0;
		}
		else {
			
			rotationXX_ON = 1;
		}  
	};

	document.getElementById("XX-direction-button").onclick = function(){
		
		// Switching the direction
		
		if( rotationXX_DIR == 1 ) {
			
			rotationXX_DIR = -1;
		}
		else {
			
			rotationXX_DIR = 1;
		}  
	};      

	document.getElementById("XX-slower-button").onclick = function(){
		
		rotationXX_SPEED *= 0.75;  
	};      

	document.getElementById("XX-faster-button").onclick = function(){
		
		rotationXX_SPEED *= 1.25;  
	};      

	document.getElementById("YY-on-off-button").onclick = function(){
		
		// Switching on / off
		
		if( rotationYY_ON ) {
			
			rotationYY_ON = 0;
		}
		else {
			
			rotationYY_ON = 1;
		}  
	};

	document.getElementById("YY-direction-button").onclick = function(){
		
		// Switching the direction
		
		if( rotationYY_DIR == 1 ) {
			
			rotationYY_DIR = -1;
		}
		else {
			
			rotationYY_DIR = 1;
		}  
	};      

	document.getElementById("YY-slower-button").onclick = function(){
		
		rotationYY_SPEED *= 0.75;  
	};      

	document.getElementById("YY-faster-button").onclick = function(){
		
		rotationYY_SPEED *= 1.25;  
	};      

	document.getElementById("ZZ-on-off-button").onclick = function(){
		
		// Switching on / off
		
		if( rotationZZ_ON ) {
			
			rotationZZ_ON = 0;
		}
		else {
			
			rotationZZ_ON = 1;
		}  
	};

	document.getElementById("ZZ-direction-button").onclick = function(){
		
		// Switching the direction
		
		if( rotationZZ_DIR == 1 ) {
			
			rotationZZ_DIR = -1;
		}
		else {
			
			rotationZZ_DIR = 1;
		}  
	};      

	document.getElementById("ZZ-slower-button").onclick = function(){
		
		rotationZZ_SPEED *= 0.75;  
	};      

	document.getElementById("ZZ-faster-button").onclick = function(){
		
		rotationZZ_SPEED *= 1.25;  
	};      

	document.getElementById("reset-button").onclick = function(){
		
		// The initial values

		// The translation vector

		tx = 0.0;

		ty = 0.0;

		tz = 0.0;

		// The rotation angles in degrees

		angleXX = -22.5;

		angleYY = 16.0;

		angleZZ = 0.0;

		// The scaling factors

		sx = 0.5;

		sy = 0.5;

		sz = 0.5;
		
		// Local Animation controls

		rotationXX_ON = 0;

		rotationXX_DIR = 1;

		rotationXX_SPEED = 1;
		
		rotationYY_ON = 0;

		rotationYY_DIR = 1;

		rotationYY_SPEED = 1;
		
		rotationZZ_ON = 0;

		rotationZZ_DIR = 1;

		rotationZZ_SPEED = 1;
		
		projectionType = 0;

		kDiff = [ 0.2, 0.48, 0.72 ]; // COLOR

		initBuffers();
	};

	document.getElementById("add-recursion-button").onclick = function(){
		numLevels = numLevels+1;
		document.getElementById("num-iterations").innerHTML = numLevels;

		switch(fractalSelected) {
			case 0 : 
			computeSierpinskiGasket();
			break;
		
			case 1 : 
				computeKochSnowflake();
				break;
			
			case 2 :
				computeMosely();
				break;

			case 3 : 
				computeMengerSponge();
				break;
			
			case 4 :
				computeJerusalemCube();
				break;
			
			case 5 :
				computeCantorDust();
				break;

		}

		initBuffers();
	}; 

	document.getElementById("reduce-recursion-button").onclick = function(){
		if (numLevels > 0){
			numLevels = numLevels-1;
			document.getElementById("num-iterations").innerHTML = numLevels;
		}
		initBuffers();
	};

	canvas.onmousedown = handleMouseDown;
    
    document.onmouseup = handleMouseUp;
    
	document.onmousemove = handleMouseMove;
	
	// Roda do rato
	canvas.addEventListener('wheel', function(event) {

		//document.onwheel = function(){ return false; }

		if(event.deltaY > 0) {
			// Aproxima
			if (sx <= 0.1) {
				sx = 0.1;
				sy = 0.1;
				sz = 0.1;
			} else {
				sx -= 0.1;
				sy -= 0.1;
				sz -= 0.1;
			}
		} 
		else {
			// Afasta
			if (sx >= 1) {
				sx = 0.9;
				sy = 0.9;
				sz = 0.9;
			} else {
				sx += 0.1;
				sy += 0.1;
				sz += 0.1;
			}
		}

		drawScene();
	}, false);

	/* document.getElementById('fractalControls').onwheel = function() { 
		console.log('fractalControls');
		return true; 
	} */
}

function preventDefault(e) {
	e = e || window.event;
	if (e.preventDefault)
		e.preventDefault();
	e.returnValue = false;
}

function disableScroll() {
	if (window.addEventListener) // older FF
		window.addEventListener('DOMMouseScroll', preventDefault, false);
	window.onwheel = preventDefault; // modern standard
	window.onmousewheel = document.onmousewheel = preventDefault; // older browsers, IE
	window.ontouchmove  = preventDefault; // mobile
}
  
function enableScroll() {
	if (window.removeEventListener)
		window.removeEventListener('DOMMouseScroll', preventDefault, false);
	window.onmousewheel = document.onmousewheel = null; 
	window.onwheel = null; 
	window.ontouchmove = null;  
	document.onkeydown = null;  
}

//----------------------------------------------------------------------------
//
// WebGL Initialization
//

function initWebGL( canvas ) {
	try {
		
		// Create the WebGL context
		
		// Some browsers still need "experimental-webgl"
		
		gl = canvas.getContext("webgl") || canvas.getContext("experimental-webgl");
		
		// DEFAULT: The viewport occupies the whole canvas 
		
		// DEFAULT: The viewport background color is WHITE
		
		// NEW - Drawing the triangles defining the model
		
		primitiveType = gl.TRIANGLES;
		
		// DEFAULT: Face culling is DISABLED
		
		// Enable FACE CULLING
		
		gl.enable( gl.CULL_FACE );
		
		// DEFAULT: The BACK FACE is culled!!
		
		// The next instruction is not needed...
		
		gl.cullFace( gl.BACK );
		
		// Enable DEPTH-TEST
		
		gl.enable( gl.DEPTH_TEST );
        
	} catch (e) {
	}
	if (!gl) {
		alert("Could not initialise WebGL, sorry! :-(");
	}        
}

//----------------------------------------------------------------------------

function runWebGL() {
	
	canvas = document.getElementById("my-canvas");
	
	initWebGL( canvas );

	shaderProgram = initShaders( gl );
	
	setEventListeners();
	
	initBuffers();
	
	tick();		// NEW --- A timer controls the rendering / animation    

	outputInfos();
}


//----------------------------------------------------------------------------
// The fractal code
//----------------------------------------------------------------------------

function computeSierpinskiGasket() {
    var v1 = [ -1.0,  0.0, -0.707 ];
    var v2 = [  0.0,  1.0,  0.707 ];
    var v3 = [  1.0,  0.0, -0.707 ];
    var v4 = [  0.0, -1.0,  0.707 ];

	vertices = [];
	normals = [];
	divideTetrahedron(v1, v2, v3, v4, numLevels);
	computeVertexNormals(vertices, normals);
    //vertices = flatten( vertices );
}

function divideTetrahedron(v1, v2, v3, v4, recursionLevel) {
	if (recursionLevel == 0) {
		var coordinatesToAdd = [].concat(v1, v2, v3,
            v3, v2, v4,
            v4, v2, v1,
            v1, v3, v4);
        for (var i = 0; i < 36; i += 1) {
            vertices.push(coordinatesToAdd[i]);
        }
	}
	else {
		var vertex12 = computeMidPoint(v1, v2);
		var vertex13 = computeMidPoint(v1, v3);
		var vertex14 = computeMidPoint(v1, v4);
		var vertex23 = computeMidPoint(v2, v3);
		var vertex24 = computeMidPoint(v2, v4);
		var vertex34 = computeMidPoint(v3, v4);

		recursionLevel--;

		divideTetrahedron(v1, vertex12, vertex13, vertex14, recursionLevel);
		divideTetrahedron(vertex12, v2, vertex23, vertex24, recursionLevel);
		divideTetrahedron(vertex13, vertex23, v3, vertex34, recursionLevel);
		divideTetrahedron(vertex14, vertex24, vertex34, v4, recursionLevel);
	}
}

//--------------------------------------------------------------------//
// Tetrahedron Koch Snowflake

function computeKochSnowflake() {
		
		// Initial vertices of the Tetrahedron
		
		
		var v1 = [ -1.0,  0.0, -0.707 ];
		var v2 = [  0.0,  1.0,  0.707 ];
		var v3 = [  1.0,  0.0, -0.707 ];
		var v4 = [  0.0, -1.0,  0.707 ];
      	  
		// Clearing the vertices array;
		
		vertices = [];
		normals = [];
		//var face1 = [ v1, v2, v3 ];
		//var face2 = [v3, v2, v4]
        //var face3 = [v4, v2, v1]
        //var face4 = [v1, v3, v4]
		divideFace( v1, v2, v3,  numLevels );
		
		divideFace( v3, v2, v4, numLevels );

		divideFace( v4, v2, v1, numLevels );
		
		divideFace( v1, v3, v4, numLevels );
		
		addVertexes ( v1, v2, v3, v4);
		computeVertexNormals(vertices, normals);
		
	}
	
function computeHeightofTriangle(side)
{
	var result = side / 2;
	result = result * Math.sqrt(3);
	return result;
}
	
function divideFace( v1, v2, v3, n )
	{
		if ( n == 0 ) {
			return;
		}
		
		else {
    
			// Compute new v
			
			var va = computeMidPoint( v1, v2);
				
			var vb = computeMidPoint( v2, v3);
			
			var vc = computeMidPoint( v1, v3);
			
			// Calculate the centroid
        
			var midpoint = computeCentroid( va, vb, vc );
			var normal;
			//Descobrir o vetor normal unitario a face 
			var normalVector = computeNormalVector( v1, v2, v3 );
			
			// Using the height of an equilateral triangle
			var height = computeHeightofTriangle(computeDistance(va, vb ));
			
			normalVector[0] = normalVector[0] * height;			
			normalVector[1] = normalVector[1] * height;	
			normalVector[2] = normalVector[2] * height;
			
			var vH = addVector(midpoint, normalVector);
			//console.log(normalVector);
			// TESTING
			
			//var v2 = midpoint;
			
			--n;

			// 4 new line segments
			divideFace( va, vb, vH, n );
			divideFace( va, vH, vc, n );			
			divideFace( vb, vc, vH, n );
			divideFace( vb, vc, vH, n );
			//divideFace( v1, va, vc, n );
			//divideFace( v2, vb, va, n );
			//divideFace( v3, vc, vb, n );

			addVertexes(vc, vb, va, vH);			
		}
	}
	
	function addVertexes ( v1, v2, v3, v4)
	{
		var coordinatesToAdd = [].concat(v1, v2, v3,
            v3, v2, v4,
            v4, v2, v1,
            v1, v3, v4);
        for (var i = 0; i < 36; i += 1) {
            vertices.push(coordinatesToAdd[i]);
        }
	}
	//-------------------------------------------------------------------//
	function addVector( u, v )
	{
		// No input checking!!
		
		var result = [];
		for ( var i = 0; i < u.length; ++i ) {
			result.push( u[i] + v[i] );
		}

		return result;
	}
	
	//----------------------------------------------------------------------------
//distancia entre dois pontos

function computeDistance (v1, v2)
{
	var aux = [v2[0]-v1[0], v2[1]-v1[1], v2[2]-v1[2]] 
	var squaresSum = aux[0] * aux[0] + aux[1] * aux[1] + aux[2] * aux[2];
    
    var res = Math.sqrt( squaresSum );
	
	return res;
}

//--------------------------------------------------------------------------------//
//Mosely snowflake																  //
//--------------------------------------------------------------------------------//
function computeMosely()
{
	//define cube
	// vertices do cubo
	 var v1 = [-1, -1, 1];       

    var v2 = [1, -1, 1];        
        
    var v3 = [1, 1, 1];     

    var v4 = [-1, 1, 1];        
    
    var v5 = [-1, -1, -1];  

    var v6 = [1, -1, -1];       

    var v7 = [1, 1, -1];        

    var v8 = [-1, 1, -1];
	
	vertices = [];
	normals = [];
	generateMosely(v1, v2, v3, v4, v5, v6, v7, v8, numLevels);
	computeVertexNormals(vertices, normals);
}

function defineCube(v1, v2, v3, v4, v5, v6, v7, v8)
{
	var toAdd = [].concat(v1, v2, v3,
                          v1, v3, v4,
                          v5, v8, v7,
                          v5, v7, v6,
                          v8, v4, v3,
                          v8, v3, v7,
                          v5, v6, v2,
                          v5, v2, v1,
                          v6, v7, v3,
                          v6, v3, v2,
                          v5, v1, v4,
                          v5, v4, v8);
        for (var i = 0; i < toAdd.length; i += 1) {
            vertices.push(toAdd[i]);
        }
}
// Auxiliary function for point interpolation --- Angel / Shreiner
	
function interpolate( u, v, s )
{
	// No imput checking!!
		
	var result = [];
	for ( var i = 0; i < u.length; ++i ) {
		result.push( (1.0 - s) * u[i] +  s * v[i] );
	}

	return result;
}
function generateMosely(v1, v2, v3, v4, v5, v6, v7, v8, n)
{
	if(n==0)
	{
		defineCube(v1, v2, v3, v4, v5, v6, v7, v8);
	}
	else
	{
		n = n - 1;
		
		var v12 = interpolate(v1, v2, 0.33);
		var v13 = interpolate(v1, v3, 0.33);
		var v14 = interpolate(v1, v4, 0.33);
		var v15 = interpolate(v1, v5, 0.33);
		var v16 = interpolate(v1, v6, 0.33);
		var v17 = interpolate(v1, v7, 0.33);
		var v18 = interpolate(v1, v8, 0.33);
		
		var v21 = interpolate(v2, v1, 0.33);
		var v23 = interpolate(v2, v3, 0.33);
		var v24 = interpolate(v2, v4, 0.33);
		var v25 = interpolate(v2, v5, 0.33);
		var v26 = interpolate(v2, v6, 0.33);
		var v27 = interpolate(v2, v7, 0.33);
		var v28 = interpolate(v2, v8, 0.33);
		
		var v31 = interpolate(v3, v1, 0.33);
		var v32 = interpolate(v3, v2, 0.33);
		var v34 = interpolate(v3, v4, 0.33);
		var v35 = interpolate(v3, v5, 0.33);
		var v36 = interpolate(v3, v6, 0.33);
		var v37 = interpolate(v3, v7, 0.33);
		var v38 = interpolate(v3, v8, 0.33);
		
		var v41 = interpolate(v4, v1, 0.33);
		var v42 = interpolate(v4, v2, 0.33);
		var v43 = interpolate(v4, v3, 0.33);
		var v45 = interpolate(v4, v5, 0.33);
		var v46 = interpolate(v4, v6, 0.33);
		var v47 = interpolate(v4, v7, 0.33);
		var v48 = interpolate(v4, v8, 0.33);
		
		var v51 = interpolate(v5, v1, 0.33);
		var v52 = interpolate(v5, v2, 0.33);
		var v53 = interpolate(v5, v3, 0.33);
		var v54 = interpolate(v5, v4, 0.33);
		var v56 = interpolate(v5, v6, 0.33);
		var v57 = interpolate(v5, v7, 0.33);
		var v58 = interpolate(v5, v8, 0.33);
		
		var v61 = interpolate(v6, v1, 0.33);
		var v62 = interpolate(v6, v2, 0.33);
		var v64 = interpolate(v6, v4, 0.33);
		var v65 = interpolate(v6, v5, 0.33);
		var v63 = interpolate(v6, v3, 0.33);
		var v67 = interpolate(v6, v7, 0.33);
		var v68 = interpolate(v6, v8, 0.33);
		
		var v71 = interpolate(v7, v1, 0.33);
		var v72 = interpolate(v7, v2, 0.33);
		var v74 = interpolate(v7, v4, 0.33);
		var v75 = interpolate(v7, v5, 0.33);
		var v76 = interpolate(v7, v6, 0.33);
		var v73 = interpolate(v7, v3, 0.33);
		var v78 = interpolate(v7, v8, 0.33);
		
		var v81 = interpolate(v8, v1, 0.33);
		var v82 = interpolate(v8, v2, 0.33);
		var v84 = interpolate(v8, v4, 0.33);
		var v85 = interpolate(v8, v5, 0.33);
		var v86 = interpolate(v8, v6, 0.33);
		var v87 = interpolate(v8, v7, 0.33);
		var v83 = interpolate(v8, v3, 0.33);
		
		
		//vertex # 	    1    2    3    4    5    6    7    8
		generateMosely(v12, v21, v24, v13, v16, v25, v28, v17, n);
		generateMosely(v24, v23, v32, v31, v28, v27, v36, v35, n);
		generateMosely(v42, v31, v34, v43, v46, v35, v38, v47, n);
		generateMosely(v14, v13, v42, v41, v18, v17, v46, v45, n);
		generateMosely(v13, v24, v31, v42, v17, v28, v35, v46, n);
			
		generateMosely(v52, v61, v64, v53, v56, v65, v68, v57, n);
		generateMosely(v64, v63, v72, v71, v68, v67, v76, v75, n);
		generateMosely(v82, v71, v74, v83, v86, v75, v78, v87, n);
		generateMosely(v54, v53, v82, v81, v58, v57, v86, v85, n);
		generateMosely(v53, v64, v71, v82, v57, v68, v75, v86, n);
		
		generateMosely(v15, v16, v17, v18, v51, v52, v53, v54, n);
		generateMosely(v25, v26, v27, v28, v61, v62, v63, v64, n);
		generateMosely(v16, v25, v28, v17, v52, v61, v64, v53, n);
		
		generateMosely(v35, v36, v37, v38, v71, v72, v73, v74, n);
		generateMosely(v45, v46, v47, v48, v81, v82, v83, v84, n);
		generateMosely(v46, v35, v38, v47, v82, v71, v74, v83, n); 
		
		generateMosely(v18, v17, v46, v45, v54, v53, v82, v81, n);
		
		generateMosely(v46, v35, v38, v47, v82, v71, v74, v83, n);
		generateMosely(v28, v27, v36, v35, v64, v63, v72, v71, n);	
	}
}


//--------------------------------------------------------------------//
// Cube Menger Sponge

function computeMengerSponge() {
	var v1 = [-1, -1, 1];       
	
	var v2 = [1, -1, 1];        
		
	var v3 = [1, 1, 1];     

	var v4 = [-1, 1, 1];        
	
	var v5 = [-1, -1, -1];  

	var v6 = [1, -1, -1];       

	var v7 = [1, 1, -1];        

	var v8 = [-1, 1, -1];
	
	vertices = [];
	normals = [];
	mengerSponge(v1, v2, v3, v4, v5, v6, v7, v8, numLevels);
	computeVertexNormals(vertices, normals);
}

function mengerSponge(v1, v2, v3, v4, v5, v6, v7, v8, recursionLevel) {	
	if(recursionLevel < 1) {
		defineCube(v1, v2, v3, v4, v5, v6, v7, v8);
	}
	else {
		recursionLevel--;
		
		// -- Divide every face into 9 equally sized squares --
		var distance = computeDistance(v3, v4);
		var newDistance = distance / 3;
		
		// Front face cubes
		var front_top_left_1 = [v3[0] - distance, v3[1] - newDistance, v3[2]];
		var front_top_left_2 = [v3[0] - (2*newDistance), v3[1] - newDistance, v3[2]];
		var front_top_left_3 = [v3[0] - (2*newDistance), v3[1], v3[2]];
		var front_top_left_4 = [v3[0] - distance, v3[1], v3[2]];
		var front_top_left_5 = [front_top_left_1[0], front_top_left_1[1], front_top_left_1[2] - newDistance];
		var front_top_left_6 = [front_top_left_2[0], front_top_left_2[1], front_top_left_2[2] - newDistance];
		var front_top_left_7 = [front_top_left_3[0], front_top_left_3[1], front_top_left_3[2] - newDistance];
		var front_top_left_8 = [front_top_left_4[0], front_top_left_4[1], front_top_left_4[2] - newDistance];

		var front_top_center_1 = front_top_left_2;
		var front_top_center_2 = [v3[0] - newDistance, v3[1]-newDistance, v3[2]];
		var front_top_center_3 = [v3[0] - newDistance, v3[1], v3[2]];
		var front_top_center_4 = front_top_left_3;
		var front_top_center_5 = [front_top_center_1[0], front_top_center_1[1], front_top_center_1[2] - newDistance];
		var front_top_center_6 = [front_top_center_2[0], front_top_center_2[1], front_top_center_2[2] - newDistance];
		var front_top_center_7 = [front_top_center_3[0], front_top_center_3[1], front_top_center_3[2] - newDistance];
		var front_top_center_8 = [front_top_center_4[0], front_top_center_4[1], front_top_center_4[2] - newDistance];

		
		var front_top_right_1 = front_top_center_2;
		var front_top_right_2 = [v3[0], v3[1]-newDistance, v3[2]];
		var front_top_right_3 = v3;
		var front_top_right_4 = front_top_center_3;
		var front_top_right_5 = [front_top_right_1[0], front_top_right_1[1], front_top_right_1[2] - newDistance];
		var front_top_right_6 = [front_top_right_2[0], front_top_right_2[1], front_top_right_2[2] - newDistance];
		var front_top_right_7 = [front_top_right_3[0], front_top_right_3[1], front_top_right_3[2] - newDistance];
		var front_top_right_8 = [front_top_right_4[0], front_top_right_4[1], front_top_right_4[2] - newDistance];

		var front_mid_left_1 = [v3[0] - distance, v3[1]-(2*newDistance), v3[2]];
		var front_mid_left_2 = [v3[0] - (2*newDistance), v3[1]-(2*newDistance), v3[2]];
		var front_mid_left_3 = front_top_left_2;
		var front_mid_left_4 = front_top_left_1;
		var front_mid_left_5 = [front_mid_left_1[0], front_mid_left_1[1], front_mid_left_1[2] - newDistance];
		var front_mid_left_6 = [front_mid_left_2[0], front_mid_left_2[1], front_mid_left_2[2] - newDistance];
		var front_mid_left_7 = [front_mid_left_3[0], front_mid_left_3[1], front_mid_left_3[2] - newDistance];
		var front_mid_left_8 = [front_mid_left_4[0], front_mid_left_4[1], front_mid_left_4[2] - newDistance];

		var front_mid_right_1 = [v3[0] - newDistance, v3[1]-(2*newDistance), v3[2]];
		var front_mid_right_2 = [v3[0], v3[1]-(2*newDistance), v3[2]];
		var front_mid_right_3 = front_top_right_2;
		var front_mid_right_4 = front_top_right_1;
		var front_mid_right_5 = [front_mid_right_1[0], front_mid_right_1[1], front_mid_right_1[2] - newDistance];
		var front_mid_right_6 = [front_mid_right_2[0], front_mid_right_2[1], front_mid_right_2[2] - newDistance];
		var front_mid_right_7 = [front_mid_right_3[0], front_mid_right_3[1], front_mid_right_3[2] - newDistance];
		var front_mid_right_8 = [front_mid_right_4[0], front_mid_right_4[1], front_mid_right_4[2] - newDistance];

		var front_bot_left_1 = [v1[0], v1[1], v1[2]];
		var front_bot_left_2 = [v1[0] + newDistance, v1[1], v1[2]];
		var front_bot_left_3 = front_mid_left_2;
		var front_bot_left_4 = front_mid_left_1;
		var front_bot_left_5 = [front_bot_left_1[0], front_bot_left_1[1], front_bot_left_1[2] - newDistance];
		var front_bot_left_6 = [front_bot_left_2[0], front_bot_left_2[1], front_bot_left_2[2] - newDistance];
		var front_bot_left_7 = [front_bot_left_3[0], front_bot_left_3[1], front_bot_left_3[2] - newDistance];
		var front_bot_left_8 = [front_bot_left_4[0], front_bot_left_4[1], front_bot_left_4[2] - newDistance];

		var front_bot_center_1 = front_bot_left_2;
		var front_bot_center_2 = [v1[0] + (2*newDistance), v1[1], v1[2]];
		var front_bot_center_3 = front_mid_right_1;
		var front_bot_center_4 = front_bot_left_3;
		var front_bot_center_5 = [front_bot_center_1[0], front_bot_center_1[1], front_bot_center_1[2] - newDistance];
		var front_bot_center_6 = [front_bot_center_2[0], front_bot_center_2[1], front_bot_center_2[2] - newDistance];
		var front_bot_center_7 = [front_bot_center_3[0], front_bot_center_3[1], front_bot_center_3[2] - newDistance];
		var front_bot_center_8 = [front_bot_center_4[0], front_bot_center_4[1], front_bot_center_4[2] - newDistance];

		var front_bot_right_1 = front_bot_center_2;
		var front_bot_right_2 = v2;
		var front_bot_right_3 = front_mid_right_2;
		var front_bot_right_4 = front_mid_right_1;
		var front_bot_right_5 = [front_bot_right_1[0], front_bot_right_1[1], front_bot_right_1[2] - newDistance];
		var front_bot_right_6 = [front_bot_right_2[0], front_bot_right_2[1], front_bot_right_2[2] - newDistance];
		var front_bot_right_7 = [front_bot_right_3[0], front_bot_right_3[1], front_bot_right_3[2] - newDistance];;
		var front_bot_right_8 = [front_bot_right_4[0], front_bot_right_4[1], front_bot_right_4[2] - newDistance];;

		// Mid cubes
		var mid_top_left_1 = front_top_left_5;
		var mid_top_left_2 = front_top_left_6;
		var mid_top_left_3 = front_top_left_7;
		var mid_top_left_4 = front_top_left_8;
		var mid_top_left_5 = [mid_top_left_1[0], mid_top_left_1[1], mid_top_left_1[2] - newDistance];
		var mid_top_left_6 = [mid_top_left_2[0], mid_top_left_2[1], mid_top_left_2[2] - newDistance];
		var mid_top_left_7 = [mid_top_left_3[0], mid_top_left_3[1], mid_top_left_3[2] - newDistance];
		var mid_top_left_8 = [mid_top_left_4[0], mid_top_left_4[1], mid_top_left_4[2] - newDistance];

		var mid_top_right_1 = front_top_right_5;
		var mid_top_right_2 = front_top_right_6;
		var mid_top_right_3 = front_top_right_7;
		var mid_top_right_4 = front_top_right_8;
		var mid_top_right_5 = [mid_top_right_1[0], mid_top_right_1[1], mid_top_right_1[2] - newDistance];
		var mid_top_right_6 = [mid_top_right_2[0], mid_top_right_2[1], mid_top_right_2[2] - newDistance];
		var mid_top_right_7 = [mid_top_right_3[0], mid_top_right_3[1], mid_top_right_3[2] - newDistance];
		var mid_top_right_8 = [mid_top_right_4[0], mid_top_right_4[1], mid_top_right_4[2] - newDistance];

		var mid_bot_left_1 = front_bot_left_5;
		var mid_bot_left_2 = front_bot_left_6;
		var mid_bot_left_3 = front_bot_left_7;
		var mid_bot_left_4 = front_bot_left_8;
		var mid_bot_left_5 = [mid_bot_left_1[0], mid_bot_left_1[1], mid_bot_left_1[2] - newDistance];
		var mid_bot_left_6 = [mid_bot_left_2[0], mid_bot_left_2[1], mid_bot_left_2[2] - newDistance];
		var mid_bot_left_7 = [mid_bot_left_3[0], mid_bot_left_3[1], mid_bot_left_3[2] - newDistance];
		var mid_bot_left_8 = [mid_bot_left_4[0], mid_bot_left_4[1], mid_bot_left_4[2] - newDistance];

		var mid_bot_right_1 = front_bot_right_5;
		var mid_bot_right_2 = front_bot_right_6;
		var mid_bot_right_3 = front_bot_right_7;
		var mid_bot_right_4 = front_bot_right_8;
		var mid_bot_right_5 = [mid_bot_right_1[0], mid_bot_right_1[1], mid_bot_right_1[2] - newDistance];
		var mid_bot_right_6 = [mid_bot_right_2[0], mid_bot_right_2[1], mid_bot_right_2[2] - newDistance];
		var mid_bot_right_7 = [mid_bot_right_3[0], mid_bot_right_3[1], mid_bot_right_3[2] - newDistance];
		var mid_bot_right_8 = [mid_bot_right_4[0], mid_bot_right_4[1], mid_bot_right_4[2] - newDistance];

		// Back cubes
		var back_top_left_1 = [front_top_left_1[0], front_top_left_1[1], front_top_left_1[2]-(2*newDistance)];
		var back_top_left_2 = [front_top_left_2[0], front_top_left_2[1], front_top_left_2[2]-(2*newDistance)];
		var back_top_left_3 = [front_top_left_3[0], front_top_left_3[1], front_top_left_3[2]-(2*newDistance)];
		var back_top_left_4 = [front_top_left_4[0], front_top_left_4[1], front_top_left_4[2]-(2*newDistance)];
		var back_top_left_5 = [back_top_left_1[0], back_top_left_1[1], back_top_left_1[2] - newDistance];
		var back_top_left_6 = [back_top_left_2[0], back_top_left_2[1], back_top_left_2[2] - newDistance];
		var back_top_left_7 = [back_top_left_3[0], back_top_left_3[1], back_top_left_3[2] - newDistance];
		var back_top_left_8 = [back_top_left_4[0], back_top_left_4[1], back_top_left_4[2] - newDistance];

		var back_top_center_1 = [front_top_center_1[0], front_top_center_1[1], front_top_center_1[2]-(2*newDistance)];
		var back_top_center_2 = [front_top_center_2[0], front_top_center_2[1], front_top_center_2[2]-(2*newDistance)];
		var back_top_center_3 = [front_top_center_3[0], front_top_center_3[1], front_top_center_3[2]-(2*newDistance)];
		var back_top_center_4 = [front_top_center_4[0], front_top_center_4[1], front_top_center_4[2]-(2*newDistance)];
		var back_top_center_5 = [back_top_center_1[0], back_top_center_1[1], back_top_center_1[2] - newDistance];
		var back_top_center_6 = [back_top_center_2[0], back_top_center_2[1], back_top_center_2[2] - newDistance];
		var back_top_center_7 = [back_top_center_3[0], back_top_center_3[1], back_top_center_3[2] - newDistance];
		var back_top_center_8 = [back_top_center_4[0], back_top_center_4[1], back_top_center_4[2] - newDistance];

		var back_top_right_1 = [front_top_right_1[0], front_top_right_1[1], front_top_right_1[2]-(2*newDistance)];
		var back_top_right_2 = [front_top_right_2[0], front_top_right_2[1], front_top_right_2[2]-(2*newDistance)];
		var back_top_right_3 = [front_top_right_3[0], front_top_right_3[1], front_top_right_3[2]-(2*newDistance)];
		var back_top_right_4 = [front_top_right_4[0], front_top_right_4[1], front_top_right_4[2]-(2*newDistance)];
		var back_top_right_5 = [back_top_right_1[0], back_top_right_1[1], back_top_right_1[2] - newDistance];
		var back_top_right_6 = [back_top_right_2[0], back_top_right_2[1], back_top_right_2[2] - newDistance];
		var back_top_right_7 = [back_top_right_3[0], back_top_right_3[1], back_top_right_3[2] - newDistance];
		var back_top_right_8 = [back_top_right_4[0], back_top_right_4[1], back_top_right_4[2] - newDistance];

		var back_mid_left_1 = [front_mid_left_1[0], front_mid_left_1[1], front_mid_left_1[2]-(2*newDistance)];
		var back_mid_left_2 = [front_mid_left_2[0], front_mid_left_2[1], front_mid_left_2[2]-(2*newDistance)];
		var back_mid_left_3 = [front_mid_left_3[0], front_mid_left_3[1], front_mid_left_3[2]-(2*newDistance)];
		var back_mid_left_4 = [front_mid_left_4[0], front_mid_left_4[1], front_mid_left_4[2]-(2*newDistance)];
		var back_mid_left_5 = [back_mid_left_1[0], back_mid_left_1[1], back_mid_left_1[2] - newDistance];
		var back_mid_left_6 = [back_mid_left_2[0], back_mid_left_2[1], back_mid_left_2[2] - newDistance];
		var back_mid_left_7 = [back_mid_left_3[0], back_mid_left_3[1], back_mid_left_3[2] - newDistance];
		var back_mid_left_8 = [back_mid_left_4[0], back_mid_left_4[1], back_mid_left_4[2] - newDistance];

		var back_mid_right_1 = [front_mid_right_1[0], front_mid_right_1[1], front_mid_right_1[2]-(2*newDistance)];
		var back_mid_right_2 = [front_mid_right_2[0], front_mid_right_2[1], front_mid_right_2[2]-(2*newDistance)];
		var back_mid_right_3 = [front_mid_right_3[0], front_mid_right_3[1], front_mid_right_3[2]-(2*newDistance)];
		var back_mid_right_4 = [front_mid_right_4[0], front_mid_right_4[1], front_mid_right_4[2]-(2*newDistance)];
		var back_mid_right_5 = [back_mid_right_1[0], back_mid_right_1[1], back_mid_right_1[2] - newDistance];
		var back_mid_right_6 = [back_mid_right_2[0], back_mid_right_2[1], back_mid_right_2[2] - newDistance];
		var back_mid_right_7 = [back_mid_right_3[0], back_mid_right_3[1], back_mid_right_3[2] - newDistance];
		var back_mid_right_8 = [back_mid_right_4[0], back_mid_right_4[1], back_top_right_4[2] - newDistance];

		var back_bot_left_1 = [front_bot_left_1[0], front_bot_left_1[1], front_bot_left_1[2]-(2*newDistance)];
		var back_bot_left_2 = [front_bot_left_2[0], front_bot_left_2[1], front_bot_left_2[2]-(2*newDistance)];
		var back_bot_left_3 = [front_bot_left_3[0], front_bot_left_3[1], front_bot_left_3[2]-(2*newDistance)];
		var back_bot_left_4 = [front_bot_left_4[0], front_bot_left_4[1], front_bot_left_4[2]-(2*newDistance)];
		var back_bot_left_5 = [back_bot_left_1[0], back_bot_left_1[1], back_bot_left_1[2] - newDistance];
		var back_bot_left_6 = [back_bot_left_2[0], back_bot_left_2[1], back_bot_left_2[2] - newDistance];
		var back_bot_left_7 = [back_bot_left_3[0], back_bot_left_3[1], back_bot_left_3[2] - newDistance];
		var back_bot_left_8 = [back_bot_left_4[0], back_bot_left_4[1], back_bot_left_4[2] - newDistance];

		var back_bot_center_1 = [front_bot_center_1[0], front_bot_center_1[1], front_bot_center_1[2]-(2*newDistance)];
		var back_bot_center_2 = [front_bot_center_2[0], front_bot_center_2[1], front_bot_center_2[2]-(2*newDistance)];
		var back_bot_center_3 = [front_bot_center_3[0], front_bot_center_3[1], front_bot_center_3[2]-(2*newDistance)];
		var back_bot_center_4 = [front_bot_center_4[0], front_bot_center_4[1], front_bot_center_4[2]-(2*newDistance)];
		var back_bot_center_5 = [back_bot_center_1[0], back_bot_center_1[1], back_bot_center_1[2] - newDistance];
		var back_bot_center_6 = [back_bot_center_2[0], back_bot_center_2[1], back_bot_center_2[2] - newDistance];
		var back_bot_center_7 = [back_bot_center_3[0], back_bot_center_3[1], back_bot_center_3[2] - newDistance];
		var back_bot_center_8 = [back_bot_center_4[0], back_bot_center_4[1], back_bot_center_4[2] - newDistance];

		var back_bot_right_1 = [front_bot_right_1[0], front_bot_right_1[1], front_bot_right_1[2]-(2*newDistance)];
		var back_bot_right_2 = [front_bot_right_2[0], front_bot_right_2[1], front_bot_right_2[2]-(2*newDistance)];
		var back_bot_right_3 = [front_bot_right_3[0], front_bot_right_3[1], front_bot_right_3[2]-(2*newDistance)];
		var back_bot_right_4 = [front_bot_right_4[0], front_bot_right_4[1], front_bot_right_4[2]-(2*newDistance)];
		var back_bot_right_5 = [back_bot_right_1[0], back_bot_right_1[1], back_bot_right_1[2] - newDistance];
		var back_bot_right_6 = [back_bot_right_2[0], back_bot_right_2[1], back_bot_right_2[2] - newDistance];
		var back_bot_right_7 = [back_bot_right_3[0], back_bot_right_3[1], back_bot_right_3[2] - newDistance];
		var back_bot_right_8 = [back_bot_right_4[0], back_bot_right_4[1], back_bot_right_4[2] - newDistance];

		mengerSponge(front_top_left_1, front_top_left_2, front_top_left_3, front_top_left_4, front_top_left_5, front_top_left_6, front_top_left_7, front_top_left_8, recursionLevel);
		mengerSponge(front_top_center_1, front_top_center_2, front_top_center_3, front_top_center_4, front_top_center_5, front_top_center_6, front_top_center_7, front_top_center_8, recursionLevel);
		mengerSponge(front_top_right_1, front_top_right_2, front_top_right_3, front_top_right_4, front_top_right_5, front_top_right_6, front_top_right_7, front_top_right_8, recursionLevel);
		mengerSponge(front_mid_left_1, front_mid_left_2, front_mid_left_3, front_mid_left_4, front_mid_left_5, front_mid_left_6, front_mid_left_7, front_mid_left_8, recursionLevel);
		mengerSponge(front_mid_right_1, front_mid_right_2, front_mid_right_3, front_mid_right_4, front_mid_right_5, front_mid_right_6, front_mid_right_7, front_mid_right_8, recursionLevel);
		mengerSponge(front_bot_left_1, front_bot_left_2, front_bot_left_3, front_bot_left_4, front_bot_left_5, front_bot_left_6, front_bot_left_7, front_bot_left_8, recursionLevel);
 		mengerSponge(front_bot_center_1, front_bot_center_2, front_bot_center_3, front_bot_center_4, front_bot_center_5, front_bot_center_6, front_bot_center_7, front_bot_center_8, recursionLevel);
		mengerSponge(front_bot_right_1, front_bot_right_2, front_bot_right_3, front_bot_right_4, front_bot_right_5, front_bot_right_6, front_bot_right_7, front_bot_right_8, recursionLevel);

		mengerSponge(mid_top_right_1, mid_top_right_2, mid_top_right_3, mid_top_right_4, mid_top_right_5, mid_top_right_6, mid_top_right_7, mid_top_right_8, recursionLevel);
		mengerSponge(mid_top_left_1, mid_top_left_2, mid_top_left_3, mid_top_left_4, mid_top_left_5, mid_top_left_6, mid_top_left_7, mid_top_left_8, recursionLevel);
		mengerSponge(mid_bot_left_1, mid_bot_left_2, mid_bot_left_3, mid_bot_left_4, mid_bot_left_5, mid_bot_left_6, mid_bot_left_7, mid_bot_left_8, recursionLevel);
		mengerSponge(mid_bot_right_1, mid_bot_right_2, mid_bot_right_3, mid_bot_right_4, mid_bot_right_5, mid_bot_right_6, mid_bot_right_7, mid_bot_right_8, recursionLevel);
 
		mengerSponge(back_top_left_1, back_top_left_2, back_top_left_3, back_top_left_4, back_top_left_5, back_top_left_6, back_top_left_7, back_top_left_8, recursionLevel);
		mengerSponge(back_top_center_1, back_top_center_2, back_top_center_3, back_top_center_4, back_top_center_5, back_top_center_6, back_top_center_7, back_top_center_8, recursionLevel);
		mengerSponge(back_top_right_1, back_top_right_2, back_top_right_3, back_top_right_4, back_top_right_5, back_top_right_6, back_top_right_7, back_top_right_8, recursionLevel);
		mengerSponge(back_mid_left_1, back_mid_left_2, back_mid_left_3, back_mid_left_4, back_mid_left_5, back_mid_left_6, back_mid_left_7, back_mid_left_8, recursionLevel);
		mengerSponge(back_mid_right_1, back_mid_right_2, back_mid_right_3, back_mid_right_4, back_mid_right_5, back_mid_right_6, back_mid_right_7, back_mid_right_8, recursionLevel);
		mengerSponge(back_bot_left_1, back_bot_left_2, back_bot_left_3, back_bot_left_4, back_bot_left_5, back_bot_left_6, back_bot_left_7, back_bot_left_8, recursionLevel);
		mengerSponge(back_bot_center_1, back_bot_center_2, back_bot_center_3, back_bot_center_4, back_bot_center_5, back_bot_center_6, back_bot_center_7, back_bot_center_8, recursionLevel);
		mengerSponge(back_bot_right_1, back_bot_right_2, back_bot_right_3, back_bot_right_4, back_bot_right_5, back_bot_right_6, back_bot_right_7, back_bot_right_8, recursionLevel);
 
	}
}

function computeJerusalemCube() {
	var v1 = [-1, -1, 1];       
	
	var v2 = [1, -1, 1];        
		
	var v3 = [1, 1, 1];     

	var v4 = [-1, 1, 1];        
	
	var v5 = [-1, -1, -1];  

	var v6 = [1, -1, -1];       

	var v7 = [1, 1, -1];        

	var v8 = [-1, 1, -1];
	
	vertices = [];
	normals = [];
	jerusalemCube(v1, v2, v3, v4, v5, v6, v7, v8, numLevels);
	computeVertexNormals(vertices, normals);
}

function jerusalemCube(v1, v2, v3, v4, v5, v6, v7, v8, recursionLevel) {
	if(recursionLevel < 1) {
		defineCube(v1, v2, v3, v4, v5, v6, v7, v8);
	}
	else {
		recursionLevel--;
	
		var distance = computeDistance(v3, v4);
		var smallCube = (1/6) * distance;
		var bigCube = (distance - smallCube)/2;

		// Front face cubes
		var front_top_left_1 = [v4[0], v4[1] - bigCube, v4[2]];
		var front_top_left_2 = [v4[0] + bigCube, v4[1] - bigCube, v4[2]];
		var front_top_left_3 = [v4[0] + bigCube, v4[1], v4[2]];
		var front_top_left_4 = v4;
		var front_top_left_5 = [front_top_left_1[0], front_top_left_1[1], front_top_left_1[2] - bigCube];
		var front_top_left_6 = [front_top_left_2[0], front_top_left_2[1], front_top_left_2[2] - bigCube];
		var front_top_left_7 = [front_top_left_3[0], front_top_left_3[1], front_top_left_3[2] - bigCube];
		var front_top_left_8 = [front_top_left_4[0], front_top_left_4[1], front_top_left_4[2] - bigCube];

		var front_top_center_1 = [v4[0] + bigCube, v4[1] - smallCube, v4[2]];
		var front_top_center_2 = [v4[0] + bigCube + smallCube, v4[1] - smallCube, v4[2]];
		var front_top_center_3 = [v4[0] + bigCube + smallCube, v4[1], v4[2]];
		var front_top_center_4 = [v4[0] + bigCube, v4[1], v4[2]];
		var front_top_center_5 = [front_top_center_1[0], front_top_center_1[1], front_top_center_1[2] - smallCube];
		var front_top_center_6 = [front_top_center_2[0], front_top_center_2[1], front_top_center_2[2] - smallCube];
		var front_top_center_7 = [front_top_center_3[0], front_top_center_3[1], front_top_center_3[2] - smallCube];
		var front_top_center_8 = [front_top_center_4[0], front_top_center_4[1], front_top_center_4[2] - smallCube];

		var front_top_right_1 = [v3[0] - bigCube, v3[1] - bigCube, v3[2]];;
		var front_top_right_2 = [v3[0], v3[1] - bigCube, v4[2]];
		var front_top_right_3 = v3;
		var front_top_right_4 = [v3[0] - bigCube, v3[1], v3[2]];
		var front_top_right_5 = [front_top_right_1[0], front_top_right_1[1], front_top_right_1[2] - bigCube];
		var front_top_right_6 = [front_top_right_2[0], front_top_right_2[1], front_top_right_2[2] - bigCube];
		var front_top_right_7 = [front_top_right_3[0], front_top_right_3[1], front_top_right_3[2] - bigCube];
		var front_top_right_8 = [front_top_right_4[0], front_top_right_4[1], front_top_right_4[2] - bigCube];

		var front_mid_left_1 = [v4[0], v4[1] - bigCube - smallCube, v4[2]];
		var front_mid_left_2 = [v4[0] + smallCube, v4[1] - bigCube - smallCube, v4[2]];
		var front_mid_left_3 = [v4[0] + smallCube, v4[1] - bigCube, v4[2]];
		var front_mid_left_4 = [v4[0], v4[1] - bigCube, v4[2]];
		var front_mid_left_5 = [front_mid_left_1[0], front_mid_left_1[1], front_mid_left_1[2] - smallCube];
		var front_mid_left_6 = [front_mid_left_2[0], front_mid_left_2[1], front_mid_left_2[2] - smallCube];
		var front_mid_left_7 = [front_mid_left_3[0], front_mid_left_3[1], front_mid_left_3[2] - smallCube];
		var front_mid_left_8 = [front_mid_left_4[0], front_mid_left_4[1], front_mid_left_4[2] - smallCube];

		var front_mid_right_1 = [v3[0] - smallCube, v3[1] - bigCube - smallCube, v3[2]];
		var front_mid_right_2 = [v3[0], v3[1] - bigCube - smallCube, v3[2]];
		var front_mid_right_3 = [v3[0], v3[1] - bigCube, v3[2]];
		var front_mid_right_4 = [v3[0] - smallCube, v3[1] - bigCube, v3[2]];
		var front_mid_right_5 = [front_mid_right_1[0], front_mid_right_1[1], front_mid_right_1[2] - smallCube];
		var front_mid_right_6 = [front_mid_right_2[0], front_mid_right_2[1], front_mid_right_2[2] - smallCube];
		var front_mid_right_7 = [front_mid_right_3[0], front_mid_right_3[1], front_mid_right_3[2] - smallCube];
		var front_mid_right_8 = [front_mid_right_4[0], front_mid_right_4[1], front_mid_right_4[2] - smallCube];

		var front_bot_left_1 = v1;
		var front_bot_left_2 = [v1[0] + bigCube, v1[1], v1[2]];
		var front_bot_left_3 = [v1[0] + bigCube, v1[1] + bigCube, v1[2]];
		var front_bot_left_4 = [v1[0], v1[1] + bigCube, v1[2]];
		var front_bot_left_5 = [front_bot_left_1[0], front_bot_left_1[1], front_bot_left_1[2] - bigCube];
		var front_bot_left_6 = [front_bot_left_2[0], front_bot_left_2[1], front_bot_left_2[2] - bigCube];
		var front_bot_left_7 = [front_bot_left_3[0], front_bot_left_3[1], front_bot_left_3[2] - bigCube];
		var front_bot_left_8 = [front_bot_left_4[0], front_bot_left_4[1], front_bot_left_4[2] - bigCube];

		var front_bot_center_1 = [v1[0] + bigCube, v1[1], v1[2]];
		var front_bot_center_2 = [v1[0] + bigCube + smallCube, v1[1], v1[2]];
		var front_bot_center_3 = [v1[0] + bigCube + smallCube, v1[1] + smallCube, v1[2]];
		var front_bot_center_4 = [v1[0] + bigCube, v1[1] + smallCube, v1[2]];
		var front_bot_center_5 = [front_bot_center_1[0], front_bot_center_1[1], front_bot_center_1[2] - smallCube];
		var front_bot_center_6 = [front_bot_center_2[0], front_bot_center_2[1], front_bot_center_2[2] - smallCube];
		var front_bot_center_7 = [front_bot_center_3[0], front_bot_center_3[1], front_bot_center_3[2] - smallCube];
		var front_bot_center_8 = [front_bot_center_4[0], front_bot_center_4[1], front_bot_center_4[2] - smallCube];

		var front_bot_right_1 = [v2[0] - bigCube, v2[1], v2[2]];
		var front_bot_right_2 = v2;
		var front_bot_right_3 = [v2[0], v2[1] + bigCube, v2[2]];
		var front_bot_right_4 = [v2[0] - bigCube, v2[1] + bigCube, v2[2]];
		var front_bot_right_5 = [front_bot_right_1[0], front_bot_right_1[1], front_bot_right_1[2] - bigCube];
		var front_bot_right_6 = [front_bot_right_2[0], front_bot_right_2[1], front_bot_right_2[2] - bigCube];
		var front_bot_right_7 = [front_bot_right_3[0], front_bot_right_3[1], front_bot_right_3[2] - bigCube];
		var front_bot_right_8 = [front_bot_right_4[0], front_bot_right_4[1], front_bot_right_4[2] - bigCube];

		// Mid cubes
		var mid_top_left_1 = [v4[0], v4[1] - smallCube, v4[2] - bigCube];
		var mid_top_left_2 = [v4[0] + smallCube, v4[1] - smallCube, v4[2] - bigCube];
		var mid_top_left_3 = [v4[0] + smallCube, v4[1], v4[2] - bigCube];
		var mid_top_left_4 = [v4[0], v4[1], v4[2] - bigCube];
		var mid_top_left_5 = [mid_top_left_1[0], mid_top_left_1[1], mid_top_left_1[2] - smallCube];
		var mid_top_left_6 = [mid_top_left_2[0], mid_top_left_2[1], mid_top_left_2[2] - smallCube];
		var mid_top_left_7 = [mid_top_left_3[0], mid_top_left_3[1], mid_top_left_3[2] - smallCube];
		var mid_top_left_8 = [mid_top_left_4[0], mid_top_left_4[1], mid_top_left_4[2] - smallCube];

		var mid_top_right_1 = [v3[0] - smallCube, v3[1] - smallCube, v3[2] - bigCube];
		var mid_top_right_2 = [v3[0], v3[1] - smallCube, v3[2] - bigCube];
		var mid_top_right_3 = [v3[0], v3[1], v3[2] - bigCube];
		var mid_top_right_4 = [v3[0] - smallCube, v3[1], v3[2] - bigCube];
		var mid_top_right_5 = [mid_top_right_1[0], mid_top_right_1[1], mid_top_right_1[2] - smallCube];
		var mid_top_right_6 = [mid_top_right_2[0], mid_top_right_2[1], mid_top_right_2[2] - smallCube];
		var mid_top_right_7 = [mid_top_right_3[0], mid_top_right_3[1], mid_top_right_3[2] - smallCube];
		var mid_top_right_8 = [mid_top_right_4[0], mid_top_right_4[1], mid_top_right_4[2] - smallCube];

		var mid_bot_left_1 = [v1[0], v1[1], v2[2] - bigCube];
		var mid_bot_left_2 = [v1[0] + smallCube, v1[1], v1[2] - bigCube];
		var mid_bot_left_3 = [v1[0] + smallCube, v1[1] + smallCube, v1[2] - bigCube];
		var mid_bot_left_4 = [v1[0], v1[1] + smallCube, v1[2] - bigCube];
		var mid_bot_left_5 = [mid_bot_left_1[0], mid_bot_left_1[1], mid_bot_left_1[2] - smallCube];
		var mid_bot_left_6 = [mid_bot_left_2[0], mid_bot_left_2[1], mid_bot_left_2[2] - smallCube];
		var mid_bot_left_7 = [mid_bot_left_3[0], mid_bot_left_3[1], mid_bot_left_3[2] - smallCube];
		var mid_bot_left_8 = [mid_bot_left_4[0], mid_bot_left_4[1], mid_bot_left_4[2] - smallCube];

		var mid_bot_right_1 = [v2[0] - smallCube, v2[1], v2[2] - bigCube];
		var mid_bot_right_2 = [v2[0], v2[1], v2[2] - bigCube];
		var mid_bot_right_3 = [v2[0], v2[1] + smallCube, v2[2] - bigCube];
		var mid_bot_right_4 = [v2[0] - smallCube, v2[1] + smallCube, v2[2] - bigCube];
		var mid_bot_right_5 = [mid_bot_right_1[0], mid_bot_right_1[1], mid_bot_right_1[2] - smallCube];
		var mid_bot_right_6 = [mid_bot_right_2[0], mid_bot_right_2[1], mid_bot_right_2[2] - smallCube];
		var mid_bot_right_7 = [mid_bot_right_3[0], mid_bot_right_3[1], mid_bot_right_3[2] - smallCube];
		var mid_bot_right_8 = [mid_bot_right_4[0], mid_bot_right_4[1], mid_bot_right_4[2] - smallCube];

		// Back cubes
		var back_top_left_1 = [v4[0], v4[1] - bigCube, v4[2] - bigCube - smallCube];
		var back_top_left_2 = [v4[0] + bigCube, v4[1] - bigCube, v4[2] - bigCube - smallCube];
		var back_top_left_3 = [v4[0] + bigCube, v4[1], v4[2] - bigCube - smallCube];
		var back_top_left_4 = [v4[0], v4[1], v4[2] - bigCube - smallCube];
		var back_top_left_5 = [back_top_left_1[0], back_top_left_1[1], back_top_left_1[2] - bigCube];
		var back_top_left_6 = [back_top_left_2[0], back_top_left_2[1], back_top_left_2[2] - bigCube];
		var back_top_left_7 = [back_top_left_3[0], back_top_left_3[1], back_top_left_3[2] - bigCube];
		var back_top_left_8 = [back_top_left_4[0], back_top_left_4[1], back_top_left_4[2] - bigCube];

		var back_top_center_1 = [v4[0] + bigCube, v4[1] - smallCube, v4[2] - (5*smallCube)];
		var back_top_center_2 = [v4[0] + bigCube + smallCube, v4[1] - smallCube, v4[2] - (5*smallCube)];
		var back_top_center_3 = [v4[0] + bigCube + smallCube, v4[1], v4[2] - (5*smallCube)];
		var back_top_center_4 = [v4[0] + bigCube, v4[1], v4[2] - (5*smallCube)];
		var back_top_center_5 = [back_top_center_1[0], back_top_center_1[1], back_top_center_1[2] - smallCube];
		var back_top_center_6 = [back_top_center_2[0], back_top_center_2[1], back_top_center_2[2] - smallCube];
		var back_top_center_7 = [back_top_center_3[0], back_top_center_3[1], back_top_center_3[2] - smallCube];
		var back_top_center_8 = [back_top_center_4[0], back_top_center_4[1], back_top_center_4[2] - smallCube];

		var back_top_right_1 = [v3[0] - bigCube, v3[1] - bigCube, v3[2] - bigCube - smallCube];;
		var back_top_right_2 = [v3[0], v3[1] - bigCube, v4[2] - bigCube - smallCube];
		var back_top_right_3 = [v3[0], v3[1], v3[2] - bigCube - smallCube];
		var back_top_right_4 = [v3[0] - bigCube, v3[1], v3[2] - bigCube - smallCube];
		var back_top_right_5 = [back_top_right_1[0], back_top_right_1[1], back_top_right_1[2] - bigCube];
		var back_top_right_6 = [back_top_right_2[0], back_top_right_2[1], back_top_right_2[2] - bigCube];
		var back_top_right_7 = [back_top_right_3[0], back_top_right_3[1], back_top_right_3[2] - bigCube];
		var back_top_right_8 = [back_top_right_4[0], back_top_right_4[1], back_top_right_4[2] - bigCube];

		var back_mid_left_1 = [v4[0], v4[1] - bigCube - smallCube, v4[2] - (2*bigCube)];
		var back_mid_left_2 = [v4[0] + smallCube, v4[1] - bigCube - smallCube, v4[2] - (2*bigCube)];
		var back_mid_left_3 = [v4[0] + smallCube, v4[1] - bigCube, v4[2] - (2*bigCube)];
		var back_mid_left_4 = [v4[0], v4[1] - bigCube, v4[2] - (2*bigCube)];
		var back_mid_left_5 = [back_mid_left_1[0], back_mid_left_1[1], back_mid_left_1[2] - smallCube];
		var back_mid_left_6 = [back_mid_left_2[0], back_mid_left_2[1], back_mid_left_2[2] - smallCube];
		var back_mid_left_7 = [back_mid_left_3[0], back_mid_left_3[1], back_mid_left_3[2] - smallCube];
		var back_mid_left_8 = [back_mid_left_4[0], back_mid_left_4[1], back_mid_left_4[2] - smallCube];

		var back_mid_right_1 = [v3[0] - smallCube, v3[1] - bigCube - smallCube, v3[2] - (2*bigCube)];
		var back_mid_right_2 = [v3[0], v3[1] - bigCube - smallCube, v3[2] - (2*bigCube)];
		var back_mid_right_3 = [v3[0], v3[1] - bigCube, v3[2] - (2*bigCube)];
		var back_mid_right_4 = [v3[0] - smallCube, v3[1] - bigCube, v3[2] - (2*bigCube)];
		var back_mid_right_5 = [back_mid_right_1[0], back_mid_right_1[1], back_mid_right_1[2] - smallCube];
		var back_mid_right_6 = [back_mid_right_2[0], back_mid_right_2[1], back_mid_right_2[2] - smallCube];
		var back_mid_right_7 = [back_mid_right_3[0], back_mid_right_3[1], back_mid_right_3[2] - smallCube];
		var back_mid_right_8 = [back_mid_right_4[0], back_mid_right_4[1], back_mid_right_4[2] - smallCube];

		var back_bot_left_1 = [v1[0], v1[1], v1[2] - bigCube - smallCube];
		var back_bot_left_2 = [v1[0] + bigCube, v1[1], v1[2] - bigCube - smallCube];
		var back_bot_left_3 = [v1[0] + bigCube, v1[1] + bigCube, v1[2] - bigCube - smallCube];
		var back_bot_left_4 = [v1[0], v1[1] + bigCube, v1[2] - bigCube - smallCube];
		var back_bot_left_5 = [back_bot_left_1[0], back_bot_left_1[1], back_bot_left_1[2] - bigCube];
		var back_bot_left_6 = [back_bot_left_2[0], back_bot_left_2[1], back_bot_left_2[2] - bigCube];
		var back_bot_left_7 = [back_bot_left_3[0], back_bot_left_3[1], back_bot_left_3[2] - bigCube];
		var back_bot_left_8 = [back_bot_left_4[0], back_bot_left_4[1], back_bot_left_4[2] - bigCube];

		var back_bot_center_1 = [v1[0] + bigCube, v1[1], v1[2] - (5*smallCube)];
		var back_bot_center_2 = [v1[0] + bigCube + smallCube, v1[1], v1[2] - (5*smallCube)];
		var back_bot_center_3 = [v1[0] + bigCube + smallCube, v1[1] + smallCube, v1[2] - (5*smallCube)];
		var back_bot_center_4 = [v1[0] + bigCube, v1[1] + smallCube, v1[2] - (5*smallCube)];
		var back_bot_center_5 = [back_bot_center_1[0], back_bot_center_1[1], back_bot_center_1[2] - smallCube];
		var back_bot_center_6 = [back_bot_center_2[0], back_bot_center_2[1], back_bot_center_2[2] - smallCube];
		var back_bot_center_7 = [back_bot_center_3[0], back_bot_center_3[1], back_bot_center_3[2] - smallCube];
		var back_bot_center_8 = [back_bot_center_4[0], back_bot_center_4[1], back_bot_center_4[2] - smallCube];

		var back_bot_right_1 = [v2[0] - bigCube, v2[1], v2[2] - bigCube - smallCube];
		var back_bot_right_2 = [v2[0], v2[1], v2[2] - bigCube - smallCube];
		var back_bot_right_3 = [v2[0], v2[1] + bigCube, v2[2] - bigCube - smallCube];
		var back_bot_right_4 = [v2[0] - bigCube, v2[1] + bigCube, v2[2] - bigCube - smallCube];
		var back_bot_right_5 = [back_bot_right_1[0], back_bot_right_1[1], back_bot_right_1[2] - bigCube];
		var back_bot_right_6 = [back_bot_right_2[0], back_bot_right_2[1], back_bot_right_2[2] - bigCube];
		var back_bot_right_7 = [back_bot_right_3[0], back_bot_right_3[1], back_bot_right_3[2] - bigCube];
		var back_bot_right_8 = [back_bot_right_4[0], back_bot_right_4[1], back_bot_right_4[2] - bigCube];


		jerusalemCube(front_top_left_1, front_top_left_2, front_top_left_3, front_top_left_4, front_top_left_5, front_top_left_6, front_top_left_7, front_top_left_8, recursionLevel);
		jerusalemCube(front_top_center_1, front_top_center_2, front_top_center_3, front_top_center_4, front_top_center_5, front_top_center_6, front_top_center_7, front_top_center_8, recursionLevel);
		jerusalemCube(front_top_right_1, front_top_right_2, front_top_right_3, front_top_right_4, front_top_right_5, front_top_right_6, front_top_right_7, front_top_right_8, recursionLevel);
		jerusalemCube(front_mid_left_1, front_mid_left_2, front_mid_left_3, front_mid_left_4, front_mid_left_5, front_mid_left_6, front_mid_left_7, front_mid_left_8, recursionLevel);
		jerusalemCube(front_mid_right_1, front_mid_right_2, front_mid_right_3, front_mid_right_4, front_mid_right_5, front_mid_right_6, front_mid_right_7, front_mid_right_8, recursionLevel);
		jerusalemCube(front_bot_left_1, front_bot_left_2, front_bot_left_3, front_bot_left_4, front_bot_left_5, front_bot_left_6, front_bot_left_7, front_bot_left_8, recursionLevel);
		jerusalemCube(front_bot_center_1, front_bot_center_2, front_bot_center_3, front_bot_center_4, front_bot_center_5, front_bot_center_6, front_bot_center_7, front_bot_center_8, recursionLevel);
		jerusalemCube(front_bot_right_1, front_bot_right_2, front_bot_right_3, front_bot_right_4, front_bot_right_5, front_bot_right_6, front_bot_right_7, front_bot_right_8, recursionLevel);

		jerusalemCube(mid_top_left_1, mid_top_left_2, mid_top_left_3, mid_top_left_4, mid_top_left_5, mid_top_left_6, mid_top_left_7, mid_top_left_8, recursionLevel);
		jerusalemCube(mid_top_right_1, mid_top_right_2, mid_top_right_3, mid_top_right_4, mid_top_right_5, mid_top_right_6, mid_top_right_7, mid_top_right_8, recursionLevel);
		jerusalemCube(mid_bot_left_1, mid_bot_left_2, mid_bot_left_3, mid_bot_left_4, mid_bot_left_5, mid_bot_left_6, mid_bot_left_7, mid_bot_left_8, recursionLevel);
		jerusalemCube(mid_bot_right_1, mid_bot_right_2, mid_bot_right_3, mid_bot_right_4, mid_bot_right_5, mid_bot_right_6, mid_bot_right_7, mid_bot_right_8, recursionLevel);
	
		jerusalemCube(back_top_left_1, back_top_left_2, back_top_left_3, back_top_left_4, back_top_left_5, back_top_left_6, back_top_left_7, back_top_left_8, recursionLevel);
		jerusalemCube(back_top_center_1, back_top_center_2, back_top_center_3, back_top_center_4, back_top_center_5, back_top_center_6, back_top_center_7, back_top_center_8, recursionLevel);
		jerusalemCube(back_top_right_1, back_top_right_2, back_top_right_3, back_top_right_4, back_top_right_5, back_top_right_6, back_top_right_7, back_top_right_8, recursionLevel);
		jerusalemCube(back_mid_left_1, back_mid_left_2, back_mid_left_3, back_mid_left_4, back_mid_left_5, back_mid_left_6, back_mid_left_7, back_mid_left_8, recursionLevel);
		jerusalemCube(back_mid_right_1, back_mid_right_2, back_mid_right_3, back_mid_right_4, back_mid_right_5, back_mid_right_6, back_mid_right_7, back_mid_right_8, recursionLevel);
		jerusalemCube(back_bot_left_1, back_bot_left_2, back_bot_left_3, back_bot_left_4, back_bot_left_5, back_bot_left_6, back_bot_left_7, back_bot_left_8, recursionLevel);
		jerusalemCube(back_bot_center_1, back_bot_center_2, back_bot_center_3, back_bot_center_4, back_bot_center_5, back_bot_center_6, back_bot_center_7, back_bot_center_8, recursionLevel);
		jerusalemCube(back_bot_right_1, back_bot_right_2, back_bot_right_3, back_bot_right_4, back_bot_right_5, back_bot_right_6, back_bot_right_7, back_bot_right_8, recursionLevel);
	}
}

function computeCantorDust () {
	var v1 = [-1, -1, 1];       
	
	var v2 = [1, -1, 1];        
		
	var v3 = [1, 1, 1];     

	var v4 = [-1, 1, 1];        
	
	var v5 = [-1, -1, -1];  

	var v6 = [1, -1, -1];       

	var v7 = [1, 1, -1];        

	var v8 = [-1, 1, -1];
	
	vertices = [];
	normals = [];
	cantorDust(v1, v2, v3, v4, v5, v6, v7, v8, numLevels);
	computeVertexNormals(vertices, normals);
}

function cantorDust(v1, v2, v3, v4, v5, v6, v7, v8, recursionLevel) {	
	if(recursionLevel < 1) {
		defineCube(v1, v2, v3, v4, v5, v6, v7, v8);
	}
	else {
		recursionLevel--;
		
		// -- Divide every face into 9 equally sized squares --
		var distance = computeDistance(v3, v4);
		var newDistance = distance / 3;
		
		// Front face cubes
		var front_top_left_1 = [v3[0] - distance, v3[1] - newDistance, v3[2]];
		var front_top_left_2 = [v3[0] - (2*newDistance), v3[1] - newDistance, v3[2]];
		var front_top_left_3 = [v3[0] - (2*newDistance), v3[1], v3[2]];
		var front_top_left_4 = [v3[0] - distance, v3[1], v3[2]];
		var front_top_left_5 = [front_top_left_1[0], front_top_left_1[1], front_top_left_1[2] - newDistance];
		var front_top_left_6 = [front_top_left_2[0], front_top_left_2[1], front_top_left_2[2] - newDistance];
		var front_top_left_7 = [front_top_left_3[0], front_top_left_3[1], front_top_left_3[2] - newDistance];
		var front_top_left_8 = [front_top_left_4[0], front_top_left_4[1], front_top_left_4[2] - newDistance];
		
		var front_top_right_1 = [v3[0] - newDistance, v3[1]-newDistance, v3[2]];;
		var front_top_right_2 = [v3[0], v3[1]-newDistance, v3[2]];
		var front_top_right_3 = v3;
		var front_top_right_4 = [v3[0] - newDistance, v3[1], v3[2]];;
		var front_top_right_5 = [front_top_right_1[0], front_top_right_1[1], front_top_right_1[2] - newDistance];
		var front_top_right_6 = [front_top_right_2[0], front_top_right_2[1], front_top_right_2[2] - newDistance];
		var front_top_right_7 = [front_top_right_3[0], front_top_right_3[1], front_top_right_3[2] - newDistance];
		var front_top_right_8 = [front_top_right_4[0], front_top_right_4[1], front_top_right_4[2] - newDistance];
		
		var front_bot_left_1 = [v1[0], v1[1], v1[2]];
		var front_bot_left_2 = [v1[0] + newDistance, v1[1], v1[2]];
		var front_bot_left_3 = [v3[0] - (2*newDistance), v3[1]-(2*newDistance), v3[2]];
		var front_bot_left_4 = [v3[0] - distance, v3[1]-(2*newDistance), v3[2]];
		var front_bot_left_5 = [front_bot_left_1[0], front_bot_left_1[1], front_bot_left_1[2] - newDistance];
		var front_bot_left_6 = [front_bot_left_2[0], front_bot_left_2[1], front_bot_left_2[2] - newDistance];
		var front_bot_left_7 = [front_bot_left_3[0], front_bot_left_3[1], front_bot_left_3[2] - newDistance];
		var front_bot_left_8 = [front_bot_left_4[0], front_bot_left_4[1], front_bot_left_4[2] - newDistance];

		var front_bot_right_1 = [v3[0] - newDistance, v3[1]-distance, v3[2]];;
		var front_bot_right_2 = v2;
		var front_bot_right_3 = [v3[0], v3[1]-(2*newDistance), v3[2]];;
		var front_bot_right_4 = [v3[0] - newDistance, v3[1]-(2*newDistance), v3[2]];
		var front_bot_right_5 = [front_bot_right_1[0], front_bot_right_1[1], front_bot_right_1[2] - newDistance];
		var front_bot_right_6 = [front_bot_right_2[0], front_bot_right_2[1], front_bot_right_2[2] - newDistance];
		var front_bot_right_7 = [front_bot_right_3[0], front_bot_right_3[1], front_bot_right_3[2] - newDistance];;
		var front_bot_right_8 = [front_bot_right_4[0], front_bot_right_4[1], front_bot_right_4[2] - newDistance];;

		// Back cubes
		var back_top_left_1 = [front_top_left_1[0], front_top_left_1[1], front_top_left_1[2]-(2*newDistance)];
		var back_top_left_2 = [front_top_left_2[0], front_top_left_2[1], front_top_left_2[2]-(2*newDistance)];
		var back_top_left_3 = [front_top_left_3[0], front_top_left_3[1], front_top_left_3[2]-(2*newDistance)];
		var back_top_left_4 = [front_top_left_4[0], front_top_left_4[1], front_top_left_4[2]-(2*newDistance)];
		var back_top_left_5 = [back_top_left_1[0], back_top_left_1[1], back_top_left_1[2] - newDistance];
		var back_top_left_6 = [back_top_left_2[0], back_top_left_2[1], back_top_left_2[2] - newDistance];
		var back_top_left_7 = [back_top_left_3[0], back_top_left_3[1], back_top_left_3[2] - newDistance];
		var back_top_left_8 = [back_top_left_4[0], back_top_left_4[1], back_top_left_4[2] - newDistance];

		var back_top_right_1 = [front_top_right_1[0], front_top_right_1[1], front_top_right_1[2]-(2*newDistance)];
		var back_top_right_2 = [front_top_right_2[0], front_top_right_2[1], front_top_right_2[2]-(2*newDistance)];
		var back_top_right_3 = [front_top_right_3[0], front_top_right_3[1], front_top_right_3[2]-(2*newDistance)];
		var back_top_right_4 = [front_top_right_4[0], front_top_right_4[1], front_top_right_4[2]-(2*newDistance)];
		var back_top_right_5 = [back_top_right_1[0], back_top_right_1[1], back_top_right_1[2] - newDistance];
		var back_top_right_6 = [back_top_right_2[0], back_top_right_2[1], back_top_right_2[2] - newDistance];
		var back_top_right_7 = [back_top_right_3[0], back_top_right_3[1], back_top_right_3[2] - newDistance];
		var back_top_right_8 = [back_top_right_4[0], back_top_right_4[1], back_top_right_4[2] - newDistance];

		var back_bot_left_1 = [front_bot_left_1[0], front_bot_left_1[1], front_bot_left_1[2]-(2*newDistance)];
		var back_bot_left_2 = [front_bot_left_2[0], front_bot_left_2[1], front_bot_left_2[2]-(2*newDistance)];
		var back_bot_left_3 = [front_bot_left_3[0], front_bot_left_3[1], front_bot_left_3[2]-(2*newDistance)];
		var back_bot_left_4 = [front_bot_left_4[0], front_bot_left_4[1], front_bot_left_4[2]-(2*newDistance)];
		var back_bot_left_5 = [back_bot_left_1[0], back_bot_left_1[1], back_bot_left_1[2] - newDistance];
		var back_bot_left_6 = [back_bot_left_2[0], back_bot_left_2[1], back_bot_left_2[2] - newDistance];
		var back_bot_left_7 = [back_bot_left_3[0], back_bot_left_3[1], back_bot_left_3[2] - newDistance];
		var back_bot_left_8 = [back_bot_left_4[0], back_bot_left_4[1], back_bot_left_4[2] - newDistance];

		var back_bot_right_1 = [front_bot_right_1[0], front_bot_right_1[1], front_bot_right_1[2]-(2*newDistance)];
		var back_bot_right_2 = [front_bot_right_2[0], front_bot_right_2[1], front_bot_right_2[2]-(2*newDistance)];
		var back_bot_right_3 = [front_bot_right_3[0], front_bot_right_3[1], front_bot_right_3[2]-(2*newDistance)];
		var back_bot_right_4 = [front_bot_right_4[0], front_bot_right_4[1], front_bot_right_4[2]-(2*newDistance)];
		var back_bot_right_5 = [back_bot_right_1[0], back_bot_right_1[1], back_bot_right_1[2] - newDistance];
		var back_bot_right_6 = [back_bot_right_2[0], back_bot_right_2[1], back_bot_right_2[2] - newDistance];
		var back_bot_right_7 = [back_bot_right_3[0], back_bot_right_3[1], back_bot_right_3[2] - newDistance];
		var back_bot_right_8 = [back_bot_right_4[0], back_bot_right_4[1], back_bot_right_4[2] - newDistance];
		
		cantorDust(front_top_left_1, front_top_left_2, front_top_left_3, front_top_left_4, front_top_left_5, front_top_left_6, front_top_left_7, front_top_left_8, recursionLevel);
		cantorDust(front_top_right_1, front_top_right_2, front_top_right_3, front_top_right_4, front_top_right_5, front_top_right_6, front_top_right_7, front_top_right_8, recursionLevel);
		cantorDust(front_bot_left_1, front_bot_left_2, front_bot_left_3, front_bot_left_4, front_bot_left_5, front_bot_left_6, front_bot_left_7, front_bot_left_8, recursionLevel);
		cantorDust(front_bot_right_1, front_bot_right_2, front_bot_right_3, front_bot_right_4, front_bot_right_5, front_bot_right_6, front_bot_right_7, front_bot_right_8, recursionLevel);
		
		cantorDust(back_top_left_1, back_top_left_2, back_top_left_3, back_top_left_4, back_top_left_5, back_top_left_6, back_top_left_7, back_top_left_8, recursionLevel);
		cantorDust(back_top_right_1, back_top_right_2, back_top_right_3, back_top_right_4, back_top_right_5, back_top_right_6, back_top_right_7, back_top_right_8, recursionLevel);
		cantorDust(back_bot_left_1, back_bot_left_2, back_bot_left_3, back_bot_left_4, back_bot_left_5, back_bot_left_6, back_bot_left_7, back_bot_left_8, recursionLevel);
		cantorDust(back_bot_right_1, back_bot_right_2, back_bot_right_3, back_bot_right_4, back_bot_right_5, back_bot_right_6, back_bot_right_7, back_bot_right_8, recursionLevel);
	}
}