The Tor Browser: browser/devtools/tilt/tilt-math.js@8bccb770b82d (annotated)

browser/devtools/tilt/tilt-math.js@8bccb770b82d (annotated)

browser/devtools/tilt/tilt-math.js

Wed, 31 Dec 2014 13:27:57 +0100

author: Michael Schloh von Bennewitz <michael@schloh.com>
date: Wed, 31 Dec 2014 13:27:57 +0100
branch: TOR_BUG_3246
changeset 6: 8bccb770b82d
permissions: -rw-r--r--

Ignore runtime configuration files generated during quality assurance.

 /* -*- Mode: javascript; tab-width: 2; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
 /* vim: set ts=2 et sw=2 tw=80: */
 /* This Source Code Form is subject to the terms of the Mozilla Public
  * License, v. 2.0. If a copy of the MPL was not distributed with this
  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
 "use strict";
 const {Cu} = require("chrome");
 let TiltUtils = require("devtools/tilt/tilt-utils");
 /**
  * Module containing high performance matrix and vector operations for WebGL.
  * Inspired by glMatrix, version 0.9.6, (c) 2011 Brandon Jones.
  */
 let EPSILON = 0.01;
 exports.EPSILON = EPSILON;
 const PI_OVER_180 = Math.PI / 180;
 const INV_PI_OVER_180 = 180 / Math.PI;
 const FIFTEEN_OVER_225 = 15 / 225;
 const ONE_OVER_255 = 1 / 255;
 /**
  * vec3 - 3 Dimensional Vector.
  */
 let vec3 = {
   /**
    * Creates a new instance of a vec3 using the Float32Array type.
    * Any array containing at least 3 numeric elements can serve as a vec3.
    *
    * @param {Array} aVec
    *                optional, vec3 containing values to initialize with
    *
    * @return {Array} a new instance of a vec3
    */
   create: function V3_create(aVec)
   {
     let dest = new Float32Array(3);
     if (aVec) {
       vec3.set(aVec, dest);
     } else {
       vec3.zero(dest);
     }
     return dest;
   },
   /**
    * Copies the values of one vec3 to another.
    *
    * @param {Array} aVec
    *                vec3 containing values to copy
    * @param {Array} aDest
    *                vec3 receiving copied values
    *
    * @return {Array} the destination vec3 receiving copied values
    */
   set: function V3_set(aVec, aDest)
   {
     aDest[0] = aVec[0];
     aDest[1] = aVec[1];
     aDest[2] = aVec[2] || 0;
     return aDest;
   },
   /**
    * Sets a vec3 to an zero vector.
    *
    * @param {Array} aDest
    *                vec3 to set
    *
    * @return {Array} the same vector
    */
   zero: function V3_zero(aDest)
   {
     aDest[0] = 0;
     aDest[1] = 0;
     aDest[2] = 0;
     return aDest;
   },
   /**
    * Performs a vector addition.
    *
    * @param {Array} aVec
    *                vec3, first operand
    * @param {Array} aVec2
    *                vec3, second operand
    * @param {Array} aDest
    *                optional, vec3 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination vec3 if specified, first operand otherwise
    */
   add: function V3_add(aVec, aVec2, aDest)
   {
     if (!aDest) {
       aDest = aVec;
     }
     aDest[0] = aVec[0] + aVec2[0];
     aDest[1] = aVec[1] + aVec2[1];
     aDest[2] = aVec[2] + aVec2[2];
     return aDest;
   },
   /**
    * Performs a vector subtraction.
    *
    * @param {Array} aVec
    *                vec3, first operand
    * @param {Array} aVec2
    *                vec3, second operand
    * @param {Array} aDest
    *                optional, vec3 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination vec3 if specified, first operand otherwise
    */
   subtract: function V3_subtract(aVec, aVec2, aDest)
   {
     if (!aDest) {
       aDest = aVec;
     }
     aDest[0] = aVec[0] - aVec2[0];
     aDest[1] = aVec[1] - aVec2[1];
     aDest[2] = aVec[2] - aVec2[2];
     return aDest;
   },
   /**
    * Negates the components of a vec3.
    *
    * @param {Array} aVec
    *                vec3 to negate
    * @param {Array} aDest
    *                optional, vec3 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination vec3 if specified, first operand otherwise
    */
   negate: function V3_negate(aVec, aDest)
   {
     if (!aDest) {
       aDest = aVec;
     }
     aDest[0] = -aVec[0];
     aDest[1] = -aVec[1];
     aDest[2] = -aVec[2];
     return aDest;
   },
   /**
    * Multiplies the components of a vec3 by a scalar value.
    *
    * @param {Array} aVec
    *                vec3 to scale
    * @param {Number} aVal
    *                 numeric value to scale by
    * @param {Array} aDest
    *                optional, vec3 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination vec3 if specified, first operand otherwise
    */
   scale: function V3_scale(aVec, aVal, aDest)
   {
     if (!aDest) {
       aDest = aVec;
     }
     aDest[0] = aVec[0] * aVal;
     aDest[1] = aVec[1] * aVal;
     aDest[2] = aVec[2] * aVal;
     return aDest;
   },
   /**
    * Generates a unit vector of the same direction as the provided vec3.
    * If vector length is 0, returns [0, 0, 0].
    *
    * @param {Array} aVec
    *                vec3 to normalize
    * @param {Array} aDest
    *                optional, vec3 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination vec3 if specified, first operand otherwise
    */
   normalize: function V3_normalize(aVec, aDest)
   {
     if (!aDest) {
       aDest = aVec;
     }
     let x = aVec[0];
     let y = aVec[1];
     let z = aVec[2];
     let len = Math.sqrt(x * x + y * y + z * z);
     if (Math.abs(len) < EPSILON) {
       aDest[0] = 0;
       aDest[1] = 0;
       aDest[2] = 0;
       return aDest;
     }
     len = 1 / len;
     aDest[0] = x * len;
     aDest[1] = y * len;
     aDest[2] = z * len;
     return aDest;
   },
   /**
    * Generates the cross product of two vectors.
    *
    * @param {Array} aVec
    *                vec3, first operand
    * @param {Array} aVec2
    *                vec3, second operand
    * @param {Array} aDest
    *                optional, vec3 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination vec3 if specified, first operand otherwise
    */
   cross: function V3_cross(aVec, aVec2, aDest)
   {
     if (!aDest) {
       aDest = aVec;
     }
     let x = aVec[0];
     let y = aVec[1];
     let z = aVec[2];
     let x2 = aVec2[0];
     let y2 = aVec2[1];
     let z2 = aVec2[2];
     aDest[0] = y * z2 - z * y2;
     aDest[1] = z * x2 - x * z2;
     aDest[2] = x * y2 - y * x2;
     return aDest;
   },
   /**
    * Caclulate the dot product of two vectors.
    *
    * @param {Array} aVec
    *                vec3, first operand
    * @param {Array} aVec2
    *                vec3, second operand
    *
    * @return {Array} dot product of the first and second operand
    */
   dot: function V3_dot(aVec, aVec2)
   {
     return aVec[0] * aVec2[0] + aVec[1] * aVec2[1] + aVec[2] * aVec2[2];
   },
   /**
    * Caclulate the length of a vec3.
    *
    * @param {Array} aVec
    *                vec3 to calculate length of
    *
    * @return {Array} length of the vec3
    */
   length: function V3_length(aVec)
   {
     let x = aVec[0];
     let y = aVec[1];
     let z = aVec[2];
     return Math.sqrt(x * x + y * y + z * z);
   },
   /**
    * Generates a unit vector pointing from one vector to another.
    *
    * @param {Array} aVec
    *                origin vec3
    * @param {Array} aVec2
    *                vec3 to point to
    * @param {Array} aDest
    *                optional, vec3 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination vec3 if specified, first operand otherwise
    */
   direction: function V3_direction(aVec, aVec2, aDest)
   {
     if (!aDest) {
       aDest = aVec;
     }
     let x = aVec[0] - aVec2[0];
     let y = aVec[1] - aVec2[1];
     let z = aVec[2] - aVec2[2];
     let len = Math.sqrt(x * x + y * y + z * z);
     if (Math.abs(len) < EPSILON) {
       aDest[0] = 0;
       aDest[1] = 0;
       aDest[2] = 0;
       return aDest;
     }
     len = 1 / len;
     aDest[0] = x * len;
     aDest[1] = y * len;
     aDest[2] = z * len;
     return aDest;
   },
   /**
    * Performs a linear interpolation between two vec3.
    *
    * @param {Array} aVec
    *                first vector
    * @param {Array} aVec2
    *                second vector
    * @param {Number} aLerp
    *                 interpolation amount between the two inputs
    * @param {Array} aDest
    *                optional, vec3 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination vec3 if specified, first operand otherwise
    */
   lerp: function V3_lerp(aVec, aVec2, aLerp, aDest)
   {
     if (!aDest) {
       aDest = aVec;
     }
     aDest[0] = aVec[0] + aLerp * (aVec2[0] - aVec[0]);
     aDest[1] = aVec[1] + aLerp * (aVec2[1] - aVec[1]);
     aDest[2] = aVec[2] + aLerp * (aVec2[2] - aVec[2]);
     return aDest;
   },
   /**
    * Projects a 3D point on a 2D screen plane.
    *
    * @param {Array} aP
    *                the [x, y, z] coordinates of the point to project
    * @param {Array} aViewport
    *                the viewport [x, y, width, height] coordinates
    * @param {Array} aMvMatrix
    *                the model view matrix
    * @param {Array} aProjMatrix
    *                the projection matrix
    * @param {Array} aDest
    *                optional parameter, the array to write the values to
    *
    * @return {Array} the projected coordinates
    */
   project: function V3_project(aP, aViewport, aMvMatrix, aProjMatrix, aDest)
   {
     /*jshint undef: false */
     let mvpMatrix = new Float32Array(16);
     let coordinates = new Float32Array(4);
     // compute the perspective * model view matrix
     mat4.multiply(aProjMatrix, aMvMatrix, mvpMatrix);
     // now transform that vector into homogenous coordinates
     coordinates[0] = aP[0];
     coordinates[1] = aP[1];
     coordinates[2] = aP[2];
     coordinates[3] = 1;
     mat4.multiplyVec4(mvpMatrix, coordinates);
     // transform the homogenous coordinates into screen space
     coordinates[0] /= coordinates[3];
     coordinates[0] *= aViewport[2] * 0.5;
     coordinates[0] += aViewport[2] * 0.5;
     coordinates[1] /= coordinates[3];
     coordinates[1] *= -aViewport[3] * 0.5;
     coordinates[1] += aViewport[3] * 0.5;
     coordinates[2] = 0;
     if (!aDest) {
       vec3.set(coordinates, aP);
     } else {
       vec3.set(coordinates, aDest);
     }
     return coordinates;
   },
   /**
    * Unprojects a 2D point to 3D space.
    *
    * @param {Array} aP
    *                the [x, y, z] coordinates of the point to unproject;
    *                the z value should range between 0 and 1, as clipping plane
    * @param {Array} aViewport
    *                the viewport [x, y, width, height] coordinates
    * @param {Array} aMvMatrix
    *                the model view matrix
    * @param {Array} aProjMatrix
    *                the projection matrix
    * @param {Array} aDest
    *                optional parameter, the array to write the values to
    *
    * @return {Array} the unprojected coordinates
    */
   unproject: function V3_unproject(
     aP, aViewport, aMvMatrix, aProjMatrix, aDest)
   {
     /*jshint undef: false */
     let mvpMatrix = new Float32Array(16);
     let coordinates = new Float32Array(4);
     // compute the inverse of the perspective * model view matrix
     mat4.multiply(aProjMatrix, aMvMatrix, mvpMatrix);
     mat4.inverse(mvpMatrix);
     // transformation of normalized coordinates (-1 to 1)
     coordinates[0] = +((aP[0] - aViewport[0]) / aViewport[2] * 2 - 1);
     coordinates[1] = -((aP[1] - aViewport[1]) / aViewport[3] * 2 - 1);
     coordinates[2] = 2 * aP[2] - 1;
     coordinates[3] = 1;
     // now transform that vector into space coordinates
     mat4.multiplyVec4(mvpMatrix, coordinates);
     // invert to normalize x, y, and z values
     coordinates[3] = 1 / coordinates[3];
     coordinates[0] *= coordinates[3];
     coordinates[1] *= coordinates[3];
     coordinates[2] *= coordinates[3];
     if (!aDest) {
       vec3.set(coordinates, aP);
     } else {
       vec3.set(coordinates, aDest);
     }
     return coordinates;
   },
   /**
    * Create a ray between two points using the current model view & projection
    * matrices. This is useful when creating a ray destined for 3D picking.
    *
    * @param {Array} aP0
    *                the [x, y, z] coordinates of the first point
    * @param {Array} aP1
    *                the [x, y, z] coordinates of the second point
    * @param {Array} aViewport
    *                the viewport [x, y, width, height] coordinates
    * @param {Array} aMvMatrix
    *                the model view matrix
    * @param {Array} aProjMatrix
    *                the projection matrix
    *
    * @return {Object} a ray object containing the direction vector between
    * the two unprojected points, the position and the lookAt
    */
   createRay: function V3_createRay(aP0, aP1, aViewport, aMvMatrix, aProjMatrix)
   {
     // unproject the two points
     vec3.unproject(aP0, aViewport, aMvMatrix, aProjMatrix, aP0);
     vec3.unproject(aP1, aViewport, aMvMatrix, aProjMatrix, aP1);
     return {
       origin: aP0,
       direction: vec3.normalize(vec3.subtract(aP1, aP0))
     };
   },
   /**
    * Returns a string representation of a vector.
    *
    * @param {Array} aVec
    *                vec3 to represent as a string
    *
    * @return {String} representation of the vector
    */
   str: function V3_str(aVec)
   {
     return '[' + aVec[0] + ", " + aVec[1] + ", " + aVec[2] + ']';
   }
 };
 exports.vec3 = vec3;
 /**
  * mat3 - 3x3 Matrix.
  */
 let mat3 = {
   /**
    * Creates a new instance of a mat3 using the Float32Array array type.
    * Any array containing at least 9 numeric elements can serve as a mat3.
    *
    * @param {Array} aMat
    *                optional, mat3 containing values to initialize with
    *
    * @return {Array} a new instance of a mat3
    */
   create: function M3_create(aMat)
   {
     let dest = new Float32Array(9);
     if (aMat) {
       mat3.set(aMat, dest);
     } else {
       mat3.identity(dest);
     }
     return dest;
   },
   /**
    * Copies the values of one mat3 to another.
    *
    * @param {Array} aMat
    *                mat3 containing values to copy
    * @param {Array} aDest
    *                mat3 receiving copied values
    *
    * @return {Array} the destination mat3 receiving copied values
    */
   set: function M3_set(aMat, aDest)
   {
     aDest[0] = aMat[0];
     aDest[1] = aMat[1];
     aDest[2] = aMat[2];
     aDest[3] = aMat[3];
     aDest[4] = aMat[4];
     aDest[5] = aMat[5];
     aDest[6] = aMat[6];
     aDest[7] = aMat[7];
     aDest[8] = aMat[8];
     return aDest;
   },
   /**
    * Sets a mat3 to an identity matrix.
    *
    * @param {Array} aDest
    *                mat3 to set
    *
    * @return {Array} the same matrix
    */
   identity: function M3_identity(aDest)
   {
     aDest[0] = 1;
     aDest[1] = 0;
     aDest[2] = 0;
     aDest[3] = 0;
     aDest[4] = 1;
     aDest[5] = 0;
     aDest[6] = 0;
     aDest[7] = 0;
     aDest[8] = 1;
     return aDest;
   },
   /**
    * Transposes a mat3 (flips the values over the diagonal).
    *
    * @param {Array} aMat
    *                mat3 to transpose
    * @param {Array} aDest
    *                optional, mat3 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat3 if specified, first operand otherwise
    */
   transpose: function M3_transpose(aMat, aDest)
   {
     if (!aDest || aMat === aDest) {
       let a01 = aMat[1];
       let a02 = aMat[2];
       let a12 = aMat[5];
       aMat[1] = aMat[3];
       aMat[2] = aMat[6];
       aMat[3] = a01;
       aMat[5] = aMat[7];
       aMat[6] = a02;
       aMat[7] = a12;
       return aMat;
     }
     aDest[0] = aMat[0];
     aDest[1] = aMat[3];
     aDest[2] = aMat[6];
     aDest[3] = aMat[1];
     aDest[4] = aMat[4];
     aDest[5] = aMat[7];
     aDest[6] = aMat[2];
     aDest[7] = aMat[5];
     aDest[8] = aMat[8];
     return aDest;
   },
   /**
    * Copies the elements of a mat3 into the upper 3x3 elements of a mat4.
    *
    * @param {Array} aMat
    *                mat3 containing values to copy
    * @param {Array} aDest
    *                optional, mat4 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat3 if specified, first operand otherwise
    */
   toMat4: function M3_toMat4(aMat, aDest)
   {
     if (!aDest) {
       aDest = new Float32Array(16);
     }
     aDest[0] = aMat[0];
     aDest[1] = aMat[1];
     aDest[2] = aMat[2];
     aDest[3] = 0;
     aDest[4] = aMat[3];
     aDest[5] = aMat[4];
     aDest[6] = aMat[5];
     aDest[7] = 0;
     aDest[8] = aMat[6];
     aDest[9] = aMat[7];
     aDest[10] = aMat[8];
     aDest[11] = 0;
     aDest[12] = 0;
     aDest[13] = 0;
     aDest[14] = 0;
     aDest[15] = 1;
     return aDest;
   },
   /**
    * Returns a string representation of a 3x3 matrix.
    *
    * @param {Array} aMat
    *                mat3 to represent as a string
    *
    * @return {String} representation of the matrix
    */
   str: function M3_str(aMat)
   {
     return "["  + aMat[0] + ", " + aMat[1] + ", " + aMat[2] +
            ", " + aMat[3] + ", " + aMat[4] + ", " + aMat[5] +
            ", " + aMat[6] + ", " + aMat[7] + ", " + aMat[8] + "]";
   }
 };
 exports.mat3 = mat3;
 /**
  * mat4 - 4x4 Matrix.
  */
 let mat4 = {
   /**
    * Creates a new instance of a mat4 using the default Float32Array type.
    * Any array containing at least 16 numeric elements can serve as a mat4.
    *
    * @param {Array} aMat
    *                optional, mat4 containing values to initialize with
    *
    * @return {Array} a new instance of a mat4
    */
   create: function M4_create(aMat)
   {
     let dest = new Float32Array(16);
     if (aMat) {
       mat4.set(aMat, dest);
     } else {
       mat4.identity(dest);
     }
     return dest;
   },
   /**
    * Copies the values of one mat4 to another
    *
    * @param {Array} aMat
    *                mat4 containing values to copy
    * @param {Array} aDest
    *                mat4 receiving copied values
    *
    * @return {Array} the destination mat4 receiving copied values
    */
   set: function M4_set(aMat, aDest)
   {
     aDest[0] = aMat[0];
     aDest[1] = aMat[1];
     aDest[2] = aMat[2];
     aDest[3] = aMat[3];
     aDest[4] = aMat[4];
     aDest[5] = aMat[5];
     aDest[6] = aMat[6];
     aDest[7] = aMat[7];
     aDest[8] = aMat[8];
     aDest[9] = aMat[9];
     aDest[10] = aMat[10];
     aDest[11] = aMat[11];
     aDest[12] = aMat[12];
     aDest[13] = aMat[13];
     aDest[14] = aMat[14];
     aDest[15] = aMat[15];
     return aDest;
   },
   /**
    * Sets a mat4 to an identity matrix.
    *
    * @param {Array} aDest
    *                mat4 to set
    *
    * @return {Array} the same matrix
    */
   identity: function M4_identity(aDest)
   {
     aDest[0] = 1;
     aDest[1] = 0;
     aDest[2] = 0;
     aDest[3] = 0;
     aDest[4] = 0;
     aDest[5] = 1;
     aDest[6] = 0;
     aDest[7] = 0;
     aDest[8] = 0;
     aDest[9] = 0;
     aDest[10] = 1;
     aDest[11] = 0;
     aDest[12] = 0;
     aDest[13] = 0;
     aDest[14] = 0;
     aDest[15] = 1;
     return aDest;
   },
   /**
    * Transposes a mat4 (flips the values over the diagonal).
    *
    * @param {Array} aMat
    *                mat4 to transpose
    * @param {Array} aDest
    *                optional, mat4 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat4 if specified, first operand otherwise
    */
   transpose: function M4_transpose(aMat, aDest)
   {
     if (!aDest || aMat === aDest) {
       let a01 = aMat[1];
       let a02 = aMat[2];
       let a03 = aMat[3];
       let a12 = aMat[6];
       let a13 = aMat[7];
       let a23 = aMat[11];
       aMat[1] = aMat[4];
       aMat[2] = aMat[8];
       aMat[3] = aMat[12];
       aMat[4] = a01;
       aMat[6] = aMat[9];
       aMat[7] = aMat[13];
       aMat[8] = a02;
       aMat[9] = a12;
       aMat[11] = aMat[14];
       aMat[12] = a03;
       aMat[13] = a13;
       aMat[14] = a23;
       return aMat;
     }
     aDest[0] = aMat[0];
     aDest[1] = aMat[4];
     aDest[2] = aMat[8];
     aDest[3] = aMat[12];
     aDest[4] = aMat[1];
     aDest[5] = aMat[5];
     aDest[6] = aMat[9];
     aDest[7] = aMat[13];
     aDest[8] = aMat[2];
     aDest[9] = aMat[6];
     aDest[10] = aMat[10];
     aDest[11] = aMat[14];
     aDest[12] = aMat[3];
     aDest[13] = aMat[7];
     aDest[14] = aMat[11];
     aDest[15] = aMat[15];
     return aDest;
   },
   /**
    * Calculate the determinant of a mat4.
    *
    * @param {Array} aMat
    *                mat4 to calculate determinant of
    *
    * @return {Number} determinant of the matrix
    */
   determinant: function M4_determinant(mat)
   {
     let a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
     let a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
     let a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];
     let a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15];
     return a30 * a21 * a12 * a03 - a20 * a31 * a12 * a03 -
            a30 * a11 * a22 * a03 + a10 * a31 * a22 * a03 +
            a20 * a11 * a32 * a03 - a10 * a21 * a32 * a03 -
            a30 * a21 * a02 * a13 + a20 * a31 * a02 * a13 +
            a30 * a01 * a22 * a13 - a00 * a31 * a22 * a13 -
            a20 * a01 * a32 * a13 + a00 * a21 * a32 * a13 +
            a30 * a11 * a02 * a23 - a10 * a31 * a02 * a23 -
            a30 * a01 * a12 * a23 + a00 * a31 * a12 * a23 +
            a10 * a01 * a32 * a23 - a00 * a11 * a32 * a23 -
            a20 * a11 * a02 * a33 + a10 * a21 * a02 * a33 +
            a20 * a01 * a12 * a33 - a00 * a21 * a12 * a33 -
            a10 * a01 * a22 * a33 + a00 * a11 * a22 * a33;
   },
   /**
    * Calculate the inverse of a mat4.
    *
    * @param {Array} aMat
    *                mat4 to calculate inverse of
    * @param {Array} aDest
    *                optional, mat4 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat4 if specified, first operand otherwise
    */
   inverse: function M4_inverse(aMat, aDest)
   {
     if (!aDest) {
       aDest = aMat;
     }
     let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3];
     let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7];
     let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11];
     let a30 = aMat[12], a31 = aMat[13], a32 = aMat[14], a33 = aMat[15];
     let b00 = a00 * a11 - a01 * a10;
     let b01 = a00 * a12 - a02 * a10;
     let b02 = a00 * a13 - a03 * a10;
     let b03 = a01 * a12 - a02 * a11;
     let b04 = a01 * a13 - a03 * a11;
     let b05 = a02 * a13 - a03 * a12;
     let b06 = a20 * a31 - a21 * a30;
     let b07 = a20 * a32 - a22 * a30;
     let b08 = a20 * a33 - a23 * a30;
     let b09 = a21 * a32 - a22 * a31;
     let b10 = a21 * a33 - a23 * a31;
     let b11 = a22 * a33 - a23 * a32;
     let id = 1 / ((b00 * b11 - b01 * b10 + b02 * b09 +
                    b03 * b08 - b04 * b07 + b05 * b06) || EPSILON);
     aDest[0] = ( a11 * b11 - a12 * b10 + a13 * b09) * id;
     aDest[1] = (-a01 * b11 + a02 * b10 - a03 * b09) * id;
     aDest[2] = ( a31 * b05 - a32 * b04 + a33 * b03) * id;
     aDest[3] = (-a21 * b05 + a22 * b04 - a23 * b03) * id;
     aDest[4] = (-a10 * b11 + a12 * b08 - a13 * b07) * id;
     aDest[5] = ( a00 * b11 - a02 * b08 + a03 * b07) * id;
     aDest[6] = (-a30 * b05 + a32 * b02 - a33 * b01) * id;
     aDest[7] = ( a20 * b05 - a22 * b02 + a23 * b01) * id;
     aDest[8] = ( a10 * b10 - a11 * b08 + a13 * b06) * id;
     aDest[9] = (-a00 * b10 + a01 * b08 - a03 * b06) * id;
     aDest[10] = ( a30 * b04 - a31 * b02 + a33 * b00) * id;
     aDest[11] = (-a20 * b04 + a21 * b02 - a23 * b00) * id;
     aDest[12] = (-a10 * b09 + a11 * b07 - a12 * b06) * id;
     aDest[13] = ( a00 * b09 - a01 * b07 + a02 * b06) * id;
     aDest[14] = (-a30 * b03 + a31 * b01 - a32 * b00) * id;
     aDest[15] = ( a20 * b03 - a21 * b01 + a22 * b00) * id;
     return aDest;
   },
   /**
    * Copies the upper 3x3 elements of a mat4 into another mat4.
    *
    * @param {Array} aMat
    *                mat4 containing values to copy
    * @param {Array} aDest
    *                optional, mat4 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat4 if specified, first operand otherwise
    */
   toRotationMat: function M4_toRotationMat(aMat, aDest)
   {
     if (!aDest) {
       aDest = new Float32Array(16);
     }
     aDest[0] = aMat[0];
     aDest[1] = aMat[1];
     aDest[2] = aMat[2];
     aDest[3] = aMat[3];
     aDest[4] = aMat[4];
     aDest[5] = aMat[5];
     aDest[6] = aMat[6];
     aDest[7] = aMat[7];
     aDest[8] = aMat[8];
     aDest[9] = aMat[9];
     aDest[10] = aMat[10];
     aDest[11] = aMat[11];
     aDest[12] = 0;
     aDest[13] = 0;
     aDest[14] = 0;
     aDest[15] = 1;
     return aDest;
   },
   /**
    * Copies the upper 3x3 elements of a mat4 into a mat3.
    *
    * @param {Array} aMat
    *                mat4 containing values to copy
    * @param {Array} aDest
    *                optional, mat3 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat3 if specified, first operand otherwise
    */
   toMat3: function M4_toMat3(aMat, aDest)
   {
     if (!aDest) {
       aDest = new Float32Array(9);
     }
     aDest[0] = aMat[0];
     aDest[1] = aMat[1];
     aDest[2] = aMat[2];
     aDest[3] = aMat[4];
     aDest[4] = aMat[5];
     aDest[5] = aMat[6];
     aDest[6] = aMat[8];
     aDest[7] = aMat[9];
     aDest[8] = aMat[10];
     return aDest;
   },
   /**
    * Calculate the inverse of the upper 3x3 elements of a mat4 and copies
    * the result into a mat3. The resulting matrix is useful for calculating
    * transformed normals.
    *
    * @param {Array} aMat
    *                mat4 containing values to invert and copy
    * @param {Array} aDest
    *                optional, mat3 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat3 if specified, first operand otherwise
    */
   toInverseMat3: function M4_toInverseMat3(aMat, aDest)
   {
     if (!aDest) {
       aDest = new Float32Array(9);
     }
     let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2];
     let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6];
     let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10];
     let b01 = a22 * a11 - a12 * a21;
     let b11 = -a22 * a10 + a12 * a20;
     let b21 = a21 * a10 - a11 * a20;
     let id = 1 / ((a00 * b01 + a01 * b11 + a02 * b21) || EPSILON);
     aDest[0] = b01 * id;
     aDest[1] = (-a22 * a01 + a02 * a21) * id;
     aDest[2] = ( a12 * a01 - a02 * a11) * id;
     aDest[3] = b11 * id;
     aDest[4] = ( a22 * a00 - a02 * a20) * id;
     aDest[5] = (-a12 * a00 + a02 * a10) * id;
     aDest[6] = b21 * id;
     aDest[7] = (-a21 * a00 + a01 * a20) * id;
     aDest[8] = ( a11 * a00 - a01 * a10) * id;
     return aDest;
   },
   /**
    * Performs a matrix multiplication.
    *
    * @param {Array} aMat
    *                first operand
    * @param {Array} aMat2
    *                second operand
    * @param {Array} aDest
    *                optional, mat4 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat4 if specified, first operand otherwise
    */
   multiply: function M4_multiply(aMat, aMat2, aDest)
   {
     if (!aDest) {
       aDest = aMat;
     }
     let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3];
     let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7];
     let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11];
     let a30 = aMat[12], a31 = aMat[13], a32 = aMat[14], a33 = aMat[15];
     let b00 = aMat2[0], b01 = aMat2[1], b02 = aMat2[2], b03 = aMat2[3];
     let b10 = aMat2[4], b11 = aMat2[5], b12 = aMat2[6], b13 = aMat2[7];
     let b20 = aMat2[8], b21 = aMat2[9], b22 = aMat2[10], b23 = aMat2[11];
     let b30 = aMat2[12], b31 = aMat2[13], b32 = aMat2[14], b33 = aMat2[15];
     aDest[0] = b00 * a00 + b01 * a10 + b02 * a20 + b03 * a30;
     aDest[1] = b00 * a01 + b01 * a11 + b02 * a21 + b03 * a31;
     aDest[2] = b00 * a02 + b01 * a12 + b02 * a22 + b03 * a32;
     aDest[3] = b00 * a03 + b01 * a13 + b02 * a23 + b03 * a33;
     aDest[4] = b10 * a00 + b11 * a10 + b12 * a20 + b13 * a30;
     aDest[5] = b10 * a01 + b11 * a11 + b12 * a21 + b13 * a31;
     aDest[6] = b10 * a02 + b11 * a12 + b12 * a22 + b13 * a32;
     aDest[7] = b10 * a03 + b11 * a13 + b12 * a23 + b13 * a33;
     aDest[8] = b20 * a00 + b21 * a10 + b22 * a20 + b23 * a30;
     aDest[9] = b20 * a01 + b21 * a11 + b22 * a21 + b23 * a31;
     aDest[10] = b20 * a02 + b21 * a12 + b22 * a22 + b23 * a32;
     aDest[11] = b20 * a03 + b21 * a13 + b22 * a23 + b23 * a33;
     aDest[12] = b30 * a00 + b31 * a10 + b32 * a20 + b33 * a30;
     aDest[13] = b30 * a01 + b31 * a11 + b32 * a21 + b33 * a31;
     aDest[14] = b30 * a02 + b31 * a12 + b32 * a22 + b33 * a32;
     aDest[15] = b30 * a03 + b31 * a13 + b32 * a23 + b33 * a33;
     return aDest;
   },
   /**
    * Transforms a vec3 with the given matrix.
    * 4th vector component is implicitly 1.
    *
    * @param {Array} aMat
    *                mat4 to transform the vector with
    * @param {Array} aVec
    *                vec3 to transform
    * @param {Array} aDest
    *                optional, vec3 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination vec3 if specified, aVec operand otherwise
    */
   multiplyVec3: function M4_multiplyVec3(aMat, aVec, aDest)
   {
     if (!aDest) {
       aDest = aVec;
     }
     let x = aVec[0];
     let y = aVec[1];
     let z = aVec[2];
     aDest[0] = aMat[0] * x + aMat[4] * y + aMat[8]  * z + aMat[12];
     aDest[1] = aMat[1] * x + aMat[5] * y + aMat[9]  * z + aMat[13];
     aDest[2] = aMat[2] * x + aMat[6] * y + aMat[10] * z + aMat[14];
     return aDest;
   },
   /**
    * Transforms a vec4 with the given matrix.
    *
    * @param {Array} aMat
    *                mat4 to transform the vector with
    * @param {Array} aVec
    *                vec4 to transform
    * @param {Array} aDest
    *                optional, vec4 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination vec4 if specified, vec4 operand otherwise
    */
   multiplyVec4: function M4_multiplyVec4(aMat, aVec, aDest)
   {
     if (!aDest) {
       aDest = aVec;
     }
     let x = aVec[0];
     let y = aVec[1];
     let z = aVec[2];
     let w = aVec[3];
     aDest[0] = aMat[0] * x + aMat[4] * y + aMat[8]  * z + aMat[12] * w;
     aDest[1] = aMat[1] * x + aMat[5] * y + aMat[9]  * z + aMat[13] * w;
     aDest[2] = aMat[2] * x + aMat[6] * y + aMat[10] * z + aMat[14] * w;
     aDest[3] = aMat[3] * x + aMat[7] * y + aMat[11] * z + aMat[15] * w;
     return aDest;
   },
   /**
    * Translates a matrix by the given vector.
    *
    * @param {Array} aMat
    *                mat4 to translate
    * @param {Array} aVec
    *                vec3 specifying the translation
    * @param {Array} aDest
    *                optional, mat4 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat4 if specified, first operand otherwise
    */
   translate: function M4_translate(aMat, aVec, aDest)
   {
     let x = aVec[0];
     let y = aVec[1];
     let z = aVec[2];
     if (!aDest || aMat === aDest) {
       aMat[12] = aMat[0] * x + aMat[4] * y + aMat[8] * z + aMat[12];
       aMat[13] = aMat[1] * x + aMat[5] * y + aMat[9] * z + aMat[13];
       aMat[14] = aMat[2] * x + aMat[6] * y + aMat[10] * z + aMat[14];
       aMat[15] = aMat[3] * x + aMat[7] * y + aMat[11] * z + aMat[15];
       return aMat;
     }
     let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3];
     let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7];
     let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11];
     aDest[0] = a00;
     aDest[1] = a01;
     aDest[2] = a02;
     aDest[3] = a03;
     aDest[4] = a10;
     aDest[5] = a11;
     aDest[6] = a12;
     aDest[7] = a13;
     aDest[8] = a20;
     aDest[9] = a21;
     aDest[10] = a22;
     aDest[11] = a23;
     aDest[12] = a00 * x + a10 * y + a20 * z + aMat[12];
     aDest[13] = a01 * x + a11 * y + a21 * z + aMat[13];
     aDest[14] = a02 * x + a12 * y + a22 * z + aMat[14];
     aDest[15] = a03 * x + a13 * y + a23 * z + aMat[15];
     return aDest;
   },
   /**
    * Scales a matrix by the given vector.
    *
    * @param {Array} aMat
    *                mat4 to translate
    * @param {Array} aVec
    *                vec3 specifying the scale on each axis
    * @param {Array} aDest
    *                optional, mat4 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat4 if specified, first operand otherwise
    */
   scale: function M4_scale(aMat, aVec, aDest)
   {
     let x = aVec[0];
     let y = aVec[1];
     let z = aVec[2];
     if (!aDest || aMat === aDest) {
       aMat[0] *= x;
       aMat[1] *= x;
       aMat[2] *= x;
       aMat[3] *= x;
       aMat[4] *= y;
       aMat[5] *= y;
       aMat[6] *= y;
       aMat[7] *= y;
       aMat[8] *= z;
       aMat[9] *= z;
       aMat[10] *= z;
       aMat[11] *= z;
       return aMat;
     }
     aDest[0] = aMat[0] * x;
     aDest[1] = aMat[1] * x;
     aDest[2] = aMat[2] * x;
     aDest[3] = aMat[3] * x;
     aDest[4] = aMat[4] * y;
     aDest[5] = aMat[5] * y;
     aDest[6] = aMat[6] * y;
     aDest[7] = aMat[7] * y;
     aDest[8] = aMat[8] * z;
     aDest[9] = aMat[9] * z;
     aDest[10] = aMat[10] * z;
     aDest[11] = aMat[11] * z;
     aDest[12] = aMat[12];
     aDest[13] = aMat[13];
     aDest[14] = aMat[14];
     aDest[15] = aMat[15];
     return aDest;
   },
   /**
    * Rotates a matrix by the given angle around the specified axis.
    * If rotating around a primary axis (x, y, z) one of the specialized
    * rotation functions should be used instead for performance,
    *
    * @param {Array} aMat
    *                mat4 to rotate
    * @param {Number} aAngle
    *                 the angle (in radians) to rotate
    * @param {Array} aAxis
    *                vec3 representing the axis to rotate around
    * @param {Array} aDest
    *                optional, mat4 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat4 if specified, first operand otherwise
    */
   rotate: function M4_rotate(aMat, aAngle, aAxis, aDest)
   {
     let x = aAxis[0];
     let y = aAxis[1];
     let z = aAxis[2];
     let len = 1 / (Math.sqrt(x * x + y * y + z * z) || EPSILON);
     x *= len;
     y *= len;
     z *= len;
     let s = Math.sin(aAngle);
     let c = Math.cos(aAngle);
     let t = 1 - c;
     let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3];
     let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7];
     let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11];
     let b00 = x * x * t + c, b01 = y * x * t + z * s, b02 = z * x * t - y * s;
     let b10 = x * y * t - z * s, b11 = y * y * t + c, b12 = z * y * t + x * s;
     let b20 = x * z * t + y * s, b21 = y * z * t - x * s, b22 = z * z * t + c;
     if (!aDest) {
       aDest = aMat;
     } else if (aMat !== aDest) {
       aDest[12] = aMat[12];
       aDest[13] = aMat[13];
       aDest[14] = aMat[14];
       aDest[15] = aMat[15];
     }
     aDest[0] = a00 * b00 + a10 * b01 + a20 * b02;
     aDest[1] = a01 * b00 + a11 * b01 + a21 * b02;
     aDest[2] = a02 * b00 + a12 * b01 + a22 * b02;
     aDest[3] = a03 * b00 + a13 * b01 + a23 * b02;
     aDest[4] = a00 * b10 + a10 * b11 + a20 * b12;
     aDest[5] = a01 * b10 + a11 * b11 + a21 * b12;
     aDest[6] = a02 * b10 + a12 * b11 + a22 * b12;
     aDest[7] = a03 * b10 + a13 * b11 + a23 * b12;
     aDest[8] = a00 * b20 + a10 * b21 + a20 * b22;
     aDest[9] = a01 * b20 + a11 * b21 + a21 * b22;
     aDest[10] = a02 * b20 + a12 * b21 + a22 * b22;
     aDest[11] = a03 * b20 + a13 * b21 + a23 * b22;
     return aDest;
   },
   /**
    * Rotates a matrix by the given angle around the X axis.
    *
    * @param {Array} aMat
    *                mat4 to rotate
    * @param {Number} aAngle
    *                 the angle (in radians) to rotate
    * @param {Array} aDest
    *                optional, mat4 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat4 if specified, first operand otherwise
    */
   rotateX: function M4_rotateX(aMat, aAngle, aDest)
   {
     let s = Math.sin(aAngle);
     let c = Math.cos(aAngle);
     let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7];
     let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11];
     if (!aDest) {
       aDest = aMat;
     } else if (aMat !== aDest) {
       aDest[0] = aMat[0];
       aDest[1] = aMat[1];
       aDest[2] = aMat[2];
       aDest[3] = aMat[3];
       aDest[12] = aMat[12];
       aDest[13] = aMat[13];
       aDest[14] = aMat[14];
       aDest[15] = aMat[15];
     }
     aDest[4] = a10 * c + a20 * s;
     aDest[5] = a11 * c + a21 * s;
     aDest[6] = a12 * c + a22 * s;
     aDest[7] = a13 * c + a23 * s;
     aDest[8] = a10 * -s + a20 * c;
     aDest[9] = a11 * -s + a21 * c;
     aDest[10] = a12 * -s + a22 * c;
     aDest[11] = a13 * -s + a23 * c;
     return aDest;
   },
   /**
    * Rotates a matrix by the given angle around the Y axix.
    *
    * @param {Array} aMat
    *                mat4 to rotate
    * @param {Number} aAngle
    *                 the angle (in radians) to rotate
    * @param {Array} aDest
    *                optional, mat4 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat4 if specified, first operand otherwise
    */
   rotateY: function M4_rotateY(aMat, aAngle, aDest)
   {
     let s = Math.sin(aAngle);
     let c = Math.cos(aAngle);
     let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3];
     let a20 = aMat[8], a21 = aMat[9], a22 = aMat[10], a23 = aMat[11];
     if (!aDest) {
       aDest = aMat;
     } else if (aMat !== aDest) {
       aDest[4] = aMat[4];
       aDest[5] = aMat[5];
       aDest[6] = aMat[6];
       aDest[7] = aMat[7];
       aDest[12] = aMat[12];
       aDest[13] = aMat[13];
       aDest[14] = aMat[14];
       aDest[15] = aMat[15];
     }
     aDest[0] = a00 * c + a20 * -s;
     aDest[1] = a01 * c + a21 * -s;
     aDest[2] = a02 * c + a22 * -s;
     aDest[3] = a03 * c + a23 * -s;
     aDest[8] = a00 * s + a20 *  c;
     aDest[9] = a01 * s + a21 *  c;
     aDest[10] = a02 * s + a22 *  c;
     aDest[11] = a03 * s + a23 *  c;
     return aDest;
   },
   /**
    * Rotates a matrix by the given angle around the Z axix.
    *
    * @param {Array} aMat
    *                mat4 to rotate
    * @param {Number} aAngle
    *                 the angle (in radians) to rotate
    * @param {Array} aDest
    *                optional, mat4 receiving operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination mat4 if specified, first operand otherwise
    */
   rotateZ: function M4_rotateZ(aMat, aAngle, aDest)
   {
     let s = Math.sin(aAngle);
     let c = Math.cos(aAngle);
     let a00 = aMat[0], a01 = aMat[1], a02 = aMat[2], a03 = aMat[3];
     let a10 = aMat[4], a11 = aMat[5], a12 = aMat[6], a13 = aMat[7];
     if (!aDest) {
       aDest = aMat;
     } else if (aMat !== aDest) {
       aDest[8] = aMat[8];
       aDest[9] = aMat[9];
       aDest[10] = aMat[10];
       aDest[11] = aMat[11];
       aDest[12] = aMat[12];
       aDest[13] = aMat[13];
       aDest[14] = aMat[14];
       aDest[15] = aMat[15];
     }
     aDest[0] = a00 * c + a10 * s;
     aDest[1] = a01 * c + a11 * s;
     aDest[2] = a02 * c + a12 * s;
     aDest[3] = a03 * c + a13 * s;
     aDest[4] = a00 * -s + a10 * c;
     aDest[5] = a01 * -s + a11 * c;
     aDest[6] = a02 * -s + a12 * c;
     aDest[7] = a03 * -s + a13 * c;
     return aDest;
   },
   /**
    * Generates a frustum matrix with the given bounds.
    *
    * @param {Number} aLeft
    *                 scalar, left bound of the frustum
    * @param {Number} aRight
    *                 scalar, right bound of the frustum
    * @param {Number} aBottom
    *                 scalar, bottom bound of the frustum
    * @param {Number} aTop
    *                 scalar, top bound of the frustum
    * @param {Number} aNear
    *                 scalar, near bound of the frustum
    * @param {Number} aFar
    *                 scalar, far bound of the frustum
    * @param {Array} aDest
    *                optional, mat4 frustum matrix will be written into
    *                if not specified result is written to a new mat4
    *
    * @return {Array} the destination mat4 if specified, a new mat4 otherwise
    */
   frustum: function M4_frustum(
     aLeft, aRight, aBottom, aTop, aNear, aFar, aDest)
   {
     if (!aDest) {
       aDest = new Float32Array(16);
     }
     let rl = (aRight - aLeft);
     let tb = (aTop - aBottom);
     let fn = (aFar - aNear);
     aDest[0] = (aNear * 2) / rl;
     aDest[1] = 0;
     aDest[2] = 0;
     aDest[3] = 0;
     aDest[4] = 0;
     aDest[5] = (aNear * 2) / tb;
     aDest[6] = 0;
     aDest[7] = 0;
     aDest[8] = (aRight + aLeft) / rl;
     aDest[9] = (aTop + aBottom) / tb;
     aDest[10] = -(aFar + aNear) / fn;
     aDest[11] = -1;
     aDest[12] = 0;
     aDest[13] = 0;
     aDest[14] = -(aFar * aNear * 2) / fn;
     aDest[15] = 0;
     return aDest;
   },
   /**
    * Generates a perspective projection matrix with the given bounds.
    *
    * @param {Number} aFovy
    *                 scalar, vertical field of view (degrees)
    * @param {Number} aAspect
    *                 scalar, aspect ratio (typically viewport width/height)
    * @param {Number} aNear
    *                 scalar, near bound of the frustum
    * @param {Number} aFar
    *                 scalar, far bound of the frustum
    * @param {Array} aDest
    *                optional, mat4 frustum matrix will be written into
    *                if not specified result is written to a new mat4
    *
    * @return {Array} the destination mat4 if specified, a new mat4 otherwise
    */
   perspective: function M4_perspective(
     aFovy, aAspect, aNear, aFar, aDest, aFlip)
   {
     let upper = aNear * Math.tan(aFovy * 0.00872664626); // PI * 180 / 2
     let right = upper * aAspect;
     let top = upper * (aFlip || 1);
     return mat4.frustum(-right, right, -top, top, aNear, aFar, aDest);
   },
   /**
    * Generates a orthogonal projection matrix with the given bounds.
    *
    * @param {Number} aLeft
    *                 scalar, left bound of the frustum
    * @param {Number} aRight
    *                 scalar, right bound of the frustum
    * @param {Number} aBottom
    *                 scalar, bottom bound of the frustum
    * @param {Number} aTop
    *                 scalar, top bound of the frustum
    * @param {Number} aNear
    *                 scalar, near bound of the frustum
    * @param {Number} aFar
    *                 scalar, far bound of the frustum
    * @param {Array} aDest
    *                optional, mat4 frustum matrix will be written into
    *                if not specified result is written to a new mat4
    *
    * @return {Array} the destination mat4 if specified, a new mat4 otherwise
    */
   ortho: function M4_ortho(aLeft, aRight, aBottom, aTop, aNear, aFar, aDest)
   {
     if (!aDest) {
       aDest = new Float32Array(16);
     }
     let rl = (aRight - aLeft);
     let tb = (aTop - aBottom);
     let fn = (aFar - aNear);
     aDest[0] = 2 / rl;
     aDest[1] = 0;
     aDest[2] = 0;
     aDest[3] = 0;
     aDest[4] = 0;
     aDest[5] = 2 / tb;
     aDest[6] = 0;
     aDest[7] = 0;
     aDest[8] = 0;
     aDest[9] = 0;
     aDest[10] = -2 / fn;
     aDest[11] = 0;
     aDest[12] = -(aLeft + aRight) / rl;
     aDest[13] = -(aTop + aBottom) / tb;
     aDest[14] = -(aFar + aNear) / fn;
     aDest[15] = 1;
     return aDest;
   },
   /**
    * Generates a look-at matrix with the given eye position, focal point, and
    * up axis.
    *
    * @param {Array} aEye
    *                vec3, position of the viewer
    * @param {Array} aCenter
    *                vec3, point the viewer is looking at
    * @param {Array} aUp
    *                vec3 pointing up
    * @param {Array} aDest
    *                optional, mat4 frustum matrix will be written into
    *                if not specified result is written to a new mat4
    *
    * @return {Array} the destination mat4 if specified, a new mat4 otherwise
    */
   lookAt: function M4_lookAt(aEye, aCenter, aUp, aDest)
   {
     if (!aDest) {
       aDest = new Float32Array(16);
     }
     let eyex = aEye[0];
     let eyey = aEye[1];
     let eyez = aEye[2];
     let upx = aUp[0];
     let upy = aUp[1];
     let upz = aUp[2];
     let centerx = aCenter[0];
     let centery = aCenter[1];
     let centerz = aCenter[2];
     let z0 = eyex - aCenter[0];
     let z1 = eyey - aCenter[1];
     let z2 = eyez - aCenter[2];
     let len = 1 / (Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2) || EPSILON);
     z0 *= len;
     z1 *= len;
     z2 *= len;
     let x0 = upy * z2 - upz * z1;
     let x1 = upz * z0 - upx * z2;
     let x2 = upx * z1 - upy * z0;
     len = 1 / (Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2) || EPSILON);
     x0 *= len;
     x1 *= len;
     x2 *= len;
     let y0 = z1 * x2 - z2 * x1;
     let y1 = z2 * x0 - z0 * x2;
     let y2 = z0 * x1 - z1 * x0;
     len = 1 / (Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2) || EPSILON);
     y0 *= len;
     y1 *= len;
     y2 *= len;
     aDest[0] = x0;
     aDest[1] = y0;
     aDest[2] = z0;
     aDest[3] = 0;
     aDest[4] = x1;
     aDest[5] = y1;
     aDest[6] = z1;
     aDest[7] = 0;
     aDest[8] = x2;
     aDest[9] = y2;
     aDest[10] = z2;
     aDest[11] = 0;
     aDest[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
     aDest[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
     aDest[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
     aDest[15] = 1;
     return aDest;
   },
   /**
    * Returns a string representation of a 4x4 matrix.
    *
    * @param {Array} aMat
    *                mat4 to represent as a string
    *
    * @return {String} representation of the matrix
    */
   str: function M4_str(mat)
   {
     return "[" + mat[0] + ", " + mat[1] + ", " + mat[2] + ", " + mat[3] +
            ", "+ mat[4] + ", " + mat[5] + ", " + mat[6] + ", " + mat[7] +
            ", "+ mat[8] + ", " + mat[9] + ", " + mat[10] + ", " + mat[11] +
            ", "+ mat[12] + ", " + mat[13] + ", " + mat[14] + ", " + mat[15] +
            "]";
   }
 };
 exports.mat4 = mat4;
 /**
  * quat4 - Quaternion.
  */
 let quat4 = {
   /**
    * Creates a new instance of a quat4 using the default Float32Array type.
    * Any array containing at least 4 numeric elements can serve as a quat4.
    *
    * @param {Array} aQuat
    *                optional, quat4 containing values to initialize with
    *
    * @return {Array} a new instance of a quat4
    */
   create: function Q4_create(aQuat)
   {
     let dest = new Float32Array(4);
     if (aQuat) {
       quat4.set(aQuat, dest);
     } else {
       quat4.identity(dest);
     }
     return dest;
   },
   /**
    * Copies the values of one quat4 to another.
    *
    * @param {Array} aQuat
    *                quat4 containing values to copy
    * @param {Array} aDest
    *                quat4 receiving copied values
    *
    * @return {Array} the destination quat4 receiving copied values
    */
   set: function Q4_set(aQuat, aDest)
   {
     aDest[0] = aQuat[0];
     aDest[1] = aQuat[1];
     aDest[2] = aQuat[2];
     aDest[3] = aQuat[3];
     return aDest;
   },
   /**
    * Sets a quat4 to an identity quaternion.
    *
    * @param {Array} aDest
    *                quat4 to set
    *
    * @return {Array} the same quaternion
    */
   identity: function Q4_identity(aDest)
   {
     aDest[0] = 0;
     aDest[1] = 0;
     aDest[2] = 0;
     aDest[3] = 1;
     return aDest;
   },
   /**
    * Calculate the W component of a quat4 from the X, Y, and Z components.
    * Assumes that quaternion is 1 unit in length.
    * Any existing W component will be ignored.
    *
    * @param {Array} aQuat
    *                quat4 to calculate W component of
    * @param {Array} aDest
    *                optional, quat4 receiving calculated values
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination quat if specified, first operand otherwise
    */
   calculateW: function Q4_calculateW(aQuat, aDest)
   {
     if (!aDest) {
       aDest = aQuat;
     }
     let x = aQuat[0];
     let y = aQuat[1];
     let z = aQuat[2];
     aDest[0] = x;
     aDest[1] = y;
     aDest[2] = z;
     aDest[3] = -Math.sqrt(Math.abs(1 - x * x - y * y - z * z));
     return aDest;
   },
   /**
    * Calculate the inverse of a quat4.
    *
    * @param {Array} aQuat
    *                quat4 to calculate the inverse of
    * @param {Array} aDest
    *                optional, quat4 receiving the inverse values
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination quat if specified, first operand otherwise
    */
   inverse: function Q4_inverse(aQuat, aDest)
   {
     if (!aDest) {
       aDest = aQuat;
     }
     aQuat[0] = -aQuat[0];
     aQuat[1] = -aQuat[1];
     aQuat[2] = -aQuat[2];
     return aQuat;
   },
   /**
    * Generates a unit quaternion of the same direction as the provided quat4.
    * If quaternion length is 0, returns [0, 0, 0, 0].
    *
    * @param {Array} aQuat
    *                quat4 to normalize
    * @param {Array} aDest
    *                optional, quat4 receiving the operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination quat if specified, first operand otherwise
    */
   normalize: function Q4_normalize(aQuat, aDest)
   {
     if (!aDest) {
       aDest = aQuat;
     }
     let x = aQuat[0];
     let y = aQuat[1];
     let z = aQuat[2];
     let w = aQuat[3];
     let len = Math.sqrt(x * x + y * y + z * z + w * w);
     if (Math.abs(len) < EPSILON) {
       aDest[0] = 0;
       aDest[1] = 0;
       aDest[2] = 0;
       aDest[3] = 0;
       return aDest;
     }
     len = 1 / len;
     aDest[0] = x * len;
     aDest[1] = y * len;
     aDest[2] = z * len;
     aDest[3] = w * len;
     return aDest;
   },
   /**
    * Calculate the length of a quat4.
    *
    * @param {Array} aQuat
    *                quat4 to calculate the length of
    *
    * @return {Number} length of the quaternion
    */
   length: function Q4_length(aQuat)
   {
     let x = aQuat[0];
     let y = aQuat[1];
     let z = aQuat[2];
     let w = aQuat[3];
     return Math.sqrt(x * x + y * y + z * z + w * w);
   },
   /**
    * Performs a quaternion multiplication.
    *
    * @param {Array} aQuat
    *                first operand
    * @param {Array} aQuat2
    *                second operand
    * @param {Array} aDest
    *                optional, quat4 receiving the operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination quat if specified, first operand otherwise
    */
   multiply: function Q4_multiply(aQuat, aQuat2, aDest)
   {
     if (!aDest) {
       aDest = aQuat;
     }
     let qax = aQuat[0];
     let qay = aQuat[1];
     let qaz = aQuat[2];
     let qaw = aQuat[3];
     let qbx = aQuat2[0];
     let qby = aQuat2[1];
     let qbz = aQuat2[2];
     let qbw = aQuat2[3];
     aDest[0] = qax * qbw + qaw * qbx + qay * qbz - qaz * qby;
     aDest[1] = qay * qbw + qaw * qby + qaz * qbx - qax * qbz;
     aDest[2] = qaz * qbw + qaw * qbz + qax * qby - qay * qbx;
     aDest[3] = qaw * qbw - qax * qbx - qay * qby - qaz * qbz;
     return aDest;
   },
   /**
    * Transforms a vec3 with the given quaternion.
    *
    * @param {Array} aQuat
    *                quat4 to transform the vector with
    * @param {Array} aVec
    *                vec3 to transform
    * @param {Array} aDest
    *                optional, vec3 receiving the operation result
    *                if not specified result is written to the first operand
    *
    * @return {Array} the destination vec3 if specified, aVec operand otherwise
    */
   multiplyVec3: function Q4_multiplyVec3(aQuat, aVec, aDest)
   {
     if (!aDest) {
       aDest = aVec;
     }
     let x = aVec[0];
     let y = aVec[1];
     let z = aVec[2];
     let qx = aQuat[0];
     let qy = aQuat[1];
     let qz = aQuat[2];
     let qw = aQuat[3];
     let ix = qw * x + qy * z - qz * y;
     let iy = qw * y + qz * x - qx * z;
     let iz = qw * z + qx * y - qy * x;
     let iw = -qx * x - qy * y - qz * z;
     aDest[0] = ix * qw + iw * -qx + iy * -qz - iz * -qy;
     aDest[1] = iy * qw + iw * -qy + iz * -qx - ix * -qz;
     aDest[2] = iz * qw + iw * -qz + ix * -qy - iy * -qx;
     return aDest;
   },
   /**
    * Performs a spherical linear interpolation between two quat4.
    *
    * @param {Array} aQuat
    *                first quaternion
    * @param {Array} aQuat2
    *                second quaternion
    * @param {Number} aSlerp
    *                 interpolation amount between the two inputs
    * @param {Array} aDest
    *                 optional, quat4 receiving the operation result
    *                 if not specified result is written to the first operand
    *
    * @return {Array} the destination quat if specified, first operand otherwise
    */
   slerp: function Q4_slerp(aQuat, aQuat2, aSlerp, aDest)
   {
     if (!aDest) {
       aDest = aQuat;
     }
     let cosHalfTheta = aQuat[0] * aQuat2[0] +
                        aQuat[1] * aQuat2[1] +
                        aQuat[2] * aQuat2[2] +
                        aQuat[3] * aQuat2[3];
     if (Math.abs(cosHalfTheta) >= 1) {
       aDest[0] = aQuat[0];
       aDest[1] = aQuat[1];
       aDest[2] = aQuat[2];
       aDest[3] = aQuat[3];
       return aDest;
     }
     let halfTheta = Math.acos(cosHalfTheta);
     let sinHalfTheta = Math.sqrt(1 - cosHalfTheta * cosHalfTheta);
     if (Math.abs(sinHalfTheta) < EPSILON) {
       aDest[0] = (aQuat[0] * 0.5 + aQuat2[0] * 0.5);
       aDest[1] = (aQuat[1] * 0.5 + aQuat2[1] * 0.5);
       aDest[2] = (aQuat[2] * 0.5 + aQuat2[2] * 0.5);
       aDest[3] = (aQuat[3] * 0.5 + aQuat2[3] * 0.5);
       return aDest;
     }
     let ratioA = Math.sin((1 - aSlerp) * halfTheta) / sinHalfTheta;
     let ratioB = Math.sin(aSlerp * halfTheta) / sinHalfTheta;
     aDest[0] = (aQuat[0] * ratioA + aQuat2[0] * ratioB);
     aDest[1] = (aQuat[1] * ratioA + aQuat2[1] * ratioB);
     aDest[2] = (aQuat[2] * ratioA + aQuat2[2] * ratioB);
     aDest[3] = (aQuat[3] * ratioA + aQuat2[3] * ratioB);
     return aDest;
   },
   /**
    * Calculates a 3x3 matrix from the given quat4.
    *
    * @param {Array} aQuat
    *                quat4 to create matrix from
    * @param {Array} aDest
    *                optional, mat3 receiving the initialization result
    *                if not specified, a new matrix is created
    *
    * @return {Array} the destination mat3 if specified, first operand otherwise
    */
   toMat3: function Q4_toMat3(aQuat, aDest)
   {
     if (!aDest) {
       aDest = new Float32Array(9);
     }
     let x = aQuat[0];
     let y = aQuat[1];
     let z = aQuat[2];
     let w = aQuat[3];
     let x2 = x + x;
     let y2 = y + y;
     let z2 = z + z;
     let xx = x * x2;
     let xy = x * y2;
     let xz = x * z2;
     let yy = y * y2;
     let yz = y * z2;
     let zz = z * z2;
     let wx = w * x2;
     let wy = w * y2;
     let wz = w * z2;
     aDest[0] = 1 - (yy + zz);
     aDest[1] = xy - wz;
     aDest[2] = xz + wy;
     aDest[3] = xy + wz;
     aDest[4] = 1 - (xx + zz);
     aDest[5] = yz - wx;
     aDest[6] = xz - wy;
     aDest[7] = yz + wx;
     aDest[8] = 1 - (xx + yy);
     return aDest;
   },
   /**
    * Calculates a 4x4 matrix from the given quat4.
    *
    * @param {Array} aQuat
    *                quat4 to create matrix from
    * @param {Array} aDest
    *                optional, mat4 receiving the initialization result
    *                if not specified, a new matrix is created
    *
    * @return {Array} the destination mat4 if specified, first operand otherwise
    */
   toMat4: function Q4_toMat4(aQuat, aDest)
   {
     if (!aDest) {
       aDest = new Float32Array(16);
     }
     let x = aQuat[0];
     let y = aQuat[1];
     let z = aQuat[2];
     let w = aQuat[3];
     let x2 = x + x;
     let y2 = y + y;
     let z2 = z + z;
     let xx = x * x2;
     let xy = x * y2;
     let xz = x * z2;
     let yy = y * y2;
     let yz = y * z2;
     let zz = z * z2;
     let wx = w * x2;
     let wy = w * y2;
     let wz = w * z2;
     aDest[0] = 1 - (yy + zz);
     aDest[1] = xy - wz;
     aDest[2] = xz + wy;
     aDest[3] = 0;
     aDest[4] = xy + wz;
     aDest[5] = 1 - (xx + zz);
     aDest[6] = yz - wx;
     aDest[7] = 0;
     aDest[8] = xz - wy;
     aDest[9] = yz + wx;
     aDest[10] = 1 - (xx + yy);
     aDest[11] = 0;
     aDest[12] = 0;
     aDest[13] = 0;
     aDest[14] = 0;
     aDest[15] = 1;
     return aDest;
   },
   /**
    * Creates a rotation quaternion from axis-angle.
    * This function expects that the axis is a normalized vector.
    *
    * @param {Array} aAxis
    *                an array of elements representing the [x, y, z] axis
    * @param {Number} aAngle
    *                 the angle of rotation
    * @param {Array} aDest
    *                optional, quat4 receiving the initialization result
    *                if not specified, a new quaternion is created
    *
    * @return {Array} the quaternion as [x, y, z, w]
    */
   fromAxis: function Q4_fromAxis(aAxis, aAngle, aDest)
   {
     if (!aDest) {
       aDest = new Float32Array(4);
     }
     let ang = aAngle * 0.5;
     let sin = Math.sin(ang);
     let cos = Math.cos(ang);
     aDest[0] = aAxis[0] * sin;
     aDest[1] = aAxis[1] * sin;
     aDest[2] = aAxis[2] * sin;
     aDest[3] = cos;
     return aDest;
   },
   /**
    * Creates a rotation quaternion from Euler angles.
    *
    * @param {Number} aYaw
    *                 the yaw angle of rotation
    * @param {Number} aPitch
    *                 the pitch angle of rotation
    * @param {Number} aRoll
    *                 the roll angle of rotation
    * @param {Array} aDest
    *                optional, quat4 receiving the initialization result
    *                if not specified, a new quaternion is created
    *
    * @return {Array} the quaternion as [x, y, z, w]
    */
   fromEuler: function Q4_fromEuler(aYaw, aPitch, aRoll, aDest)
   {
     if (!aDest) {
       aDest = new Float32Array(4);
     }
     let x = aPitch * 0.5;
     let y = aYaw * 0.5;
     let z = aRoll * 0.5;
     let sinr = Math.sin(x);
     let sinp = Math.sin(y);
     let siny = Math.sin(z);
     let cosr = Math.cos(x);
     let cosp = Math.cos(y);
     let cosy = Math.cos(z);
     aDest[0] = sinr * cosp * cosy - cosr * sinp * siny;
     aDest[1] = cosr * sinp * cosy + sinr * cosp * siny;
     aDest[2] = cosr * cosp * siny - sinr * sinp * cosy;
     aDest[3] = cosr * cosp * cosy + sinr * sinp * siny;
     return aDest;
   },
   /**
    * Returns a string representation of a quaternion.
    *
    * @param {Array} aQuat
    *                quat4 to represent as a string
    *
    * @return {String} representation of the quaternion
    */
   str: function Q4_str(aQuat) {
     return "[" + aQuat[0] + ", " +
                  aQuat[1] + ", " +
                  aQuat[2] + ", " +
                  aQuat[3] + "]";
   }
 };
 exports.quat4 = quat4;
 /**
  * Various algebraic math functions required by the engine.
  */
 let TiltMath = {
   /**
    * Helper function, converts degrees to radians.
    *
    * @param {Number} aDegrees
    *                 the degrees to be converted to radians
    *
    * @return {Number} the degrees converted to radians
    */
   radians: function TM_radians(aDegrees)
   {
     return aDegrees * PI_OVER_180;
   },
   /**
    * Helper function, converts radians to degrees.
    *
    * @param {Number} aRadians
    *                 the radians to be converted to degrees
    *
    * @return {Number} the radians converted to degrees
    */
   degrees: function TM_degrees(aRadians)
   {
     return aRadians * INV_PI_OVER_180;
   },
   /**
    * Re-maps a number from one range to another.
    *
    * @param {Number} aValue
    *                 the number to map
    * @param {Number} aLow1
    *                 the normal lower bound of the number
    * @param {Number} aHigh1
    *                 the normal upper bound of the number
    * @param {Number} aLow2
    *                 the new lower bound of the number
    * @param {Number} aHigh2
    *                 the new upper bound of the number
    *
    * @return {Number} the remapped number
    */
   map: function TM_map(aValue, aLow1, aHigh1, aLow2, aHigh2)
   {
     return aLow2 + (aHigh2 - aLow2) * ((aValue - aLow1) / (aHigh1 - aLow1));
   },
   /**
    * Returns if number is power of two.
    *
    * @param {Number} aNumber
    *                 the number to be verified
    *
    * @return {Boolean} true if x is power of two
    */
   isPowerOfTwo: function TM_isPowerOfTwo(aNumber)
   {
     return !(aNumber & (aNumber - 1));
   },
   /**
    * Returns the next closest power of two greater than a number.
    *
    * @param {Number} aNumber
    *                 the number to be converted
    *
    * @return {Number} the next closest power of two for x
    */
   nextPowerOfTwo: function TM_nextPowerOfTwo(aNumber)
   {
     --aNumber;
     for (let i = 1; i < 32; i <<= 1) {
       aNumber = aNumber | aNumber >> i;
     }
     return aNumber + 1;
   },
   /**
    * A convenient way of limiting values to a set boundary.
    *
    * @param {Number} aValue
    *                 the number to be limited
    * @param {Number} aMin
    *                 the minimum allowed value for the number
    * @param {Number} aMax
    *                 the maximum allowed value for the number
    */
   clamp: function TM_clamp(aValue, aMin, aMax)
   {
     return Math.max(aMin, Math.min(aMax, aValue));
   },
   /**
    * Convenient way to clamp a value to 0..1
    *
    * @param {Number} aValue
    *                 the number to be limited
    */
   saturate: function TM_saturate(aValue)
   {
     return Math.max(0, Math.min(1, aValue));
   },
   /**
    * Converts a hex color to rgba.
    * If the passed param is invalid, it will be converted to [0, 0, 0, 1];
    *
    * @param {String} aColor
    *                 color expressed in hex, or using rgb() or rgba()
    *
    * @return {Array} with 4 color 0..1 components: [red, green, blue, alpha]
    */
   hex2rgba: (function()
   {
     let cache = {};
     return function TM_hex2rgba(aColor) {
       let hex = aColor.charAt(0) === "#" ? aColor.substring(1) : aColor;
       // check the cache to see if this color wasn't converted already
       if (cache[hex] !== undefined) {
         return cache[hex];
       }
       // e.g. "f00"
       if (hex.length === 3) {
         let r = parseInt(hex.substring(0, 1), 16) * FIFTEEN_OVER_225;
         let g = parseInt(hex.substring(1, 2), 16) * FIFTEEN_OVER_225;
         let b = parseInt(hex.substring(2, 3), 16) * FIFTEEN_OVER_225;
         return (cache[hex] = [r, g, b, 1]);
       }
       // e.g. "f008"
       if (hex.length === 4) {
         let r = parseInt(hex.substring(0, 1), 16) * FIFTEEN_OVER_225;
         let g = parseInt(hex.substring(1, 2), 16) * FIFTEEN_OVER_225;
         let b = parseInt(hex.substring(2, 3), 16) * FIFTEEN_OVER_225;
         let a = parseInt(hex.substring(3, 4), 16) * FIFTEEN_OVER_225;
         return (cache[hex] = [r, g, b, a]);
       }
       // e.g. "ff0000"
       if (hex.length === 6) {
         let r = parseInt(hex.substring(0, 2), 16) * ONE_OVER_255;
         let g = parseInt(hex.substring(2, 4), 16) * ONE_OVER_255;
         let b = parseInt(hex.substring(4, 6), 16) * ONE_OVER_255;
         let a = 1;
         return (cache[hex] = [r, g, b, a]);
       }
       // e.g "ff0000aa"
       if (hex.length === 8) {
         let r = parseInt(hex.substring(0, 2), 16) * ONE_OVER_255;
         let g = parseInt(hex.substring(2, 4), 16) * ONE_OVER_255;
         let b = parseInt(hex.substring(4, 6), 16) * ONE_OVER_255;
         let a = parseInt(hex.substring(6, 8), 16) * ONE_OVER_255;
         return (cache[hex] = [r, g, b, a]);
       }
       // e.g. "rgba(255, 0, 0, 0.5)"
       if (hex.match("^rgba")) {
         let rgba = hex.substring(5, hex.length - 1).split(",");
         rgba[0] *= ONE_OVER_255;
         rgba[1] *= ONE_OVER_255;
         rgba[2] *= ONE_OVER_255;
         // in CSS, the alpha component of rgba() is already in the range 0..1
         return (cache[hex] = rgba);
       }
       // e.g. "rgb(255, 0, 0)"
       if (hex.match("^rgb")) {
         let rgba = hex.substring(4, hex.length - 1).split(",");
         rgba[0] *= ONE_OVER_255;
         rgba[1] *= ONE_OVER_255;
         rgba[2] *= ONE_OVER_255;
         rgba[3] = 1;
         return (cache[hex] = rgba);
       }
       // your argument is invalid
       return (cache[hex] = [0, 0, 0, 1]);
     };
   }())
 };
 exports.TiltMath = TiltMath;
 // bind the owner object to the necessary functions
 TiltUtils.bindObjectFunc(vec3);
 TiltUtils.bindObjectFunc(mat3);
 TiltUtils.bindObjectFunc(mat4);
 TiltUtils.bindObjectFunc(quat4);
 TiltUtils.bindObjectFunc(TiltMath);