JSDoc: Source: mat4.js

# Source: mat4.js

    /* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV.

    Permission is hereby granted, free of charge, to any person obtaining a copy
    of this software and associated documentation files (the "Software"), to deal
    in the Software without restriction, including without limitation the rights
    to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
    copies of the Software, and to permit persons to whom the Software is
    furnished to do so, subject to the following conditions:

    The above copyright notice and this permission notice shall be included in
    all copies or substantial portions of the Software.

    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
    FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
    AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
    LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
    OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
    THE SOFTWARE. */

    import * as glMatrix from "./common";

    /**
     * 4x4 Matrix
     * @module mat4
     */

    /**
     * Creates a new identity mat4
     *
     * @returns {mat4} a new 4x4 matrix
     */
    export function create() {
      let out = new glMatrix.ARRAY_TYPE(16);
      out[0] = 1;
      out[1] = 0;
      out[2] = 0;
      out[3] = 0;
      out[4] = 0;
      out[5] = 1;
      out[6] = 0;
      out[7] = 0;
      out[8] = 0;
      out[9] = 0;
      out[10] = 1;
      out[11] = 0;
      out[12] = 0;
      out[13] = 0;
      out[14] = 0;
      out[15] = 1;
      return out;
    }

    /**
     * Creates a new mat4 initialized with values from an existing matrix
     *
     * @param {mat4} a matrix to clone
     * @returns {mat4} a new 4x4 matrix
     */
    export function clone(a) {
      let out = new glMatrix.ARRAY_TYPE(16);
      out[0] = a[0];
      out[1] = a[1];
      out[2] = a[2];
      out[3] = a[3];
      out[4] = a[4];
      out[5] = a[5];
      out[6] = a[6];
      out[7] = a[7];
      out[8] = a[8];
      out[9] = a[9];
      out[10] = a[10];
      out[11] = a[11];
      out[12] = a[12];
      out[13] = a[13];
      out[14] = a[14];
      out[15] = a[15];
      return out;
    }

    /**
     * Copy the values from one mat4 to another
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    export function copy(out, a) {
      out[0] = a[0];
      out[1] = a[1];
      out[2] = a[2];
      out[3] = a[3];
      out[4] = a[4];
      out[5] = a[5];
      out[6] = a[6];
      out[7] = a[7];
      out[8] = a[8];
      out[9] = a[9];
      out[10] = a[10];
      out[11] = a[11];
      out[12] = a[12];
      out[13] = a[13];
      out[14] = a[14];
      out[15] = a[15];
      return out;
    }

    /**
     * Create a new mat4 with the given values
     *
     * @param {Number} m00 Component in column 0, row 0 position (index 0)
     * @param {Number} m01 Component in column 0, row 1 position (index 1)
     * @param {Number} m02 Component in column 0, row 2 position (index 2)
     * @param {Number} m03 Component in column 0, row 3 position (index 3)
     * @param {Number} m10 Component in column 1, row 0 position (index 4)
     * @param {Number} m11 Component in column 1, row 1 position (index 5)
     * @param {Number} m12 Component in column 1, row 2 position (index 6)
     * @param {Number} m13 Component in column 1, row 3 position (index 7)
     * @param {Number} m20 Component in column 2, row 0 position (index 8)
     * @param {Number} m21 Component in column 2, row 1 position (index 9)
     * @param {Number} m22 Component in column 2, row 2 position (index 10)
     * @param {Number} m23 Component in column 2, row 3 position (index 11)
     * @param {Number} m30 Component in column 3, row 0 position (index 12)
     * @param {Number} m31 Component in column 3, row 1 position (index 13)
     * @param {Number} m32 Component in column 3, row 2 position (index 14)
     * @param {Number} m33 Component in column 3, row 3 position (index 15)
     * @returns {mat4} A new mat4
     */
    export function fromValues(m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) {
      let out = new glMatrix.ARRAY_TYPE(16);
      out[0] = m00;
      out[1] = m01;
      out[2] = m02;
      out[3] = m03;
      out[4] = m10;
      out[5] = m11;
      out[6] = m12;
      out[7] = m13;
      out[8] = m20;
      out[9] = m21;
      out[10] = m22;
      out[11] = m23;
      out[12] = m30;
      out[13] = m31;
      out[14] = m32;
      out[15] = m33;
      return out;
    }

    /**
     * Set the components of a mat4 to the given values
     *
     * @param {mat4} out the receiving matrix
     * @param {Number} m00 Component in column 0, row 0 position (index 0)
     * @param {Number} m01 Component in column 0, row 1 position (index 1)
     * @param {Number} m02 Component in column 0, row 2 position (index 2)
     * @param {Number} m03 Component in column 0, row 3 position (index 3)
     * @param {Number} m10 Component in column 1, row 0 position (index 4)
     * @param {Number} m11 Component in column 1, row 1 position (index 5)
     * @param {Number} m12 Component in column 1, row 2 position (index 6)
     * @param {Number} m13 Component in column 1, row 3 position (index 7)
     * @param {Number} m20 Component in column 2, row 0 position (index 8)
     * @param {Number} m21 Component in column 2, row 1 position (index 9)
     * @param {Number} m22 Component in column 2, row 2 position (index 10)
     * @param {Number} m23 Component in column 2, row 3 position (index 11)
     * @param {Number} m30 Component in column 3, row 0 position (index 12)
     * @param {Number} m31 Component in column 3, row 1 position (index 13)
     * @param {Number} m32 Component in column 3, row 2 position (index 14)
     * @param {Number} m33 Component in column 3, row 3 position (index 15)
     * @returns {mat4} out
     */
    export function set(out, m00, m01, m02, m03, m10, m11, m12, m13, m20, m21, m22, m23, m30, m31, m32, m33) {
      out[0] = m00;
      out[1] = m01;
      out[2] = m02;
      out[3] = m03;
      out[4] = m10;
      out[5] = m11;
      out[6] = m12;
      out[7] = m13;
      out[8] = m20;
      out[9] = m21;
      out[10] = m22;
      out[11] = m23;
      out[12] = m30;
      out[13] = m31;
      out[14] = m32;
      out[15] = m33;
      return out;
    }

    /**
     * Set a mat4 to the identity matrix
     *
     * @param {mat4} out the receiving matrix
     * @returns {mat4} out
     */
    export function identity(out) {
      out[0] = 1;
      out[1] = 0;
      out[2] = 0;
      out[3] = 0;
      out[4] = 0;
      out[5] = 1;
      out[6] = 0;
      out[7] = 0;
      out[8] = 0;
      out[9] = 0;
      out[10] = 1;
      out[11] = 0;
      out[12] = 0;
      out[13] = 0;
      out[14] = 0;
      out[15] = 1;
      return out;
    }

    /**
     * Transpose the values of a mat4
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    export function transpose(out, a) {
      // If we are transposing ourselves we can skip a few steps but have to cache some values
      if (out === a) {
        let a01 = a[1], a02 = a[2], a03 = a[3];
        let a12 = a[6], a13 = a[7];
        let a23 = a[11];

        out[1] = a[4];
        out[2] = a[8];
        out[3] = a[12];
        out[4] = a01;
        out[6] = a[9];
        out[7] = a[13];
        out[8] = a02;
        out[9] = a12;
        out[11] = a[14];
        out[12] = a03;
        out[13] = a13;
        out[14] = a23;
      } else {
        out[0] = a[0];
        out[1] = a[4];
        out[2] = a[8];
        out[3] = a[12];
        out[4] = a[1];
        out[5] = a[5];
        out[6] = a[9];
        out[7] = a[13];
        out[8] = a[2];
        out[9] = a[6];
        out[10] = a[10];
        out[11] = a[14];
        out[12] = a[3];
        out[13] = a[7];
        out[14] = a[11];
        out[15] = a[15];
      }

      return out;
    }

    /**
     * Inverts a mat4
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    export function invert(out, a) {
      let a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3];
      let a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7];
      let a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11];
      let a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];

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

      // Calculate the determinant
      let det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;

      if (!det) {
        return null;
      }
      det = 1.0 / det;

      out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
      out[1] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
      out[2] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
      out[3] = (a22 * b04 - a21 * b05 - a23 * b03) * det;
      out[4] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
      out[5] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
      out[6] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
      out[7] = (a20 * b05 - a22 * b02 + a23 * b01) * det;
      out[8] = (a10 * b10 - a11 * b08 + a13 * b06) * det;
      out[9] = (a01 * b08 - a00 * b10 - a03 * b06) * det;
      out[10] = (a30 * b04 - a31 * b02 + a33 * b00) * det;
      out[11] = (a21 * b02 - a20 * b04 - a23 * b00) * det;
      out[12] = (a11 * b07 - a10 * b09 - a12 * b06) * det;
      out[13] = (a00 * b09 - a01 * b07 + a02 * b06) * det;
      out[14] = (a31 * b01 - a30 * b03 - a32 * b00) * det;
      out[15] = (a20 * b03 - a21 * b01 + a22 * b00) * det;

      return out;
    }

    /**
     * Calculates the adjugate of a mat4
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the source matrix
     * @returns {mat4} out
     */
    export function adjoint(out, a) {
      let a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3];
      let a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7];
      let a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11];
      let a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];

      out[0]  =  (a11 * (a22 * a33 - a23 * a32) - a21 * (a12 * a33 - a13 * a32) + a31 * (a12 * a23 - a13 * a22));
      out[1]  = -(a01 * (a22 * a33 - a23 * a32) - a21 * (a02 * a33 - a03 * a32) + a31 * (a02 * a23 - a03 * a22));
      out[2]  =  (a01 * (a12 * a33 - a13 * a32) - a11 * (a02 * a33 - a03 * a32) + a31 * (a02 * a13 - a03 * a12));
      out[3]  = -(a01 * (a12 * a23 - a13 * a22) - a11 * (a02 * a23 - a03 * a22) + a21 * (a02 * a13 - a03 * a12));
      out[4]  = -(a10 * (a22 * a33 - a23 * a32) - a20 * (a12 * a33 - a13 * a32) + a30 * (a12 * a23 - a13 * a22));
      out[5]  =  (a00 * (a22 * a33 - a23 * a32) - a20 * (a02 * a33 - a03 * a32) + a30 * (a02 * a23 - a03 * a22));
      out[6]  = -(a00 * (a12 * a33 - a13 * a32) - a10 * (a02 * a33 - a03 * a32) + a30 * (a02 * a13 - a03 * a12));
      out[7]  =  (a00 * (a12 * a23 - a13 * a22) - a10 * (a02 * a23 - a03 * a22) + a20 * (a02 * a13 - a03 * a12));
      out[8]  =  (a10 * (a21 * a33 - a23 * a31) - a20 * (a11 * a33 - a13 * a31) + a30 * (a11 * a23 - a13 * a21));
      out[9]  = -(a00 * (a21 * a33 - a23 * a31) - a20 * (a01 * a33 - a03 * a31) + a30 * (a01 * a23 - a03 * a21));
      out[10] =  (a00 * (a11 * a33 - a13 * a31) - a10 * (a01 * a33 - a03 * a31) + a30 * (a01 * a13 - a03 * a11));
      out[11] = -(a00 * (a11 * a23 - a13 * a21) - a10 * (a01 * a23 - a03 * a21) + a20 * (a01 * a13 - a03 * a11));
      out[12] = -(a10 * (a21 * a32 - a22 * a31) - a20 * (a11 * a32 - a12 * a31) + a30 * (a11 * a22 - a12 * a21));
      out[13] =  (a00 * (a21 * a32 - a22 * a31) - a20 * (a01 * a32 - a02 * a31) + a30 * (a01 * a22 - a02 * a21));
      out[14] = -(a00 * (a11 * a32 - a12 * a31) - a10 * (a01 * a32 - a02 * a31) + a30 * (a01 * a12 - a02 * a11));
      out[15] =  (a00 * (a11 * a22 - a12 * a21) - a10 * (a01 * a22 - a02 * a21) + a20 * (a01 * a12 - a02 * a11));
      return out;
    }

    /**
     * Calculates the determinant of a mat4
     *
     * @param {mat4} a the source matrix
     * @returns {Number} determinant of a
     */
    export function determinant(a) {
      let a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3];
      let a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7];
      let a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11];
      let a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];

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

      // Calculate the determinant
      return b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
    }

    /**
     * Multiplies two mat4s
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the first operand
     * @param {mat4} b the second operand
     * @returns {mat4} out
     */
    export function multiply(out, a, b) {
      let a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3];
      let a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7];
      let a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11];
      let a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];

      // Cache only the current line of the second matrix
      let b0  = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
      out[0] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
      out[1] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
      out[2] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
      out[3] = b0*a03 + b1*a13 + b2*a23 + b3*a33;

      b0 = b[4]; b1 = b[5]; b2 = b[6]; b3 = b[7];
      out[4] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
      out[5] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
      out[6] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
      out[7] = b0*a03 + b1*a13 + b2*a23 + b3*a33;

      b0 = b[8]; b1 = b[9]; b2 = b[10]; b3 = b[11];
      out[8] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
      out[9] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
      out[10] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
      out[11] = b0*a03 + b1*a13 + b2*a23 + b3*a33;

      b0 = b[12]; b1 = b[13]; b2 = b[14]; b3 = b[15];
      out[12] = b0*a00 + b1*a10 + b2*a20 + b3*a30;
      out[13] = b0*a01 + b1*a11 + b2*a21 + b3*a31;
      out[14] = b0*a02 + b1*a12 + b2*a22 + b3*a32;
      out[15] = b0*a03 + b1*a13 + b2*a23 + b3*a33;
      return out;
    }

    /**
     * Translate a mat4 by the given vector
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to translate
     * @param {vec3} v vector to translate by
     * @returns {mat4} out
     */
    export function translate(out, a, v) {
      let x = v[0], y = v[1], z = v[2];
      let a00, a01, a02, a03;
      let a10, a11, a12, a13;
      let a20, a21, a22, a23;

      if (a === out) {
        out[12] = a[0] * x + a[4] * y + a[8] * z + a[12];
        out[13] = a[1] * x + a[5] * y + a[9] * z + a[13];
        out[14] = a[2] * x + a[6] * y + a[10] * z + a[14];
        out[15] = a[3] * x + a[7] * y + a[11] * z + a[15];
      } else {
        a00 = a[0]; a01 = a[1]; a02 = a[2]; a03 = a[3];
        a10 = a[4]; a11 = a[5]; a12 = a[6]; a13 = a[7];
        a20 = a[8]; a21 = a[9]; a22 = a[10]; a23 = a[11];

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

        out[12] = a00 * x + a10 * y + a20 * z + a[12];
        out[13] = a01 * x + a11 * y + a21 * z + a[13];
        out[14] = a02 * x + a12 * y + a22 * z + a[14];
        out[15] = a03 * x + a13 * y + a23 * z + a[15];
      }

      return out;
    }

    /**
     * Scales the mat4 by the dimensions in the given vec3 not using vectorization
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to scale
     * @param {vec3} v the vec3 to scale the matrix by
     * @returns {mat4} out
     **/
    export function scale(out, a, v) {
      let x = v[0], y = v[1], z = v[2];

      out[0] = a[0] * x;
      out[1] = a[1] * x;
      out[2] = a[2] * x;
      out[3] = a[3] * x;
      out[4] = a[4] * y;
      out[5] = a[5] * y;
      out[6] = a[6] * y;
      out[7] = a[7] * y;
      out[8] = a[8] * z;
      out[9] = a[9] * z;
      out[10] = a[10] * z;
      out[11] = a[11] * z;
      out[12] = a[12];
      out[13] = a[13];
      out[14] = a[14];
      out[15] = a[15];
      return out;
    }

    /**
     * Rotates a mat4 by the given angle around the given axis
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @param {vec3} axis the axis to rotate around
     * @returns {mat4} out
     */
    export function rotate(out, a, rad, axis) {
      let x = axis[0], y = axis[1], z = axis[2];
      let len = Math.sqrt(x * x + y * y + z * z);
      let s, c, t;
      let a00, a01, a02, a03;
      let a10, a11, a12, a13;
      let a20, a21, a22, a23;
      let b00, b01, b02;
      let b10, b11, b12;
      let b20, b21, b22;

      if (Math.abs(len) < glMatrix.EPSILON) { return null; }

      len = 1 / len;
      x *= len;
      y *= len;
      z *= len;

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

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

      // Perform rotation-specific matrix multiplication
      out[0] = a00 * b00 + a10 * b01 + a20 * b02;
      out[1] = a01 * b00 + a11 * b01 + a21 * b02;
      out[2] = a02 * b00 + a12 * b01 + a22 * b02;
      out[3] = a03 * b00 + a13 * b01 + a23 * b02;
      out[4] = a00 * b10 + a10 * b11 + a20 * b12;
      out[5] = a01 * b10 + a11 * b11 + a21 * b12;
      out[6] = a02 * b10 + a12 * b11 + a22 * b12;
      out[7] = a03 * b10 + a13 * b11 + a23 * b12;
      out[8] = a00 * b20 + a10 * b21 + a20 * b22;
      out[9] = a01 * b20 + a11 * b21 + a21 * b22;
      out[10] = a02 * b20 + a12 * b21 + a22 * b22;
      out[11] = a03 * b20 + a13 * b21 + a23 * b22;

      if (a !== out) { // If the source and destination differ, copy the unchanged last row
        out[12] = a[12];
        out[13] = a[13];
        out[14] = a[14];
        out[15] = a[15];
      }
      return out;
    }

    /**
     * Rotates a matrix by the given angle around the X axis
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    export function rotateX(out, a, rad) {
      let s = Math.sin(rad);
      let c = Math.cos(rad);
      let a10 = a[4];
      let a11 = a[5];
      let a12 = a[6];
      let a13 = a[7];
      let a20 = a[8];
      let a21 = a[9];
      let a22 = a[10];
      let a23 = a[11];

      if (a !== out) { // If the source and destination differ, copy the unchanged rows
        out[0]  = a[0];
        out[1]  = a[1];
        out[2]  = a[2];
        out[3]  = a[3];
        out[12] = a[12];
        out[13] = a[13];
        out[14] = a[14];
        out[15] = a[15];
      }

      // Perform axis-specific matrix multiplication
      out[4] = a10 * c + a20 * s;
      out[5] = a11 * c + a21 * s;
      out[6] = a12 * c + a22 * s;
      out[7] = a13 * c + a23 * s;
      out[8] = a20 * c - a10 * s;
      out[9] = a21 * c - a11 * s;
      out[10] = a22 * c - a12 * s;
      out[11] = a23 * c - a13 * s;
      return out;
    }

    /**
     * Rotates a matrix by the given angle around the Y axis
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    export function rotateY(out, a, rad) {
      let s = Math.sin(rad);
      let c = Math.cos(rad);
      let a00 = a[0];
      let a01 = a[1];
      let a02 = a[2];
      let a03 = a[3];
      let a20 = a[8];
      let a21 = a[9];
      let a22 = a[10];
      let a23 = a[11];

      if (a !== out) { // If the source and destination differ, copy the unchanged rows
        out[4]  = a[4];
        out[5]  = a[5];
        out[6]  = a[6];
        out[7]  = a[7];
        out[12] = a[12];
        out[13] = a[13];
        out[14] = a[14];
        out[15] = a[15];
      }

      // Perform axis-specific matrix multiplication
      out[0] = a00 * c - a20 * s;
      out[1] = a01 * c - a21 * s;
      out[2] = a02 * c - a22 * s;
      out[3] = a03 * c - a23 * s;
      out[8] = a00 * s + a20 * c;
      out[9] = a01 * s + a21 * c;
      out[10] = a02 * s + a22 * c;
      out[11] = a03 * s + a23 * c;
      return out;
    }

    /**
     * Rotates a matrix by the given angle around the Z axis
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to rotate
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    export function rotateZ(out, a, rad) {
      let s = Math.sin(rad);
      let c = Math.cos(rad);
      let a00 = a[0];
      let a01 = a[1];
      let a02 = a[2];
      let a03 = a[3];
      let a10 = a[4];
      let a11 = a[5];
      let a12 = a[6];
      let a13 = a[7];

      if (a !== out) { // If the source and destination differ, copy the unchanged last row
        out[8]  = a[8];
        out[9]  = a[9];
        out[10] = a[10];
        out[11] = a[11];
        out[12] = a[12];
        out[13] = a[13];
        out[14] = a[14];
        out[15] = a[15];
      }

      // Perform axis-specific matrix multiplication
      out[0] = a00 * c + a10 * s;
      out[1] = a01 * c + a11 * s;
      out[2] = a02 * c + a12 * s;
      out[3] = a03 * c + a13 * s;
      out[4] = a10 * c - a00 * s;
      out[5] = a11 * c - a01 * s;
      out[6] = a12 * c - a02 * s;
      out[7] = a13 * c - a03 * s;
      return out;
    }

    /**
     * Creates a matrix from a vector translation
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.translate(dest, dest, vec);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {vec3} v Translation vector
     * @returns {mat4} out
     */
    export function fromTranslation(out, v) {
      out[0] = 1;
      out[1] = 0;
      out[2] = 0;
      out[3] = 0;
      out[4] = 0;
      out[5] = 1;
      out[6] = 0;
      out[7] = 0;
      out[8] = 0;
      out[9] = 0;
      out[10] = 1;
      out[11] = 0;
      out[12] = v[0];
      out[13] = v[1];
      out[14] = v[2];
      out[15] = 1;
      return out;
    }

    /**
     * Creates a matrix from a vector scaling
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.scale(dest, dest, vec);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {vec3} v Scaling vector
     * @returns {mat4} out
     */
    export function fromScaling(out, v) {
      out[0] = v[0];
      out[1] = 0;
      out[2] = 0;
      out[3] = 0;
      out[4] = 0;
      out[5] = v[1];
      out[6] = 0;
      out[7] = 0;
      out[8] = 0;
      out[9] = 0;
      out[10] = v[2];
      out[11] = 0;
      out[12] = 0;
      out[13] = 0;
      out[14] = 0;
      out[15] = 1;
      return out;
    }

    /**
     * Creates a matrix from a given angle around a given axis
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.rotate(dest, dest, rad, axis);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {Number} rad the angle to rotate the matrix by
     * @param {vec3} axis the axis to rotate around
     * @returns {mat4} out
     */
    export function fromRotation(out, rad, axis) {
      let x = axis[0], y = axis[1], z = axis[2];
      let len = Math.sqrt(x * x + y * y + z * z);
      let s, c, t;

      if (Math.abs(len) < glMatrix.EPSILON) { return null; }

      len = 1 / len;
      x *= len;
      y *= len;
      z *= len;

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

      // Perform rotation-specific matrix multiplication
      out[0] = x * x * t + c;
      out[1] = y * x * t + z * s;
      out[2] = z * x * t - y * s;
      out[3] = 0;
      out[4] = x * y * t - z * s;
      out[5] = y * y * t + c;
      out[6] = z * y * t + x * s;
      out[7] = 0;
      out[8] = x * z * t + y * s;
      out[9] = y * z * t - x * s;
      out[10] = z * z * t + c;
      out[11] = 0;
      out[12] = 0;
      out[13] = 0;
      out[14] = 0;
      out[15] = 1;
      return out;
    }

    /**
     * Creates a matrix from the given angle around the X axis
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.rotateX(dest, dest, rad);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    export function fromXRotation(out, rad) {
      let s = Math.sin(rad);
      let c = Math.cos(rad);

      // Perform axis-specific matrix multiplication
      out[0]  = 1;
      out[1]  = 0;
      out[2]  = 0;
      out[3]  = 0;
      out[4] = 0;
      out[5] = c;
      out[6] = s;
      out[7] = 0;
      out[8] = 0;
      out[9] = -s;
      out[10] = c;
      out[11] = 0;
      out[12] = 0;
      out[13] = 0;
      out[14] = 0;
      out[15] = 1;
      return out;
    }

    /**
     * Creates a matrix from the given angle around the Y axis
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.rotateY(dest, dest, rad);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    export function fromYRotation(out, rad) {
      let s = Math.sin(rad);
      let c = Math.cos(rad);

      // Perform axis-specific matrix multiplication
      out[0]  = c;
      out[1]  = 0;
      out[2]  = -s;
      out[3]  = 0;
      out[4] = 0;
      out[5] = 1;
      out[6] = 0;
      out[7] = 0;
      out[8] = s;
      out[9] = 0;
      out[10] = c;
      out[11] = 0;
      out[12] = 0;
      out[13] = 0;
      out[14] = 0;
      out[15] = 1;
      return out;
    }

    /**
     * Creates a matrix from the given angle around the Z axis
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.rotateZ(dest, dest, rad);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {Number} rad the angle to rotate the matrix by
     * @returns {mat4} out
     */
    export function fromZRotation(out, rad) {
      let s = Math.sin(rad);
      let c = Math.cos(rad);

      // Perform axis-specific matrix multiplication
      out[0]  = c;
      out[1]  = s;
      out[2]  = 0;
      out[3]  = 0;
      out[4] = -s;
      out[5] = c;
      out[6] = 0;
      out[7] = 0;
      out[8] = 0;
      out[9] = 0;
      out[10] = 1;
      out[11] = 0;
      out[12] = 0;
      out[13] = 0;
      out[14] = 0;
      out[15] = 1;
      return out;
    }

    /**
     * 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);
     *     let quatMat = mat4.create();
     *     quat4.toMat4(quat, quatMat);
     *     mat4.multiply(dest, quatMat);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {quat4} q Rotation quaternion
     * @param {vec3} v Translation vector
     * @returns {mat4} out
     */
    export function fromRotationTranslation(out, q, v) {
      // Quaternion math
      let x = q[0], y = q[1], z = q[2], w = q[3];
      let x2 = x + x;
      let y2 = y + y;
      let z2 = z + z;

      let xx = x * x2;
      let xy = x * y2;
      let xz = x * z2;
      let yy = y * y2;
      let yz = y * z2;
      let zz = z * z2;
      let wx = w * x2;
      let wy = w * y2;
      let wz = w * z2;

      out[0] = 1 - (yy + zz);
      out[1] = xy + wz;
      out[2] = xz - wy;
      out[3] = 0;
      out[4] = xy - wz;
      out[5] = 1 - (xx + zz);
      out[6] = yz + wx;
      out[7] = 0;
      out[8] = xz + wy;
      out[9] = yz - wx;
      out[10] = 1 - (xx + yy);
      out[11] = 0;
      out[12] = v[0];
      out[13] = v[1];
      out[14] = v[2];
      out[15] = 1;

      return out;
    }

    /**
     * Returns the translation vector component of a transformation
     *  matrix. If a matrix is built with fromRotationTranslation,
     *  the returned vector will be the same as the translation vector
     *  originally supplied.
     * @param  {vec3} out Vector to receive translation component
     * @param  {mat4} mat Matrix to be decomposed (input)
     * @return {vec3} out
     */
    export function getTranslation(out, mat) {
      out[0] = mat[12];
      out[1] = mat[13];
      out[2] = mat[14];

      return out;
    }

    /**
     * Returns the scaling factor component of a transformation
     *  matrix. If a matrix is built with fromRotationTranslationScale
     *  with a normalized Quaternion paramter, the returned vector will be
     *  the same as the scaling vector
     *  originally supplied.
     * @param  {vec3} out Vector to receive scaling factor component
     * @param  {mat4} mat Matrix to be decomposed (input)
     * @return {vec3} out
     */
    export function getScaling(out, mat) {
      let m11 = mat[0];
      let m12 = mat[1];
      let m13 = mat[2];
      let m21 = mat[4];
      let m22 = mat[5];
      let m23 = mat[6];
      let m31 = mat[8];
      let m32 = mat[9];
      let m33 = mat[10];

      out[0] = Math.sqrt(m11 * m11 + m12 * m12 + m13 * m13);
      out[1] = Math.sqrt(m21 * m21 + m22 * m22 + m23 * m23);
      out[2] = Math.sqrt(m31 * m31 + m32 * m32 + m33 * m33);

      return out;
    }

    /**
     * Returns a quaternion representing the rotational component
     *  of a transformation matrix. If a matrix is built with
     *  fromRotationTranslation, the returned quaternion will be the
     *  same as the quaternion originally supplied.
     * @param {quat} out Quaternion to receive the rotation component
     * @param {mat4} mat Matrix to be decomposed (input)
     * @return {quat} out
     */
    export function getRotation(out, mat) {
      // Algorithm taken from http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
      let trace = mat[0] + mat[5] + mat[10];
      let S = 0;

      if (trace > 0) {
        S = Math.sqrt(trace + 1.0) * 2;
        out[3] = 0.25 * S;
        out[0] = (mat[6] - mat[9]) / S;
        out[1] = (mat[8] - mat[2]) / S;
        out[2] = (mat[1] - mat[4]) / S;
      } else if ((mat[0] > mat[5])&(mat[0] > mat[10])) {
        S = Math.sqrt(1.0 + mat[0] - mat[5] - mat[10]) * 2;
        out[3] = (mat[6] - mat[9]) / S;
        out[0] = 0.25 * S;
        out[1] = (mat[1] + mat[4]) / S;
        out[2] = (mat[8] + mat[2]) / S;
      } else if (mat[5] > mat[10]) {
        S = Math.sqrt(1.0 + mat[5] - mat[0] - mat[10]) * 2;
        out[3] = (mat[8] - mat[2]) / S;
        out[0] = (mat[1] + mat[4]) / S;
        out[1] = 0.25 * S;
        out[2] = (mat[6] + mat[9]) / S;
      } else {
        S = Math.sqrt(1.0 + mat[10] - mat[0] - mat[5]) * 2;
        out[3] = (mat[1] - mat[4]) / S;
        out[0] = (mat[8] + mat[2]) / S;
        out[1] = (mat[6] + mat[9]) / S;
        out[2] = 0.25 * S;
      }

      return out;
    }

    /**
     * Creates a matrix from a quaternion rotation, vector translation and vector scale
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.translate(dest, vec);
     *     let quatMat = mat4.create();
     *     quat4.toMat4(quat, quatMat);
     *     mat4.multiply(dest, quatMat);
     *     mat4.scale(dest, scale)
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {quat4} q Rotation quaternion
     * @param {vec3} v Translation vector
     * @param {vec3} s Scaling vector
     * @returns {mat4} out
     */
    export function fromRotationTranslationScale(out, q, v, s) {
      // Quaternion math
      let x = q[0], y = q[1], z = q[2], w = q[3];
      let x2 = x + x;
      let y2 = y + y;
      let z2 = z + z;

      let xx = x * x2;
      let xy = x * y2;
      let xz = x * z2;
      let yy = y * y2;
      let yz = y * z2;
      let zz = z * z2;
      let wx = w * x2;
      let wy = w * y2;
      let wz = w * z2;
      let sx = s[0];
      let sy = s[1];
      let sz = s[2];

      out[0] = (1 - (yy + zz)) * sx;
      out[1] = (xy + wz) * sx;
      out[2] = (xz - wy) * sx;
      out[3] = 0;
      out[4] = (xy - wz) * sy;
      out[5] = (1 - (xx + zz)) * sy;
      out[6] = (yz + wx) * sy;
      out[7] = 0;
      out[8] = (xz + wy) * sz;
      out[9] = (yz - wx) * sz;
      out[10] = (1 - (xx + yy)) * sz;
      out[11] = 0;
      out[12] = v[0];
      out[13] = v[1];
      out[14] = v[2];
      out[15] = 1;

      return out;
    }

    /**
     * Creates a matrix from a quaternion rotation, vector translation and vector scale, rotating and scaling around the given origin
     * This is equivalent to (but much faster than):
     *
     *     mat4.identity(dest);
     *     mat4.translate(dest, vec);
     *     mat4.translate(dest, origin);
     *     let quatMat = mat4.create();
     *     quat4.toMat4(quat, quatMat);
     *     mat4.multiply(dest, quatMat);
     *     mat4.scale(dest, scale)
     *     mat4.translate(dest, negativeOrigin);
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {quat4} q Rotation quaternion
     * @param {vec3} v Translation vector
     * @param {vec3} s Scaling vector
     * @param {vec3} o The origin vector around which to scale and rotate
     * @returns {mat4} out
     */
    export function fromRotationTranslationScaleOrigin(out, q, v, s, o) {
      // Quaternion math
      let x = q[0], y = q[1], z = q[2], w = q[3];
      let x2 = x + x;
      let y2 = y + y;
      let z2 = z + z;

      let xx = x * x2;
      let xy = x * y2;
      let xz = x * z2;
      let yy = y * y2;
      let yz = y * z2;
      let zz = z * z2;
      let wx = w * x2;
      let wy = w * y2;
      let wz = w * z2;

      let sx = s[0];
      let sy = s[1];
      let sz = s[2];

      let ox = o[0];
      let oy = o[1];
      let oz = o[2];

      out[0] = (1 - (yy + zz)) * sx;
      out[1] = (xy + wz) * sx;
      out[2] = (xz - wy) * sx;
      out[3] = 0;
      out[4] = (xy - wz) * sy;
      out[5] = (1 - (xx + zz)) * sy;
      out[6] = (yz + wx) * sy;
      out[7] = 0;
      out[8] = (xz + wy) * sz;
      out[9] = (yz - wx) * sz;
      out[10] = (1 - (xx + yy)) * sz;
      out[11] = 0;
      out[12] = v[0] + ox - (out[0] * ox + out[4] * oy + out[8] * oz);
      out[13] = v[1] + oy - (out[1] * ox + out[5] * oy + out[9] * oz);
      out[14] = v[2] + oz - (out[2] * ox + out[6] * oy + out[10] * oz);
      out[15] = 1;

      return out;
    }

    /**
     * Calculates a 4x4 matrix from the given quaternion
     *
     * @param {mat4} out mat4 receiving operation result
     * @param {quat} q Quaternion to create matrix from
     *
     * @returns {mat4} out
     */
    export function fromQuat(out, q) {
      let x = q[0], y = q[1], z = q[2], w = q[3];
      let x2 = x + x;
      let y2 = y + y;
      let z2 = z + z;

      let xx = x * x2;
      let yx = y * x2;
      let yy = y * y2;
      let zx = z * x2;
      let zy = z * y2;
      let zz = z * z2;
      let wx = w * x2;
      let wy = w * y2;
      let wz = w * z2;

      out[0] = 1 - yy - zz;
      out[1] = yx + wz;
      out[2] = zx - wy;
      out[3] = 0;

      out[4] = yx - wz;
      out[5] = 1 - xx - zz;
      out[6] = zy + wx;
      out[7] = 0;

      out[8] = zx + wy;
      out[9] = zy - wx;
      out[10] = 1 - xx - yy;
      out[11] = 0;

      out[12] = 0;
      out[13] = 0;
      out[14] = 0;
      out[15] = 1;

      return out;
    }

    /**
     * Generates a frustum matrix with the given bounds
     *
     * @param {mat4} out mat4 frustum matrix will be written into
     * @param {Number} left Left bound of the frustum
     * @param {Number} right Right bound of the frustum
     * @param {Number} bottom Bottom bound of the frustum
     * @param {Number} top Top bound of the frustum
     * @param {Number} near Near bound of the frustum
     * @param {Number} far Far bound of the frustum
     * @returns {mat4} out
     */
    export function frustum(out, left, right, bottom, top, near, far) {
      let rl = 1 / (right - left);
      let tb = 1 / (top - bottom);
      let nf = 1 / (near - far);
      out[0] = (near * 2) * rl;
      out[1] = 0;
      out[2] = 0;
      out[3] = 0;
      out[4] = 0;
      out[5] = (near * 2) * tb;
      out[6] = 0;
      out[7] = 0;
      out[8] = (right + left) * rl;
      out[9] = (top + bottom) * tb;
      out[10] = (far + near) * nf;
      out[11] = -1;
      out[12] = 0;
      out[13] = 0;
      out[14] = (far * near * 2) * nf;
      out[15] = 0;
      return out;
    }

    /**
     * Generates a perspective projection matrix with the given bounds
     *
     * @param {mat4} out mat4 frustum matrix will be written into
     * @param {number} fovy Vertical field of view in radians
     * @param {number} aspect Aspect ratio. typically viewport width/height
     * @param {number} near Near bound of the frustum
     * @param {number} far Far bound of the frustum
     * @returns {mat4} out
     */
    export function perspective(out, fovy, aspect, near, far) {
      let f = 1.0 / Math.tan(fovy / 2);
      let nf = 1 / (near - far);
      out[0] = f / aspect;
      out[1] = 0;
      out[2] = 0;
      out[3] = 0;
      out[4] = 0;
      out[5] = f;
      out[6] = 0;
      out[7] = 0;
      out[8] = 0;
      out[9] = 0;
      out[10] = (far + near) * nf;
      out[11] = -1;
      out[12] = 0;
      out[13] = 0;
      out[14] = (2 * far * near) * nf;
      out[15] = 0;
      return out;
    }

    /**
     * Generates a perspective projection matrix with the given field of view.
     * This is primarily useful for generating projection matrices to be used
     * with the still experiemental WebVR API.
     *
     * @param {mat4} out mat4 frustum matrix will be written into
     * @param {Object} fov Object containing the following values: upDegrees, downDegrees, leftDegrees, rightDegrees
     * @param {number} near Near bound of the frustum
     * @param {number} far Far bound of the frustum
     * @returns {mat4} out
     */
    export function perspectiveFromFieldOfView(out, fov, near, far) {
      let upTan = Math.tan(fov.upDegrees * Math.PI/180.0);
      let downTan = Math.tan(fov.downDegrees * Math.PI/180.0);
      let leftTan = Math.tan(fov.leftDegrees * Math.PI/180.0);
      let rightTan = Math.tan(fov.rightDegrees * Math.PI/180.0);
      let xScale = 2.0 / (leftTan + rightTan);
      let yScale = 2.0 / (upTan + downTan);

      out[0] = xScale;
      out[1] = 0.0;
      out[2] = 0.0;
      out[3] = 0.0;
      out[4] = 0.0;
      out[5] = yScale;
      out[6] = 0.0;
      out[7] = 0.0;
      out[8] = -((leftTan - rightTan) * xScale * 0.5);
      out[9] = ((upTan - downTan) * yScale * 0.5);
      out[10] = far / (near - far);
      out[11] = -1.0;
      out[12] = 0.0;
      out[13] = 0.0;
      out[14] = (far * near) / (near - far);
      out[15] = 0.0;
      return out;
    }

    /**
     * Generates a orthogonal projection matrix with the given bounds
     *
     * @param {mat4} out mat4 frustum matrix will be written into
     * @param {number} left Left bound of the frustum
     * @param {number} right Right bound of the frustum
     * @param {number} bottom Bottom bound of the frustum
     * @param {number} top Top bound of the frustum
     * @param {number} near Near bound of the frustum
     * @param {number} far Far bound of the frustum
     * @returns {mat4} out
     */
    export function ortho(out, left, right, bottom, top, near, far) {
      let lr = 1 / (left - right);
      let bt = 1 / (bottom - top);
      let nf = 1 / (near - far);
      out[0] = -2 * lr;
      out[1] = 0;
      out[2] = 0;
      out[3] = 0;
      out[4] = 0;
      out[5] = -2 * bt;
      out[6] = 0;
      out[7] = 0;
      out[8] = 0;
      out[9] = 0;
      out[10] = 2 * nf;
      out[11] = 0;
      out[12] = (left + right) * lr;
      out[13] = (top + bottom) * bt;
      out[14] = (far + near) * nf;
      out[15] = 1;
      return out;
    }

    /**
     * Generates a look-at matrix with the given eye position, focal point, and up axis
     *
     * @param {mat4} out mat4 frustum matrix will be written into
     * @param {vec3} eye Position of the viewer
     * @param {vec3} center Point the viewer is looking at
     * @param {vec3} up vec3 pointing up
     * @returns {mat4} out
     */
    export function lookAt(out, eye, center, up) {
      let x0, x1, x2, y0, y1, y2, z0, z1, z2, len;
      let eyex = eye[0];
      let eyey = eye[1];
      let eyez = eye[2];
      let upx = up[0];
      let upy = up[1];
      let upz = up[2];
      let centerx = center[0];
      let centery = center[1];
      let centerz = center[2];

      if (Math.abs(eyex - centerx) < glMatrix.EPSILON &&
          Math.abs(eyey - centery) < glMatrix.EPSILON &&
          Math.abs(eyez - centerz) < glMatrix.EPSILON) {
        return mat4.identity(out);
      }

      z0 = eyex - centerx;
      z1 = eyey - centery;
      z2 = eyez - centerz;

      len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
      z0 *= len;
      z1 *= len;
      z2 *= len;

      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;
      }

      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;
      }

      out[0] = x0;
      out[1] = y0;
      out[2] = z0;
      out[3] = 0;
      out[4] = x1;
      out[5] = y1;
      out[6] = z1;
      out[7] = 0;
      out[8] = x2;
      out[9] = y2;
      out[10] = z2;
      out[11] = 0;
      out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
      out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
      out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
      out[15] = 1;

      return out;
    }

    /**
     * Generates a matrix that makes something look at something else.
     *
     * @param {mat4} out mat4 frustum matrix will be written into
     * @param {vec3} eye Position of the viewer
     * @param {vec3} center Point the viewer is looking at
     * @param {vec3} up vec3 pointing up
     * @returns {mat4} out
     */
    export function targetTo(out, eye, target, up) {
      let eyex = eye[0],
          eyey = eye[1],
          eyez = eye[2],
          upx = up[0],
          upy = up[1],
          upz = up[2];

      let z0 = eyex - target[0],
          z1 = eyey - target[1],
          z2 = eyez - target[2];

      let len = z0*z0 + z1*z1 + z2*z2;
      if (len > 0) {
        len = 1 / Math.sqrt(len);
        z0 *= len;
        z1 *= len;
        z2 *= len;
      }

      let x0 = upy * z2 - upz * z1,
          x1 = upz * z0 - upx * z2,
          x2 = upx * z1 - upy * z0;

      out[0] = x0;
      out[1] = x1;
      out[2] = x2;
      out[3] = 0;
      out[4] = z1 * x2 - z2 * x1;
      out[5] = z2 * x0 - z0 * x2;
      out[6] = z0 * x1 - z1 * x0;
      out[7] = 0;
      out[8] = z0;
      out[9] = z1;
      out[10] = z2;
      out[11] = 0;
      out[12] = eyex;
      out[13] = eyey;
      out[14] = eyez;
      out[15] = 1;
      return out;
    };

    /**
     * Returns a string representation of a mat4
     *
     * @param {mat4} a matrix to represent as a string
     * @returns {String} string representation of the matrix
     */
    export function str(a) {
      return 'mat4(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ', ' +
              a[4] + ', ' + a[5] + ', ' + a[6] + ', ' + a[7] + ', ' +
              a[8] + ', ' + a[9] + ', ' + a[10] + ', ' + a[11] + ', ' +
              a[12] + ', ' + a[13] + ', ' + a[14] + ', ' + a[15] + ')';
    }

    /**
     * Returns Frobenius norm of a mat4
     *
     * @param {mat4} a the matrix to calculate Frobenius norm of
     * @returns {Number} Frobenius norm
     */
    export function frob(a) {
      return(Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2) + Math.pow(a[4], 2) + Math.pow(a[5], 2) + Math.pow(a[6], 2) + Math.pow(a[7], 2) + Math.pow(a[8], 2) + Math.pow(a[9], 2) + Math.pow(a[10], 2) + Math.pow(a[11], 2) + Math.pow(a[12], 2) + Math.pow(a[13], 2) + Math.pow(a[14], 2) + Math.pow(a[15], 2) ))
    }

    /**
     * Adds two mat4's
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the first operand
     * @param {mat4} b the second operand
     * @returns {mat4} out
     */
    export function add(out, a, b) {
      out[0] = a[0] + b[0];
      out[1] = a[1] + b[1];
      out[2] = a[2] + b[2];
      out[3] = a[3] + b[3];
      out[4] = a[4] + b[4];
      out[5] = a[5] + b[5];
      out[6] = a[6] + b[6];
      out[7] = a[7] + b[7];
      out[8] = a[8] + b[8];
      out[9] = a[9] + b[9];
      out[10] = a[10] + b[10];
      out[11] = a[11] + b[11];
      out[12] = a[12] + b[12];
      out[13] = a[13] + b[13];
      out[14] = a[14] + b[14];
      out[15] = a[15] + b[15];
      return out;
    }

    /**
     * Subtracts matrix b from matrix a
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the first operand
     * @param {mat4} b the second operand
     * @returns {mat4} out
     */
    export function subtract(out, a, b) {
      out[0] = a[0] - b[0];
      out[1] = a[1] - b[1];
      out[2] = a[2] - b[2];
      out[3] = a[3] - b[3];
      out[4] = a[4] - b[4];
      out[5] = a[5] - b[5];
      out[6] = a[6] - b[6];
      out[7] = a[7] - b[7];
      out[8] = a[8] - b[8];
      out[9] = a[9] - b[9];
      out[10] = a[10] - b[10];
      out[11] = a[11] - b[11];
      out[12] = a[12] - b[12];
      out[13] = a[13] - b[13];
      out[14] = a[14] - b[14];
      out[15] = a[15] - b[15];
      return out;
    }

    /**
     * Multiply each element of the matrix by a scalar.
     *
     * @param {mat4} out the receiving matrix
     * @param {mat4} a the matrix to scale
     * @param {Number} b amount to scale the matrix's elements by
     * @returns {mat4} out
     */
    export function multiplyScalar(out, a, b) {
      out[0] = a[0] * b;
      out[1] = a[1] * b;
      out[2] = a[2] * b;
      out[3] = a[3] * b;
      out[4] = a[4] * b;
      out[5] = a[5] * b;
      out[6] = a[6] * b;
      out[7] = a[7] * b;
      out[8] = a[8] * b;
      out[9] = a[9] * b;
      out[10] = a[10] * b;
      out[11] = a[11] * b;
      out[12] = a[12] * b;
      out[13] = a[13] * b;
      out[14] = a[14] * b;
      out[15] = a[15] * b;
      return out;
    }

    /**
     * Adds two mat4's after multiplying each element of the second operand by a scalar value.
     *
     * @param {mat4} out the receiving vector
     * @param {mat4} a the first operand
     * @param {mat4} b the second operand
     * @param {Number} scale the amount to scale b's elements by before adding
     * @returns {mat4} out
     */
    export function multiplyScalarAndAdd(out, a, b, scale) {
      out[0] = a[0] + (b[0] * scale);
      out[1] = a[1] + (b[1] * scale);
      out[2] = a[2] + (b[2] * scale);
      out[3] = a[3] + (b[3] * scale);
      out[4] = a[4] + (b[4] * scale);
      out[5] = a[5] + (b[5] * scale);
      out[6] = a[6] + (b[6] * scale);
      out[7] = a[7] + (b[7] * scale);
      out[8] = a[8] + (b[8] * scale);
      out[9] = a[9] + (b[9] * scale);
      out[10] = a[10] + (b[10] * scale);
      out[11] = a[11] + (b[11] * scale);
      out[12] = a[12] + (b[12] * scale);
      out[13] = a[13] + (b[13] * scale);
      out[14] = a[14] + (b[14] * scale);
      out[15] = a[15] + (b[15] * scale);
      return out;
    }

    /**
     * Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
     *
     * @param {mat4} a The first matrix.
     * @param {mat4} b The second matrix.
     * @returns {Boolean} True if the matrices are equal, false otherwise.
     */
    export function exactEquals(a, b) {
      return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3] &&
             a[4] === b[4] && a[5] === b[5] && a[6] === b[6] && a[7] === b[7] &&
             a[8] === b[8] && a[9] === b[9] && a[10] === b[10] && a[11] === b[11] &&
             a[12] === b[12] && a[13] === b[13] && a[14] === b[14] && a[15] === b[15];
    }

    /**
     * Returns whether or not the matrices have approximately the same elements in the same position.
     *
     * @param {mat4} a The first matrix.
     * @param {mat4} b The second matrix.
     * @returns {Boolean} True if the matrices are equal, false otherwise.
     */
    export function equals(a, b) {
      let a0  = a[0],  a1  = a[1],  a2  = a[2],  a3  = a[3];
      let a4  = a[4],  a5  = a[5],  a6  = a[6],  a7  = a[7];
      let a8  = a[8],  a9  = a[9],  a10 = a[10], a11 = a[11];
      let a12 = a[12], a13 = a[13], a14 = a[14], a15 = a[15];

      let b0  = b[0],  b1  = b[1],  b2  = b[2],  b3  = b[3];
      let b4  = b[4],  b5  = b[5],  b6  = b[6],  b7  = b[7];
      let b8  = b[8],  b9  = b[9],  b10 = b[10], b11 = b[11];
      let b12 = b[12], b13 = b[13], b14 = b[14], b15 = b[15];

      return (Math.abs(a0 - b0) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a0), Math.abs(b0)) &&
              Math.abs(a1 - b1) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a1), Math.abs(b1)) &&
              Math.abs(a2 - b2) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a2), Math.abs(b2)) &&
              Math.abs(a3 - b3) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a3), Math.abs(b3)) &&
              Math.abs(a4 - b4) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a4), Math.abs(b4)) &&
              Math.abs(a5 - b5) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a5), Math.abs(b5)) &&
              Math.abs(a6 - b6) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a6), Math.abs(b6)) &&
              Math.abs(a7 - b7) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a7), Math.abs(b7)) &&
              Math.abs(a8 - b8) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a8), Math.abs(b8)) &&
              Math.abs(a9 - b9) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a9), Math.abs(b9)) &&
              Math.abs(a10 - b10) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a10), Math.abs(b10)) &&
              Math.abs(a11 - b11) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a11), Math.abs(b11)) &&
              Math.abs(a12 - b12) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a12), Math.abs(b12)) &&
              Math.abs(a13 - b13) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a13), Math.abs(b13)) &&
              Math.abs(a14 - b14) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a14), Math.abs(b14)) &&
              Math.abs(a15 - b15) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a15), Math.abs(b15)));
    }

    /**
     * Alias for {@link mat4.multiply}
     * @function
     */
    export const mul = multiply;

    /**
     * Alias for {@link mat4.subtract}
     * @function
     */
    export const sub = subtract;