gl-matrix.js

/* 
 * gl-matrix.js - High performance matrix and vector operations for WebGL
 * Version 1.1
 */

/*
 * 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.
 */

"use strict";

// Type declarations
(function() {
    // account for CommonJS environments
    var _global = (typeof(exports) != 'undefined') ? global : window;
    _global.glMatrixArrayType = _global.MatrixArray = null;
    _global.vec3 = {};
    _global.mat3 = {};
    _global.mat4 = {};
    _global.quat4 = {};

    // explicitly sets and returns the type of array to use within glMatrix
    _global.setMatrixArrayType = function(type) {
        return glMatrixArrayType = MatrixArray = type;
    };

    // auto-detects and returns the best type of array to use within glMatrix, falling
    // back to Array if typed arrays are unsupported
    _global.determineMatrixArrayType = function() {
        return setMatrixArrayType((typeof Float32Array !== 'undefined') ? Float32Array : Array);
    };

    determineMatrixArrayType();
})();

/*
 * vec3 - 3 Dimensional Vector
 */

/*
 * 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 MatrixArray(3);

    if (vec) {
        dest[0] = vec[0];
        dest[1] = vec[1];
        dest[2] = vec[2];
    } else {
        dest[0] = dest[1] = dest[2] = 0;
    }

    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],
        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],
        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],
        y = vec[1] - vec2[1],
        z = vec[2] - vec2[2],
        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
 */

/*
 * 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 MatrixArray(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) {
    if (!dest) { dest = mat3.create(); }
    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],
            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[15] = 1;
    dest[14] = 0;
    dest[13] = 0;
    dest[12] = 0;

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

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

    dest[3] = 0;
    dest[2] = mat[2];
    dest[1] = mat[1];
    dest[0] = mat[0];

    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
 */

/*
 * 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 MatrixArray(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) {
    if (!dest) { dest = mat4.create(); }
    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],
            a12 = mat[6], a13 = mat[7],
            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],
        a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7],
        a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11],
        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, null if matrix cannot be inverted
 */
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],
        a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7],
        a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11],
        a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15],

        b00 = a00 * a11 - a01 * a10,
        b01 = a00 * a12 - a02 * a10,
        b02 = a00 * a13 - a03 * a10,
        b03 = a01 * a12 - a02 * a11,
        b04 = a01 * a13 - a03 * a11,
        b05 = a02 * a13 - a03 * a12,
        b06 = a20 * a31 - a21 * a30,
        b07 = a20 * a32 - a22 * a30,
        b08 = a20 * a33 - a23 * a30,
        b09 = a21 * a32 - a22 * a31,
        b10 = a21 * a33 - a23 * a31,
        b11 = a22 * a33 - a23 * a32,

        d = (b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06),
        invDet;

        // Calculate the determinant
        if (!d) { return null; }
        invDet = 1 / d;

    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, null if the matrix cannot be inverted
 */
mat4.toInverseMat3 = function (mat, dest) {
    // Cache the matrix values (makes for huge speed increases!)
    var a00 = mat[0], a01 = mat[1], a02 = mat[2],
        a10 = mat[4], a11 = mat[5], a12 = mat[6],
        a20 = mat[8], a21 = mat[9], a22 = mat[10],

        b01 = a22 * a11 - a12 * a21,
        b11 = -a22 * a10 + a12 * a20,
        b21 = a21 * a10 - a11 * a20,

        d = a00 * b01 + a01 * b11 + a02 * b21,
        id;

    if (!d) { return null; }
    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],
        a10 = mat[4], a11 = mat[5], a12 = mat[6], a13 = mat[7],
        a20 = mat[8], a21 = mat[9], a22 = mat[10], a23 = mat[11],
        a30 = mat[12], a31 = mat[13], a32 = mat[14], a33 = mat[15],

        b00 = mat2[0], b01 = mat2[1], b02 = mat2[2], b03 = mat2[3],
        b10 = mat2[4], b11 = mat2[5], b12 = mat2[6], b13 = mat2[7],
        b20 = mat2[8], b21 = mat2[9], b22 = mat2[10], b23 = mat2[11],
        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],
        a00, a01, a02, a03,
        a10, a11, a12, a13,
        a20, a21, a22, a23;

    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;
    }

    a00 = mat[0]; a01 = mat[1]; a02 = mat[2]; a03 = mat[3];
    a10 = mat[4]; a11 = mat[5]; a12 = mat[6]; a13 = mat[7];
    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],
        len = Math.sqrt(x * x + y * y + z * z),
        s, c, t,
        a00, a01, a02, a03,
        a10, a11, a12, a13,
        a20, a21, a22, a23,
        b00, b01, b02,
        b10, b11, b12,
        b20, b21, b22;

    if (!len) { return null; }
    if (len !== 1) {
        len = 1 / len;
        x *= len;
        y *= len;
        z *= len;
    }

    s = Math.sin(angle);
    c = Math.cos(angle);
    t = 1 - c;

    a00 = mat[0]; a01 = mat[1]; a02 = mat[2]; a03 = mat[3];
    a10 = mat[4]; a11 = mat[5]; a12 = mat[6]; a13 = mat[7];
    a20 = mat[8]; a21 = mat[9]; a22 = mat[10]; a23 = mat[11];

    // Construct the elements of the rotation matrix
    b00 = x * x * t + c; b01 = y * x * t + z * s; b02 = z * x * t - y * s;
    b10 = x * y * t - z * s; b11 = y * y * t + c; b12 = z * y * t + x * s;
    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),
        c = Math.cos(angle),
        a10 = mat[4],
        a11 = mat[5],
        a12 = mat[6],
        a13 = mat[7],
        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),
        c = Math.cos(angle),
        a00 = mat[0],
        a01 = mat[1],
        a02 = mat[2],
        a03 = mat[3],
        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),
        c = Math.cos(angle),
        a00 = mat[0],
        a01 = mat[1],
        a02 = mat[2],
        a03 = mat[3],
        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),
        tb = (top - bottom),
        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),
        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),
        tb = (top - bottom),
        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.lookAt
 * 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 x0, x1, x2, y0, y1, y2, z0, z1, z2, len,
        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);
    }

    //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.fromRotationTranslation
 * Creates a matrix from a quaternion rotation and vector translation
 * This is equivalent to (but much faster than):
 *
 *     mat4.identity(dest);
 *     mat4.translate(dest, vec);
 *     var quatMat = mat4.create();
 *     quat4.toMat4(quat, quatMat);
 *     mat4.multiply(dest, quatMat);
 *
 * Params:
 * quat - quat4 specifying the rotation by
 * vec - vec3 specifying the translation
 * dest - Optional, mat4 receiving operation result. If not specified result is written to a new mat4
 *
 * Returns:
 * dest if specified, a new mat4 otherwise
 */
mat4.fromRotationTranslation = function (quat, vec, dest) {
    if (!dest) { dest = mat4.create(); }

    // Quaternion math
    var x = quat[0], y = quat[1], z = quat[2], w = quat[3],
        x2 = x + x,
        y2 = y + y,
        z2 = z + z,

        xx = x * x2,
        xy = x * y2,
        xz = x * z2,
        yy = y * y2,
        yz = y * z2,
        zz = z * z2,
        wx = w * x2,
        wy = w * y2,
        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] = vec[0];
    dest[13] = vec[1];
    dest[14] = vec[2];
    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.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 MatrixArray(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],
        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],
        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],
        qx = quat[0], qy = quat[1], qz = quat[2], qw = quat[3],

        // calculate quat * vec
        ix = qw * x + qy * z - qz * y,
        iy = qw * y + qz * x - qx * z,
        iz = qw * z + qx * y - qy * x,
        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],
        x2 = x + x,
        y2 = y + y,
        z2 = z + z,

        xx = x * x2,
        xy = x * y2,
        xz = x * z2,
        yy = y * y2,
        yz = y * z2,
        zz = z * z2,
        wx = w * x2,
        wy = w * y2,
        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],
        x2 = x + x,
        y2 = y + y,
        z2 = z + z,

        xx = x * x2,
        xy = x * y2,
        xz = x * z2,
        yy = y * y2,
        yz = y * z2,
        zz = z * z2,
        wx = w * x2,
        wy = w * y2,
        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],
        halfTheta,
        sinHalfTheta,
        ratioA,
        ratioB;

    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;
    }

    halfTheta = Math.acos(cosHalfTheta);
    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;
    }

    ratioA = Math.sin((1 - slerp) * halfTheta) / sinHalfTheta;
    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] + ']';
};