glMatrix.js

/* 
 * glMatrix.js - High performance matrix and vector operations for WebGL
 * version 0.9.6
 */
 
/*
 * Copyright (c) 2011 Brandon Jones
 *
 * This software is provided 'as-is', without any express or implied
 * warranty. In no event will the authors be held liable for any damages
 * arising from the use of this software.
 *
 * Permission is granted to anyone to use this software for any purpose,
 * including commercial applications, and to alter it and redistribute it
 * freely, subject to the following restrictions:
 *
 *    1. The origin of this software must not be misrepresented; you must not
 *    claim that you wrote the original software. If you use this software
 *    in a product, an acknowledgment in the product documentation would be
 *    appreciated but is not required.
 *
 *    2. Altered source versions must be plainly marked as such, and must not
 *    be misrepresented as being the original software.
 *
 *    3. This notice may not be removed or altered from any source
 *    distribution.
 */

// Fallback for systems that don't support WebGL
if(typeof Float32Array != 'undefined') {
        glMatrixArrayType = Float32Array;
} else if(typeof WebGLFloatArray != 'undefined') {
        glMatrixArrayType = WebGLFloatArray; // This is officially deprecated and should dissapear in future revisions.
} else {
        glMatrixArrayType = Array;
}

/*
 * vec3 - 3 Dimensional Vector
 */
var vec3 = {};

/*
 * vec3.create
 * Creates a new instance of a vec3 using the default array type
 * Any javascript array containing at least 3 numeric elements can serve as a vec3
 *
 * Params:
 * vec - Optional, vec3 containing values to initialize with
 *
 * Returns:
 * New vec3
 */
vec3.create = function(vec) {
        var dest = new glMatrixArrayType(3);
        
        if(vec) {
                dest[0] = vec[0];
                dest[1] = vec[1];
                dest[2] = vec[2];
        }
        
        return dest;
};

/*
 * vec3.set
 * Copies the values of one vec3 to another
 *
 * Params:
 * vec - vec3 containing values to copy
 * dest - vec3 receiving copied values
 *
 * Returns:
 * dest
 */
vec3.set = function(vec, dest) {
        dest[0] = vec[0];
        dest[1] = vec[1];
        dest[2] = vec[2];
        
        return dest;
};

/*
 * vec3.add
 * Performs a vector addition
 *
 * Params:
 * vec - vec3, first operand
 * vec2 - vec3, second operand
 * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
 *
 * Returns:
 * dest if specified, vec otherwise
 */
vec3.add = function(vec, vec2, dest) {
        if(!dest || vec == dest) {
                vec[0] += vec2[0];
                vec[1] += vec2[1];
                vec[2] += vec2[2];
                return vec;
        }
        
        dest[0] = vec[0] + vec2[0];
        dest[1] = vec[1] + vec2[1];
        dest[2] = vec[2] + vec2[2];
        return dest;
};

/*
 * vec3.subtract
 * Performs a vector subtraction
 *
 * Params:
 * vec - vec3, first operand
 * vec2 - vec3, second operand
 * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
 *
 * Returns:
 * dest if specified, vec otherwise
 */
vec3.subtract = function(vec, vec2, dest) {
        if(!dest || vec == dest) {
                vec[0] -= vec2[0];
                vec[1] -= vec2[1];
                vec[2] -= vec2[2];
                return vec;
        }
        
        dest[0] = vec[0] - vec2[0];
        dest[1] = vec[1] - vec2[1];
        dest[2] = vec[2] - vec2[2];
        return dest;
};

/*
 * vec3.negate
 * Negates the components of a vec3
 *
 * Params:
 * vec - vec3 to negate
 * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
 *
 * Returns:
 * dest if specified, vec otherwise
 */
vec3.negate = function(vec, dest) {
        if(!dest) { dest = vec; }
        
        dest[0] = -vec[0];
        dest[1] = -vec[1];
        dest[2] = -vec[2];
        return dest;
};

/*
 * vec3.scale
 * Multiplies the components of a vec3 by a scalar value
 *
 * Params:
 * vec - vec3 to scale
 * val - Numeric value to scale by
 * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
 *
 * Returns:
 * dest if specified, vec otherwise
 */
vec3.scale = function(vec, val, dest) {
        if(!dest || vec == dest) {
                vec[0] *= val;
                vec[1] *= val;
                vec[2] *= val;
                return vec;
        }
        
        dest[0] = vec[0]*val;
        dest[1] = vec[1]*val;
        dest[2] = vec[2]*val;
        return dest;
};

/*
 * vec3.normalize
 * Generates a unit vector of the same direction as the provided vec3
 * If vector length is 0, returns [0, 0, 0]
 *
 * Params:
 * vec - vec3 to normalize
 * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
 *
 * Returns:
 * dest if specified, vec otherwise
 */
vec3.normalize = function(vec, dest) {
        if(!dest) { dest = vec; }
        
        var x = vec[0], y = vec[1], z = vec[2];
        var len = Math.sqrt(x*x + y*y + z*z);
        
        if (!len) {
                dest[0] = 0;
                dest[1] = 0;
                dest[2] = 0;
                return dest;
        } else if (len == 1) {
                dest[0] = x;
                dest[1] = y;
                dest[2] = z;
                return dest;
        }
        
        len = 1 / len;
        dest[0] = x*len;
        dest[1] = y*len;
        dest[2] = z*len;
        return dest;
};

/*
 * vec3.cross
 * Generates the cross product of two vec3s
 *
 * Params:
 * vec - vec3, first operand
 * vec2 - vec3, second operand
 * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
 *
 * Returns:
 * dest if specified, vec otherwise
 */
vec3.cross = function(vec, vec2, dest){
        if(!dest) { dest = vec; }
        
        var x = vec[0], y = vec[1], z = vec[2];
        var x2 = vec2[0], y2 = vec2[1], z2 = vec2[2];
        
        dest[0] = y*z2 - z*y2;
        dest[1] = z*x2 - x*z2;
        dest[2] = x*y2 - y*x2;
        return dest;
};

/*
 * vec3.length
 * Caclulates the length of a vec3
 *
 * Params:
 * vec - vec3 to calculate length of
 *
 * Returns:
 * Length of vec
 */
vec3.length = function(vec){
        var x = vec[0], y = vec[1], z = vec[2];
        return Math.sqrt(x*x + y*y + z*z);
};

/*
 * vec3.dot
 * Caclulates the dot product of two vec3s
 *
 * Params:
 * vec - vec3, first operand
 * vec2 - vec3, second operand
 *
 * Returns:
 * Dot product of vec and vec2
 */
vec3.dot = function(vec, vec2){
        return vec[0]*vec2[0] + vec[1]*vec2[1] + vec[2]*vec2[2];
};

/*
 * vec3.direction
 * Generates a unit vector pointing from one vector to another
 *
 * Params:
 * vec - origin vec3
 * vec2 - vec3 to point to
 * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
 *
 * Returns:
 * dest if specified, vec otherwise
 */
vec3.direction = function(vec, vec2, dest) {
        if(!dest) { dest = vec; }
        
        var x = vec[0] - vec2[0];
        var y = vec[1] - vec2[1];
        var z = vec[2] - vec2[2];
        
        var len = Math.sqrt(x*x + y*y + z*z);
        if (!len) { 
                dest[0] = 0; 
                dest[1] = 0; 
                dest[2] = 0;
                return dest; 
        }
        
        len = 1 / len;
        dest[0] = x * len; 
        dest[1] = y * len; 
        dest[2] = z * len;
        return dest; 
};

/*
 * vec3.lerp
 * Performs a linear interpolation between two vec3
 *
 * Params:
 * vec - vec3, first vector
 * vec2 - vec3, second vector
 * lerp - interpolation amount between the two inputs
 * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
 *
 * Returns:
 * dest if specified, vec otherwise
 */
vec3.lerp = function(vec, vec2, lerp, dest){
    if(!dest) { dest = vec; }
    
    dest[0] = vec[0] + lerp * (vec2[0] - vec[0]);
    dest[1] = vec[1] + lerp * (vec2[1] - vec[1]);
    dest[2] = vec[2] + lerp * (vec2[2] - vec[2]);
    
    return dest;
}

/*
 * vec3.str
 * Returns a string representation of a vector
 *
 * Params:
 * vec - vec3 to represent as a string
 *
 * Returns:
 * string representation of vec
 */
vec3.str = function(vec) {
        return '[' + vec[0] + ', ' + vec[1] + ', ' + vec[2] + ']'; 
};

/*
 * mat3 - 3x3 Matrix
 */
var mat3 = {};

/*
 * mat3.create
 * Creates a new instance of a mat3 using the default array type
 * Any javascript array containing at least 9 numeric elements can serve as a mat3
 *
 * Params:
 * mat - Optional, mat3 containing values to initialize with
 *
 * Returns:
 * New mat3
 */
mat3.create = function(mat) {
        var dest = new glMatrixArrayType(9);
        
        if(mat) {
                dest[0] = mat[0];
                dest[1] = mat[1];
                dest[2] = mat[2];
                dest[3] = mat[3];
                dest[4] = mat[4];
                dest[5] = mat[5];
                dest[6] = mat[6];
                dest[7] = mat[7];
                dest[8] = mat[8];
        }
        
        return dest;
};

/*
 * mat3.set
 * Copies the values of one mat3 to another
 *
 * Params:
 * mat - mat3 containing values to copy
 * dest - mat3 receiving copied values
 *
 * Returns:
 * dest
 */
mat3.set = function(mat, dest) {
        dest[0] = mat[0];
        dest[1] = mat[1];
        dest[2] = mat[2];
        dest[3] = mat[3];
        dest[4] = mat[4];
        dest[5] = mat[5];
        dest[6] = mat[6];
        dest[7] = mat[7];
        dest[8] = mat[8];
        return dest;
};

/*
 * mat3.identity
 * Sets a mat3 to an identity matrix
 *
 * Params:
 * dest - mat3 to set
 *
 * Returns:
 * dest
 */
mat3.identity = function(dest) {
        dest[0] = 1;
        dest[1] = 0;
        dest[2] = 0;
        dest[3] = 0;
        dest[4] = 1;
        dest[5] = 0;
        dest[6] = 0;
        dest[7] = 0;
        dest[8] = 1;
        return dest;
};

/*
 * mat4.transpose
 * Transposes a mat3 (flips the values over the diagonal)
 *
 * Params:
 * mat - mat3 to transpose
 * dest - Optional, mat3 receiving transposed values. If not specified result is written to mat
 *
 * Returns:
 * dest is specified, mat otherwise
 */
mat3.transpose = function(mat, dest) {
        // If we are transposing ourselves we can skip a few steps but have to cache some values
        if(!dest || mat == dest) { 
                var a01 = mat[1], a02 = mat[2];
                var a12 = mat[5];
                
        mat[1] = mat[3];
        mat[2] = mat[6];
        mat[3] = a01;
        mat[5] = mat[7];
        mat[6] = a02;
        mat[7] = a12;
                return mat;
        }
        
        dest[0] = mat[0];
        dest[1] = mat[3];
        dest[2] = mat[6];
        dest[3] = mat[1];
        dest[4] = mat[4];
        dest[5] = mat[7];
        dest[6] = mat[2];
        dest[7] = mat[5];
        dest[8] = mat[8];
        return dest;
};

/*
 * mat3.toMat4
 * Copies the elements of a mat3 into the upper 3x3 elements of a mat4
 *
 * Params:
 * mat - mat3 containing values to copy
 * dest - Optional, mat4 receiving copied values
 *
 * Returns:
 * dest if specified, a new mat4 otherwise
 */
mat3.toMat4 = function(mat, dest) {
        if(!dest) { dest = mat4.create(); }
        
        dest[0] = mat[0];
        dest[1] = mat[1];
        dest[2] = mat[2];
        dest[3] = 0;

        dest[4] = mat[3];
        dest[5] = mat[4];
        dest[6] = mat[5];
        dest[7] = 0;

        dest[8] = mat[6];
        dest[9] = mat[7];
        dest[10] = mat[8];
        dest[11] = 0;

        dest[12] = 0;
        dest[13] = 0;
        dest[14] = 0;
        dest[15] = 1;
        
        return dest;
}

/*
 * mat3.str
 * Returns a string representation of a mat3
 *
 * Params:
 * mat - mat3 to represent as a string
 *
 * Returns:
 * string representation of mat
 */
mat3.str = function(mat) {
        return '[' + mat[0] + ', ' + mat[1] + ', ' + mat[2] + 
                ', ' + mat[3] + ', '+ mat[4] + ', ' + mat[5] + 
                ', ' + mat[6] + ', ' + mat[7] + ', '+ mat[8] + ']';
};

/*
 * mat4 - 4x4 Matrix
 */
var mat4 = {};

/*
 * mat4.create
 * Creates a new instance of a mat4 using the default array type
 * Any javascript array containing at least 16 numeric elements can serve as a mat4
 *
 * Params:
 * mat - Optional, mat4 containing values to initialize with
 *
 * Returns:
 * New mat4
 */
mat4.create = function(mat) {
        var dest = new glMatrixArrayType(16);
        
        if(mat) {
                dest[0] = mat[0];
                dest[1] = mat[1];
                dest[2] = mat[2];
                dest[3] = mat[3];
                dest[4] = mat[4];
                dest[5] = mat[5];
                dest[6] = mat[6];
                dest[7] = mat[7];
                dest[8] = mat[8];
                dest[9] = mat[9];
                dest[10] = mat[10];
                dest[11] = mat[11];
                dest[12] = mat[12];
                dest[13] = mat[13];
                dest[14] = mat[14];
                dest[15] = mat[15];
        }
        
        return dest;
};

/*
 * mat4.set
 * Copies the values of one mat4 to another
 *
 * Params:
 * mat - mat4 containing values to copy
 * dest - mat4 receiving copied values
 *
 * Returns:
 * dest
 */
mat4.set = function(mat, dest) {
        dest[0] = mat[0];
        dest[1] = mat[1];
        dest[2] = mat[2];
        dest[3] = mat[3];
        dest[4] = mat[4];
        dest[5] = mat[5];
        dest[6] = mat[6];
        dest[7] = mat[7];
        dest[8] = mat[8];
        dest[9] = mat[9];
        dest[10] = mat[10];
        dest[11] = mat[11];
        dest[12] = mat[12];
        dest[13] = mat[13];
        dest[14] = mat[14];
        dest[15] = mat[15];
        return dest;
};

/*
 * mat4.identity
 * Sets a mat4 to an identity matrix
 *
 * Params:
 * dest - mat4 to set
 *
 * Returns:
 * dest
 */
mat4.identity = function(dest) {
        dest[0] = 1;
        dest[1] = 0;
        dest[2] = 0;
        dest[3] = 0;
        dest[4] = 0;
        dest[5] = 1;
        dest[6] = 0;
        dest[7] = 0;
        dest[8] = 0;
        dest[9] = 0;
        dest[10] = 1;
        dest[11] = 0;
        dest[12] = 0;
        dest[13] = 0;
        dest[14] = 0;
        dest[15] = 1;
        return dest;
};

/*
 * mat4.transpose
 * Transposes a mat4 (flips the values over the diagonal)
 *
 * Params:
 * mat - mat4 to transpose
 * dest - Optional, mat4 receiving transposed values. If not specified result is written to mat
 *
 * Returns:
 * dest is specified, mat otherwise
 */
mat4.transpose = function(mat, dest) {
        // If we are transposing ourselves we can skip a few steps but have to cache some values
        if(!dest || mat == dest) { 
                var a01 = mat[1], a02 = mat[2], a03 = mat[3];
                var a12 = mat[6], a13 = mat[7];
                var a23 = mat[11];
                
                mat[1] = mat[4];
                mat[2] = mat[8];
                mat[3] = mat[12];
                mat[4] = a01;
                mat[6] = mat[9];
                mat[7] = mat[13];
                mat[8] = a02;
                mat[9] = a12;
                mat[11] = mat[14];
                mat[12] = a03;
                mat[13] = a13;
                mat[14] = a23;
                return mat;
        }
        
        dest[0] = mat[0];
        dest[1] = mat[4];
        dest[2] = mat[8];
        dest[3] = mat[12];
        dest[4] = mat[1];
        dest[5] = mat[5];
        dest[6] = mat[9];
        dest[7] = mat[13];
        dest[8] = mat[2];
        dest[9] = mat[6];
        dest[10] = mat[10];
        dest[11] = mat[14];
        dest[12] = mat[3];
        dest[13] = mat[7];
        dest[14] = mat[11];
        dest[15] = mat[15];
        return dest;
};

/*
 * mat4.determinant
 * Calculates the determinant of a mat4
 *
 * Params:
 * mat - mat4 to calculate determinant of
 *
 * Returns:
 * determinant of mat
 */
mat4.determinant = function(mat) {
        // Cache the matrix values (makes for huge speed increases!)
        var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
        var a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
        var a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];
        var 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;
};

/*
 * mat4.inverse
 * Calculates the inverse matrix of a mat4
 *
 * Params:
 * mat - mat4 to calculate inverse of
 * dest - Optional, mat4 receiving inverse matrix. If not specified result is written to mat
 *
 * Returns:
 * dest is specified, mat otherwise
 */
mat4.inverse = function(mat, dest) {
        if(!dest) { dest = mat; }
        
        // Cache the matrix values (makes for huge speed increases!)
        var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
        var a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
        var a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];
        var a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15];
        
        var b00 = a00*a11 - a01*a10;
        var b01 = a00*a12 - a02*a10;
        var b02 = a00*a13 - a03*a10;
        var b03 = a01*a12 - a02*a11;
        var b04 = a01*a13 - a03*a11;
        var b05 = a02*a13 - a03*a12;
        var b06 = a20*a31 - a21*a30;
        var b07 = a20*a32 - a22*a30;
        var b08 = a20*a33 - a23*a30;
        var b09 = a21*a32 - a22*a31;
        var b10 = a21*a33 - a23*a31;
        var b11 = a22*a33 - a23*a32;
        
        // Calculate the determinant (inlined to avoid double-caching)
        var invDet = 1/(b00*b11 - b01*b10 + b02*b09 + b03*b08 - b04*b07 + b05*b06);
        
        dest[0] = (a11*b11 - a12*b10 + a13*b09)*invDet;
        dest[1] = (-a01*b11 + a02*b10 - a03*b09)*invDet;
        dest[2] = (a31*b05 - a32*b04 + a33*b03)*invDet;
        dest[3] = (-a21*b05 + a22*b04 - a23*b03)*invDet;
        dest[4] = (-a10*b11 + a12*b08 - a13*b07)*invDet;
        dest[5] = (a00*b11 - a02*b08 + a03*b07)*invDet;
        dest[6] = (-a30*b05 + a32*b02 - a33*b01)*invDet;
        dest[7] = (a20*b05 - a22*b02 + a23*b01)*invDet;
        dest[8] = (a10*b10 - a11*b08 + a13*b06)*invDet;
        dest[9] = (-a00*b10 + a01*b08 - a03*b06)*invDet;
        dest[10] = (a30*b04 - a31*b02 + a33*b00)*invDet;
        dest[11] = (-a20*b04 + a21*b02 - a23*b00)*invDet;
        dest[12] = (-a10*b09 + a11*b07 - a12*b06)*invDet;
        dest[13] = (a00*b09 - a01*b07 + a02*b06)*invDet;
        dest[14] = (-a30*b03 + a31*b01 - a32*b00)*invDet;
        dest[15] = (a20*b03 - a21*b01 + a22*b00)*invDet;
        
        return dest;
};

/*
 * mat4.toRotationMat
 * Copies the upper 3x3 elements of a mat4 into another mat4
 *
 * Params:
 * mat - mat4 containing values to copy
 * dest - Optional, mat4 receiving copied values
 *
 * Returns:
 * dest is specified, a new mat4 otherwise
 */
mat4.toRotationMat = function(mat, dest) {
        if(!dest) { dest = mat4.create(); }
        
        dest[0] = mat[0];
        dest[1] = mat[1];
        dest[2] = mat[2];
        dest[3] = mat[3];
        dest[4] = mat[4];
        dest[5] = mat[5];
        dest[6] = mat[6];
        dest[7] = mat[7];
        dest[8] = mat[8];
        dest[9] = mat[9];
        dest[10] = mat[10];
        dest[11] = mat[11];
        dest[12] = 0;
        dest[13] = 0;
        dest[14] = 0;
        dest[15] = 1;
        
        return dest;
};

/*
 * mat4.toMat3
 * Copies the upper 3x3 elements of a mat4 into a mat3
 *
 * Params:
 * mat - mat4 containing values to copy
 * dest - Optional, mat3 receiving copied values
 *
 * Returns:
 * dest is specified, a new mat3 otherwise
 */
mat4.toMat3 = function(mat, dest) {
        if(!dest) { dest = mat3.create(); }
        
        dest[0] = mat[0];
        dest[1] = mat[1];
        dest[2] = mat[2];
        dest[3] = mat[4];
        dest[4] = mat[5];
        dest[5] = mat[6];
        dest[6] = mat[8];
        dest[7] = mat[9];
        dest[8] = mat[10];
        
        return dest;
};

/*
 * mat4.toInverseMat3
 * Calculates 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
 *
 * Params:
 * mat - mat4 containing values to invert and copy
 * dest - Optional, mat3 receiving values
 *
 * Returns:
 * dest is specified, a new mat3 otherwise
 */
mat4.toInverseMat3 = function(mat, dest) {
        // Cache the matrix values (makes for huge speed increases!)
        var a00 = mat[0], a01 = mat[1], a02 = mat[2];
        var a10 = mat[4], a11 = mat[5], a12 = mat[6];
        var a20 = mat[8], a21 = mat[9], a22 = mat[10];
        
        var b01 = a22*a11-a12*a21;
        var b11 = -a22*a10+a12*a20;
        var b21 = a21*a10-a11*a20;
                
        var d = a00*b01 + a01*b11 + a02*b21;
        if (!d) { return null; }
        var id = 1/d;
        
        if(!dest) { dest = mat3.create(); }
        
        dest[0] = b01*id;
        dest[1] = (-a22*a01 + a02*a21)*id;
        dest[2] = (a12*a01 - a02*a11)*id;
        dest[3] = b11*id;
        dest[4] = (a22*a00 - a02*a20)*id;
        dest[5] = (-a12*a00 + a02*a10)*id;
        dest[6] = b21*id;
        dest[7] = (-a21*a00 + a01*a20)*id;
        dest[8] = (a11*a00 - a01*a10)*id;
        
        return dest;
};

/*
 * mat4.multiply
 * Performs a matrix multiplication
 *
 * Params:
 * mat - mat4, first operand
 * mat2 - mat4, second operand
 * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
 *
 * Returns:
 * dest if specified, mat otherwise
 */
mat4.multiply = function(mat, mat2, dest) {
        if(!dest) { dest = mat }
        
        // Cache the matrix values (makes for huge speed increases!)
        var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
        var a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
        var a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];
        var a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15];
        
        var b00 = mat2[0], b01 = mat2[1], b02 = mat2[2], b03 = mat2[3];
        var b10 = mat2[4], b11 = mat2[5], b12 = mat2[6], b13 = mat2[7];
        var b20 = mat2[8], b21 = mat2[9], b22 = mat2[10], b23 = mat2[11];
        var b30 = mat2[12], b31 = mat2[13], b32 = mat2[14], b33 = mat2[15];
        
        dest[0] = b00*a00 + b01*a10 + b02*a20 + b03*a30;
        dest[1] = b00*a01 + b01*a11 + b02*a21 + b03*a31;
        dest[2] = b00*a02 + b01*a12 + b02*a22 + b03*a32;
        dest[3] = b00*a03 + b01*a13 + b02*a23 + b03*a33;
        dest[4] = b10*a00 + b11*a10 + b12*a20 + b13*a30;
        dest[5] = b10*a01 + b11*a11 + b12*a21 + b13*a31;
        dest[6] = b10*a02 + b11*a12 + b12*a22 + b13*a32;
        dest[7] = b10*a03 + b11*a13 + b12*a23 + b13*a33;
        dest[8] = b20*a00 + b21*a10 + b22*a20 + b23*a30;
        dest[9] = b20*a01 + b21*a11 + b22*a21 + b23*a31;
        dest[10] = b20*a02 + b21*a12 + b22*a22 + b23*a32;
        dest[11] = b20*a03 + b21*a13 + b22*a23 + b23*a33;
        dest[12] = b30*a00 + b31*a10 + b32*a20 + b33*a30;
        dest[13] = b30*a01 + b31*a11 + b32*a21 + b33*a31;
        dest[14] = b30*a02 + b31*a12 + b32*a22 + b33*a32;
        dest[15] = b30*a03 + b31*a13 + b32*a23 + b33*a33;
        
        return dest;
};

/*
 * mat4.multiplyVec3
 * Transforms a vec3 with the given matrix
 * 4th vector component is implicitly '1'
 *
 * Params:
 * mat - mat4 to transform the vector with
 * vec - vec3 to transform
 * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
 *
 * Returns:
 * dest if specified, vec otherwise
 */
mat4.multiplyVec3 = function(mat, vec, dest) {
        if(!dest) { dest = vec }
        
        var x = vec[0], y = vec[1], z = vec[2];
        
        dest[0] = mat[0]*x + mat[4]*y + mat[8]*z + mat[12];
        dest[1] = mat[1]*x + mat[5]*y + mat[9]*z + mat[13];
        dest[2] = mat[2]*x + mat[6]*y + mat[10]*z + mat[14];
        
        return dest;
};

/*
 * mat4.multiplyVec4
 * Transforms a vec4 with the given matrix
 *
 * Params:
 * mat - mat4 to transform the vector with
 * vec - vec4 to transform
 * dest - Optional, vec4 receiving operation result. If not specified result is written to vec
 *
 * Returns:
 * dest if specified, vec otherwise
 */
mat4.multiplyVec4 = function(mat, vec, dest) {
        if(!dest) { dest = vec }
        
        var x = vec[0], y = vec[1], z = vec[2], w = vec[3];
        
        dest[0] = mat[0]*x + mat[4]*y + mat[8]*z + mat[12]*w;
        dest[1] = mat[1]*x + mat[5]*y + mat[9]*z + mat[13]*w;
        dest[2] = mat[2]*x + mat[6]*y + mat[10]*z + mat[14]*w;
        dest[3] = mat[3]*x + mat[7]*y + mat[11]*z + mat[15]*w;
        
        return dest;
};

/*
 * mat4.translate
 * Translates a matrix by the given vector
 *
 * Params:
 * mat - mat4 to translate
 * vec - vec3 specifying the translation
 * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
 *
 * Returns:
 * dest if specified, mat otherwise
 */
mat4.translate = function(mat, vec, dest) {
        var x = vec[0], y = vec[1], z = vec[2];
        
        if(!dest || mat == dest) {
                mat[12] = mat[0]*x + mat[4]*y + mat[8]*z + mat[12];
                mat[13] = mat[1]*x + mat[5]*y + mat[9]*z + mat[13];
                mat[14] = mat[2]*x + mat[6]*y + mat[10]*z + mat[14];
                mat[15] = mat[3]*x + mat[7]*y + mat[11]*z + mat[15];
                return mat;
        }
        
        var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
        var a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
        var a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];
        
        dest[0] = a00;
        dest[1] = a01;
        dest[2] = a02;
        dest[3] = a03;
        dest[4] = a10;
        dest[5] = a11;
        dest[6] = a12;
        dest[7] = a13;
        dest[8] = a20;
        dest[9] = a21;
        dest[10] = a22;
        dest[11] = a23;
        
        dest[12] = a00*x + a10*y + a20*z + mat[12];
        dest[13] = a01*x + a11*y + a21*z + mat[13];
        dest[14] = a02*x + a12*y + a22*z + mat[14];
        dest[15] = a03*x + a13*y + a23*z + mat[15];
        return dest;
};

/*
 * mat4.scale
 * Scales a matrix by the given vector
 *
 * Params:
 * mat - mat4 to scale
 * vec - vec3 specifying the scale for each axis
 * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
 *
 * Returns:
 * dest if specified, mat otherwise
 */
mat4.scale = function(mat, vec, dest) {
        var x = vec[0], y = vec[1], z = vec[2];
        
        if(!dest || mat == dest) {
                mat[0] *= x;
                mat[1] *= x;
                mat[2] *= x;
                mat[3] *= x;
                mat[4] *= y;
                mat[5] *= y;
                mat[6] *= y;
                mat[7] *= y;
                mat[8] *= z;
                mat[9] *= z;
                mat[10] *= z;
                mat[11] *= z;
                return mat;
        }
        
        dest[0] = mat[0]*x;
        dest[1] = mat[1]*x;
        dest[2] = mat[2]*x;
        dest[3] = mat[3]*x;
        dest[4] = mat[4]*y;
        dest[5] = mat[5]*y;
        dest[6] = mat[6]*y;
        dest[7] = mat[7]*y;
        dest[8] = mat[8]*z;
        dest[9] = mat[9]*z;
        dest[10] = mat[10]*z;
        dest[11] = mat[11]*z;
        dest[12] = mat[12];
        dest[13] = mat[13];
        dest[14] = mat[14];
        dest[15] = mat[15];
        return dest;
};

/*
 * mat4.rotate
 * 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
 *
 * Params:
 * mat - mat4 to rotate
 * angle - angle (in radians) to rotate
 * axis - vec3 representing the axis to rotate around 
 * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
 *
 * Returns:
 * dest if specified, mat otherwise
 */
mat4.rotate = function(mat, angle, axis, dest) {
        var x = axis[0], y = axis[1], z = axis[2];
        var len = Math.sqrt(x*x + y*y + z*z);
        if (!len) { return null; }
        if (len != 1) {
                len = 1 / len;
                x *= len; 
                y *= len; 
                z *= len;
        }
        
        var s = Math.sin(angle);
        var c = Math.cos(angle);
        var t = 1-c;
        
        // Cache the matrix values (makes for huge speed increases!)
        var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
        var a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
        var a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];
        
        // Construct the elements of the rotation matrix
        var b00 = x*x*t + c, b01 = y*x*t + z*s, b02 = z*x*t - y*s;
        var b10 = x*y*t - z*s, b11 = y*y*t + c, b12 = z*y*t + x*s;
        var b20 = x*z*t + y*s, b21 = y*z*t - x*s, b22 = z*z*t + c;
        
        if(!dest) { 
                dest = mat 
        } else if(mat != dest) { // If the source and destination differ, copy the unchanged last row
                dest[12] = mat[12];
                dest[13] = mat[13];
                dest[14] = mat[14];
                dest[15] = mat[15];
        }
        
        // Perform rotation-specific matrix multiplication
        dest[0] = a00*b00 + a10*b01 + a20*b02;
        dest[1] = a01*b00 + a11*b01 + a21*b02;
        dest[2] = a02*b00 + a12*b01 + a22*b02;
        dest[3] = a03*b00 + a13*b01 + a23*b02;
        
        dest[4] = a00*b10 + a10*b11 + a20*b12;
        dest[5] = a01*b10 + a11*b11 + a21*b12;
        dest[6] = a02*b10 + a12*b11 + a22*b12;
        dest[7] = a03*b10 + a13*b11 + a23*b12;
        
        dest[8] = a00*b20 + a10*b21 + a20*b22;
        dest[9] = a01*b20 + a11*b21 + a21*b22;
        dest[10] = a02*b20 + a12*b21 + a22*b22;
        dest[11] = a03*b20 + a13*b21 + a23*b22;
        return dest;
};

/*
 * mat4.rotateX
 * Rotates a matrix by the given angle around the X axis
 *
 * Params:
 * mat - mat4 to rotate
 * angle - angle (in radians) to rotate
 * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
 *
 * Returns:
 * dest if specified, mat otherwise
 */
mat4.rotateX = function(mat, angle, dest) {
        var s = Math.sin(angle);
        var c = Math.cos(angle);
        
        // Cache the matrix values (makes for huge speed increases!)
        var a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
        var a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];

        if(!dest) { 
                dest = mat 
        } else if(mat != dest) { // If the source and destination differ, copy the unchanged rows
                dest[0] = mat[0];
                dest[1] = mat[1];
                dest[2] = mat[2];
                dest[3] = mat[3];
                
                dest[12] = mat[12];
                dest[13] = mat[13];
                dest[14] = mat[14];
                dest[15] = mat[15];
        }
        
        // Perform axis-specific matrix multiplication
        dest[4] = a10*c + a20*s;
        dest[5] = a11*c + a21*s;
        dest[6] = a12*c + a22*s;
        dest[7] = a13*c + a23*s;
        
        dest[8] = a10*-s + a20*c;
        dest[9] = a11*-s + a21*c;
        dest[10] = a12*-s + a22*c;
        dest[11] = a13*-s + a23*c;
        return dest;
};

/*
 * mat4.rotateY
 * Rotates a matrix by the given angle around the Y axis
 *
 * Params:
 * mat - mat4 to rotate
 * angle - angle (in radians) to rotate
 * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
 *
 * Returns:
 * dest if specified, mat otherwise
 */
mat4.rotateY = function(mat, angle, dest) {
        var s = Math.sin(angle);
        var c = Math.cos(angle);
        
        // Cache the matrix values (makes for huge speed increases!)
        var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
        var a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11];
        
        if(!dest) { 
                dest = mat 
        } else if(mat != dest) { // If the source and destination differ, copy the unchanged rows
                dest[4] = mat[4];
                dest[5] = mat[5];
                dest[6] = mat[6];
                dest[7] = mat[7];
                
                dest[12] = mat[12];
                dest[13] = mat[13];
                dest[14] = mat[14];
                dest[15] = mat[15];
        }
        
        // Perform axis-specific matrix multiplication
        dest[0] = a00*c + a20*-s;
        dest[1] = a01*c + a21*-s;
        dest[2] = a02*c + a22*-s;
        dest[3] = a03*c + a23*-s;
        
        dest[8] = a00*s + a20*c;
        dest[9] = a01*s + a21*c;
        dest[10] = a02*s + a22*c;
        dest[11] = a03*s + a23*c;
        return dest;
};

/*
 * mat4.rotateZ
 * Rotates a matrix by the given angle around the Z axis
 *
 * Params:
 * mat - mat4 to rotate
 * angle - angle (in radians) to rotate
 * dest - Optional, mat4 receiving operation result. If not specified result is written to mat
 *
 * Returns:
 * dest if specified, mat otherwise
 */
mat4.rotateZ = function(mat, angle, dest) {
        var s = Math.sin(angle);
        var c = Math.cos(angle);
        
        // Cache the matrix values (makes for huge speed increases!)
        var a00 = mat[0], a01 = mat[1], a02 = mat[2], a03 = mat[3];
        var a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7];
        
        if(!dest) { 
                dest = mat 
        } else if(mat != dest) { // If the source and destination differ, copy the unchanged last row
                dest[8] = mat[8];
                dest[9] = mat[9];
                dest[10] = mat[10];
                dest[11] = mat[11];
                
                dest[12] = mat[12];
                dest[13] = mat[13];
                dest[14] = mat[14];
                dest[15] = mat[15];
        }
        
        // Perform axis-specific matrix multiplication
        dest[0] = a00*c + a10*s;
        dest[1] = a01*c + a11*s;
        dest[2] = a02*c + a12*s;
        dest[3] = a03*c + a13*s;
        
        dest[4] = a00*-s + a10*c;
        dest[5] = a01*-s + a11*c;
        dest[6] = a02*-s + a12*c;
        dest[7] = a03*-s + a13*c;
        
        return dest;
};

/*
 * mat4.frustum
 * Generates a frustum matrix with the given bounds
 *
 * Params:
 * left, right - scalar, left and right bounds of the frustum
 * bottom, top - scalar, bottom and top bounds of the frustum
 * near, far - scalar, near and far bounds of the frustum
 * dest - Optional, mat4 frustum matrix will be written into
 *
 * Returns:
 * dest if specified, a new mat4 otherwise
 */
mat4.frustum = function(left, right, bottom, top, near, far, dest) {
        if(!dest) { dest = mat4.create(); }
        var rl = (right - left);
        var tb = (top - bottom);
        var fn = (far - near);
        dest[0] = (near*2) / rl;
        dest[1] = 0;
        dest[2] = 0;
        dest[3] = 0;
        dest[4] = 0;
        dest[5] = (near*2) / tb;
        dest[6] = 0;
        dest[7] = 0;
        dest[8] = (right + left) / rl;
        dest[9] = (top + bottom) / tb;
        dest[10] = -(far + near) / fn;
        dest[11] = -1;
        dest[12] = 0;
        dest[13] = 0;
        dest[14] = -(far*near*2) / fn;
        dest[15] = 0;
        return dest;
};

/*
 * mat4.perspective
 * Generates a perspective projection matrix with the given bounds
 *
 * Params:
 * fovy - scalar, vertical field of view
 * aspect - scalar, aspect ratio. typically viewport width/height
 * near, far - scalar, near and far bounds of the frustum
 * dest - Optional, mat4 frustum matrix will be written into
 *
 * Returns:
 * dest if specified, a new mat4 otherwise
 */
mat4.perspective = function(fovy, aspect, near, far, dest) {
        var top = near*Math.tan(fovy*Math.PI / 360.0);
        var right = top*aspect;
        return mat4.frustum(-right, right, -top, top, near, far, dest);
};

/*
 * mat4.ortho
 * Generates a orthogonal projection matrix with the given bounds
 *
 * Params:
 * left, right - scalar, left and right bounds of the frustum
 * bottom, top - scalar, bottom and top bounds of the frustum
 * near, far - scalar, near and far bounds of the frustum
 * dest - Optional, mat4 frustum matrix will be written into
 *
 * Returns:
 * dest if specified, a new mat4 otherwise
 */
mat4.ortho = function(left, right, bottom, top, near, far, dest) {
        if(!dest) { dest = mat4.create(); }
        var rl = (right - left);
        var tb = (top - bottom);
        var fn = (far - near);
        dest[0] = 2 / rl;
        dest[1] = 0;
        dest[2] = 0;
        dest[3] = 0;
        dest[4] = 0;
        dest[5] = 2 / tb;
        dest[6] = 0;
        dest[7] = 0;
        dest[8] = 0;
        dest[9] = 0;
        dest[10] = -2 / fn;
        dest[11] = 0;
        dest[12] = -(left + right) / rl;
        dest[13] = -(top + bottom) / tb;
        dest[14] = -(far + near) / fn;
        dest[15] = 1;
        return dest;
};

/*
 * mat4.ortho
 * Generates a look-at matrix with the given eye position, focal point, and up axis
 *
 * Params:
 * eye - vec3, position of the viewer
 * center - vec3, point the viewer is looking at
 * up - vec3 pointing "up"
 * dest - Optional, mat4 frustum matrix will be written into
 *
 * Returns:
 * dest if specified, a new mat4 otherwise
 */
mat4.lookAt = function(eye, center, up, dest) {
        if(!dest) { dest = mat4.create(); }
        
        var eyex = eye[0],
                eyey = eye[1],
                eyez = eye[2],
                upx = up[0],
                upy = up[1],
                upz = up[2],
                centerx = center[0],
                centery = center[1],
                centerz = center[2];

        if (eyex == centerx && eyey == centery && eyez == centerz) {
                return mat4.identity(dest);
        }
        
        var z0,z1,z2,x0,x1,x2,y0,y1,y2,len;
        
        //vec3.direction(eye, center, z);
        z0 = eyex - center[0];
        z1 = eyey - center[1];
        z2 = eyez - center[2];
        
        // normalize (no check needed for 0 because of early return)
        len = 1/Math.sqrt(z0*z0 + z1*z1 + z2*z2);
        z0 *= len;
        z1 *= len;
        z2 *= len;
        
        //vec3.normalize(vec3.cross(up, z, x));
        x0 = upy*z2 - upz*z1;
        x1 = upz*z0 - upx*z2;
        x2 = upx*z1 - upy*z0;
        len = Math.sqrt(x0*x0 + x1*x1 + x2*x2);
        if (!len) {
                x0 = 0;
                x1 = 0;
                x2 = 0;
        } else {
                len = 1/len;
                x0 *= len;
                x1 *= len;
                x2 *= len;
        };
        
        //vec3.normalize(vec3.cross(z, x, y));
        y0 = z1*x2 - z2*x1;
        y1 = z2*x0 - z0*x2;
        y2 = z0*x1 - z1*x0;
        
        len = Math.sqrt(y0*y0 + y1*y1 + y2*y2);
        if (!len) {
                y0 = 0;
                y1 = 0;
                y2 = 0;
        } else {
                len = 1/len;
                y0 *= len;
                y1 *= len;
                y2 *= len;
        }
        
        dest[0] = x0;
        dest[1] = y0;
        dest[2] = z0;
        dest[3] = 0;
        dest[4] = x1;
        dest[5] = y1;
        dest[6] = z1;
        dest[7] = 0;
        dest[8] = x2;
        dest[9] = y2;
        dest[10] = z2;
        dest[11] = 0;
        dest[12] = -(x0*eyex + x1*eyey + x2*eyez);
        dest[13] = -(y0*eyex + y1*eyey + y2*eyez);
        dest[14] = -(z0*eyex + z1*eyey + z2*eyez);
        dest[15] = 1;
        
        return dest;
};

/*
 * mat4.str
 * Returns a string representation of a mat4
 *
 * Params:
 * mat - mat4 to represent as a string
 *
 * Returns:
 * string representation of mat
 */
mat4.str = function(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] + ']';
};

/*
 * quat4 - Quaternions 
 */
quat4 = {};

/*
 * quat4.create
 * Creates a new instance of a quat4 using the default array type
 * Any javascript array containing at least 4 numeric elements can serve as a quat4
 *
 * Params:
 * quat - Optional, quat4 containing values to initialize with
 *
 * Returns:
 * New quat4
 */
quat4.create = function(quat) {
        var dest = new glMatrixArrayType(4);
        
        if(quat) {
                dest[0] = quat[0];
                dest[1] = quat[1];
                dest[2] = quat[2];
                dest[3] = quat[3];
        }
        
        return dest;
};

/*
 * quat4.set
 * Copies the values of one quat4 to another
 *
 * Params:
 * quat - quat4 containing values to copy
 * dest - quat4 receiving copied values
 *
 * Returns:
 * dest
 */
quat4.set = function(quat, dest) {
        dest[0] = quat[0];
        dest[1] = quat[1];
        dest[2] = quat[2];
        dest[3] = quat[3];
        
        return dest;
};

/*
 * quat4.calculateW
 * Calculates 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. 
 *
 * Params:
 * quat - quat4 to calculate W component of
 * dest - Optional, quat4 receiving calculated values. If not specified result is written to quat
 *
 * Returns:
 * dest if specified, quat otherwise
 */
quat4.calculateW = function(quat, dest) {
        var x = quat[0], y = quat[1], z = quat[2];

        if(!dest || quat == dest) {
                quat[3] = -Math.sqrt(Math.abs(1.0 - x*x - y*y - z*z));
                return quat;
        }
        dest[0] = x;
        dest[1] = y;
        dest[2] = z;
        dest[3] = -Math.sqrt(Math.abs(1.0 - x*x - y*y - z*z));
        return dest;
}

/*
 * quat4.inverse
 * Calculates the inverse of a quat4
 *
 * Params:
 * quat - quat4 to calculate inverse of
 * dest - Optional, quat4 receiving inverse values. If not specified result is written to quat
 *
 * Returns:
 * dest if specified, quat otherwise
 */
quat4.inverse = function(quat, dest) {
        if(!dest || quat == dest) {
                quat[0] *= -1;
                quat[1] *= -1;
                quat[2] *= -1;
                return quat;
        }
        dest[0] = -quat[0];
        dest[1] = -quat[1];
        dest[2] = -quat[2];
        dest[3] = quat[3];
        return dest;
}

/*
 * quat4.length
 * Calculates the length of a quat4
 *
 * Params:
 * quat - quat4 to calculate length of
 *
 * Returns:
 * Length of quat
 */
quat4.length = function(quat) {
        var x = quat[0], y = quat[1], z = quat[2], w = quat[3];
        return Math.sqrt(x*x + y*y + z*z + w*w);
}

/*
 * quat4.normalize
 * Generates a unit quaternion of the same direction as the provided quat4
 * If quaternion length is 0, returns [0, 0, 0, 0]
 *
 * Params:
 * quat - quat4 to normalize
 * dest - Optional, quat4 receiving operation result. If not specified result is written to quat
 *
 * Returns:
 * dest if specified, quat otherwise
 */
quat4.normalize = function(quat, dest) {
        if(!dest) { dest = quat; }
        
        var x = quat[0], y = quat[1], z = quat[2], w = quat[3];
        var len = Math.sqrt(x*x + y*y + z*z + w*w);
        if(len == 0) {
                dest[0] = 0;
                dest[1] = 0;
                dest[2] = 0;
                dest[3] = 0;
                return dest;
        }
        len = 1/len;
        dest[0] = x * len;
        dest[1] = y * len;
        dest[2] = z * len;
        dest[3] = w * len;
        
        return dest;
}

/*
 * quat4.multiply
 * Performs a quaternion multiplication
 *
 * Params:
 * quat - quat4, first operand
 * quat2 - quat4, second operand
 * dest - Optional, quat4 receiving operation result. If not specified result is written to quat
 *
 * Returns:
 * dest if specified, quat otherwise
 */
quat4.multiply = function(quat, quat2, dest) {
        if(!dest) { dest = quat; }
        
        var qax = quat[0], qay = quat[1], qaz = quat[2], qaw = quat[3];
        var qbx = quat2[0], qby = quat2[1], qbz = quat2[2], qbw = quat2[3];
        
        dest[0] = qax*qbw + qaw*qbx + qay*qbz - qaz*qby;
        dest[1] = qay*qbw + qaw*qby + qaz*qbx - qax*qbz;
        dest[2] = qaz*qbw + qaw*qbz + qax*qby - qay*qbx;
        dest[3] = qaw*qbw - qax*qbx - qay*qby - qaz*qbz;
        
        return dest;
}

/*
 * quat4.multiplyVec3
 * Transforms a vec3 with the given quaternion
 *
 * Params:
 * quat - quat4 to transform the vector with
 * vec - vec3 to transform
 * dest - Optional, vec3 receiving operation result. If not specified result is written to vec
 *
 * Returns:
 * dest if specified, vec otherwise
 */
quat4.multiplyVec3 = function(quat, vec, dest) {
        if(!dest) { dest = vec; }
        
        var x = vec[0], y = vec[1], z = vec[2];
        var qx = quat[0], qy = quat[1], qz = quat[2], qw = quat[3];

        // calculate quat * vec
        var ix = qw*x + qy*z - qz*y;
        var iy = qw*y + qz*x - qx*z;
        var iz = qw*z + qx*y - qy*x;
        var iw = -qx*x - qy*y - qz*z;
        
        // calculate result * inverse quat
        dest[0] = ix*qw + iw*-qx + iy*-qz - iz*-qy;
        dest[1] = iy*qw + iw*-qy + iz*-qx - ix*-qz;
        dest[2] = iz*qw + iw*-qz + ix*-qy - iy*-qx;
        
        return dest;
}

/*
 * quat4.toMat3
 * Calculates a 3x3 matrix from the given quat4
 *
 * Params:
 * quat - quat4 to create matrix from
 * dest - Optional, mat3 receiving operation result
 *
 * Returns:
 * dest if specified, a new mat3 otherwise
 */
quat4.toMat3 = function(quat, dest) {
        if(!dest) { dest = mat3.create(); }
        
        var x = quat[0], y = quat[1], z = quat[2], w = quat[3];

        var x2 = x + x;
        var y2 = y + y;
        var z2 = z + z;

        var xx = x*x2;
        var xy = x*y2;
        var xz = x*z2;

        var yy = y*y2;
        var yz = y*z2;
        var zz = z*z2;

        var wx = w*x2;
        var wy = w*y2;
        var wz = w*z2;

        dest[0] = 1 - (yy + zz);
        dest[1] = xy - wz;
        dest[2] = xz + wy;

        dest[3] = xy + wz;
        dest[4] = 1 - (xx + zz);
        dest[5] = yz - wx;

        dest[6] = xz - wy;
        dest[7] = yz + wx;
        dest[8] = 1 - (xx + yy);
        
        return dest;
}

/*
 * quat4.toMat4
 * Calculates a 4x4 matrix from the given quat4
 *
 * Params:
 * quat - quat4 to create matrix from
 * dest - Optional, mat4 receiving operation result
 *
 * Returns:
 * dest if specified, a new mat4 otherwise
 */
quat4.toMat4 = function(quat, dest) {
        if(!dest) { dest = mat4.create(); }
        
        var x = quat[0], y = quat[1], z = quat[2], w = quat[3];

        var x2 = x + x;
        var y2 = y + y;
        var z2 = z + z;

        var xx = x*x2;
        var xy = x*y2;
        var xz = x*z2;

        var yy = y*y2;
        var yz = y*z2;
        var zz = z*z2;

        var wx = w*x2;
        var wy = w*y2;
        var wz = w*z2;

        dest[0] = 1 - (yy + zz);
        dest[1] = xy - wz;
        dest[2] = xz + wy;
        dest[3] = 0;

        dest[4] = xy + wz;
        dest[5] = 1 - (xx + zz);
        dest[6] = yz - wx;
        dest[7] = 0;

        dest[8] = xz - wy;
        dest[9] = yz + wx;
        dest[10] = 1 - (xx + yy);
        dest[11] = 0;

        dest[12] = 0;
        dest[13] = 0;
        dest[14] = 0;
        dest[15] = 1;
        
        return dest;
}

/*
 * quat4.slerp
 * Performs a spherical linear interpolation between two quat4
 *
 * Params:
 * quat - quat4, first quaternion
 * quat2 - quat4, second quaternion
 * slerp - interpolation amount between the two inputs
 * dest - Optional, quat4 receiving operation result. If not specified result is written to quat
 *
 * Returns:
 * dest if specified, quat otherwise
 */
quat4.slerp = function(quat, quat2, slerp, dest) {
    if(!dest) { dest = quat; }
    
        var cosHalfTheta =  quat[0]*quat2[0] + quat[1]*quat2[1] + quat[2]*quat2[2] + quat[3]*quat2[3];
        
        if (Math.abs(cosHalfTheta) >= 1.0){
            if(dest != quat) {
                    dest[0] = quat[0];
                    dest[1] = quat[1];
                    dest[2] = quat[2];
                    dest[3] = quat[3];
                }
                return dest;
        }
        
        var halfTheta = Math.acos(cosHalfTheta);
        var sinHalfTheta = Math.sqrt(1.0 - cosHalfTheta*cosHalfTheta);

        if (Math.abs(sinHalfTheta) < 0.001){
                dest[0] = (quat[0]*0.5 + quat2[0]*0.5);
                dest[1] = (quat[1]*0.5 + quat2[1]*0.5);
                dest[2] = (quat[2]*0.5 + quat2[2]*0.5);
                dest[3] = (quat[3]*0.5 + quat2[3]*0.5);
                return dest;
        }
        
        var ratioA = Math.sin((1 - slerp)*halfTheta) / sinHalfTheta;
        var ratioB = Math.sin(slerp*halfTheta) / sinHalfTheta; 
        
        dest[0] = (quat[0]*ratioA + quat2[0]*ratioB);
        dest[1] = (quat[1]*ratioA + quat2[1]*ratioB);
        dest[2] = (quat[2]*ratioA + quat2[2]*ratioB);
        dest[3] = (quat[3]*ratioA + quat2[3]*ratioB);
        
        return dest;
}


/*
 * quat4.str
 * Returns a string representation of a quaternion
 *
 * Params:
 * quat - quat4 to represent as a string
 *
 * Returns:
 * string representation of quat
 */
quat4.str = function(quat) {
        return '[' + quat[0] + ', ' + quat[1] + ', ' + quat[2] + ', ' + quat[3] + ']'; 
}