src/gl-matrix/mat3.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. */

var glMatrix = require("./common.js");

/**
 * @class 3x3 Matrix
 * @name mat3
 */
var mat3 = {};

/**
 * Creates a new identity mat3
 *
 * @returns {mat3} a new 3x3 matrix
 */
mat3.create = function() {
    var out = new glMatrix.ARRAY_TYPE(9);
    out[0] = 1;
    out[1] = 0;
    out[2] = 0;
    out[3] = 0;
    out[4] = 1;
    out[5] = 0;
    out[6] = 0;
    out[7] = 0;
    out[8] = 1;
    return out;
};

/**
 * Copies the upper-left 3x3 values into the given mat3.
 *
 * @param {mat3} out the receiving 3x3 matrix
 * @param {mat4} a   the source 4x4 matrix
 * @returns {mat3} out
 */
mat3.fromMat4 = function(out, a) {
    out[0] = a[0];
    out[1] = a[1];
    out[2] = a[2];
    out[3] = a[4];
    out[4] = a[5];
    out[5] = a[6];
    out[6] = a[8];
    out[7] = a[9];
    out[8] = a[10];
    return out;
};

/**
 * Creates a new mat3 initialized with values from an existing matrix
 *
 * @param {mat3} a matrix to clone
 * @returns {mat3} a new 3x3 matrix
 */
mat3.clone = function(a) {
    var out = new glMatrix.ARRAY_TYPE(9);
    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];
    return out;
};

/**
 * Copy the values from one mat3 to another
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
mat3.copy = function(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];
    return out;
};

/**
 * Set a mat3 to the identity matrix
 *
 * @param {mat3} out the receiving matrix
 * @returns {mat3} out
 */
mat3.identity = function(out) {
    out[0] = 1;
    out[1] = 0;
    out[2] = 0;
    out[3] = 0;
    out[4] = 1;
    out[5] = 0;
    out[6] = 0;
    out[7] = 0;
    out[8] = 1;
    return out;
};

/**
 * Transpose the values of a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
mat3.transpose = function(out, a) {
    // If we are transposing ourselves we can skip a few steps but have to cache some values
    if (out === a) {
        var a01 = a[1], a02 = a[2], a12 = a[5];
        out[1] = a[3];
        out[2] = a[6];
        out[3] = a01;
        out[5] = a[7];
        out[6] = a02;
        out[7] = a12;
    } else {
        out[0] = a[0];
        out[1] = a[3];
        out[2] = a[6];
        out[3] = a[1];
        out[4] = a[4];
        out[5] = a[7];
        out[6] = a[2];
        out[7] = a[5];
        out[8] = a[8];
    }

    return out;
};

/**
 * Inverts a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
mat3.invert = function(out, a) {
    var a00 = a[0], a01 = a[1], a02 = a[2],
        a10 = a[3], a11 = a[4], a12 = a[5],
        a20 = a[6], a21 = a[7], a22 = a[8],

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

        // Calculate the determinant
        det = a00 * b01 + a01 * b11 + a02 * b21;

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

    out[0] = b01 * det;
    out[1] = (-a22 * a01 + a02 * a21) * det;
    out[2] = (a12 * a01 - a02 * a11) * det;
    out[3] = b11 * det;
    out[4] = (a22 * a00 - a02 * a20) * det;
    out[5] = (-a12 * a00 + a02 * a10) * det;
    out[6] = b21 * det;
    out[7] = (-a21 * a00 + a01 * a20) * det;
    out[8] = (a11 * a00 - a01 * a10) * det;
    return out;
};

/**
 * Calculates the adjugate of a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
mat3.adjoint = function(out, a) {
    var a00 = a[0], a01 = a[1], a02 = a[2],
        a10 = a[3], a11 = a[4], a12 = a[5],
        a20 = a[6], a21 = a[7], a22 = a[8];

    out[0] = (a11 * a22 - a12 * a21);
    out[1] = (a02 * a21 - a01 * a22);
    out[2] = (a01 * a12 - a02 * a11);
    out[3] = (a12 * a20 - a10 * a22);
    out[4] = (a00 * a22 - a02 * a20);
    out[5] = (a02 * a10 - a00 * a12);
    out[6] = (a10 * a21 - a11 * a20);
    out[7] = (a01 * a20 - a00 * a21);
    out[8] = (a00 * a11 - a01 * a10);
    return out;
};

/**
 * Calculates the determinant of a mat3
 *
 * @param {mat3} a the source matrix
 * @returns {Number} determinant of a
 */
mat3.determinant = function (a) {
    var a00 = a[0], a01 = a[1], a02 = a[2],
        a10 = a[3], a11 = a[4], a12 = a[5],
        a20 = a[6], a21 = a[7], a22 = a[8];

    return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20);
};

/**
 * Multiplies two mat3's
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the first operand
 * @param {mat3} b the second operand
 * @returns {mat3} out
 */
mat3.multiply = function (out, a, b) {
    var a00 = a[0], a01 = a[1], a02 = a[2],
        a10 = a[3], a11 = a[4], a12 = a[5],
        a20 = a[6], a21 = a[7], a22 = a[8],

        b00 = b[0], b01 = b[1], b02 = b[2],
        b10 = b[3], b11 = b[4], b12 = b[5],
        b20 = b[6], b21 = b[7], b22 = b[8];

    out[0] = b00 * a00 + b01 * a10 + b02 * a20;
    out[1] = b00 * a01 + b01 * a11 + b02 * a21;
    out[2] = b00 * a02 + b01 * a12 + b02 * a22;

    out[3] = b10 * a00 + b11 * a10 + b12 * a20;
    out[4] = b10 * a01 + b11 * a11 + b12 * a21;
    out[5] = b10 * a02 + b11 * a12 + b12 * a22;

    out[6] = b20 * a00 + b21 * a10 + b22 * a20;
    out[7] = b20 * a01 + b21 * a11 + b22 * a21;
    out[8] = b20 * a02 + b21 * a12 + b22 * a22;
    return out;
};

/**
 * Alias for {@link mat3.multiply}
 * @function
 */
mat3.mul = mat3.multiply;

/**
 * Translate a mat3 by the given vector
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to translate
 * @param {vec2} v vector to translate by
 * @returns {mat3} out
 */
mat3.translate = function(out, a, v) {
    var a00 = a[0], a01 = a[1], a02 = a[2],
        a10 = a[3], a11 = a[4], a12 = a[5],
        a20 = a[6], a21 = a[7], a22 = a[8],
        x = v[0], y = v[1];

    out[0] = a00;
    out[1] = a01;
    out[2] = a02;

    out[3] = a10;
    out[4] = a11;
    out[5] = a12;

    out[6] = x * a00 + y * a10 + a20;
    out[7] = x * a01 + y * a11 + a21;
    out[8] = x * a02 + y * a12 + a22;
    return out;
};

/**
 * Rotates a mat3 by the given angle
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to rotate
 * @param {Number} rad the angle to rotate the matrix by
 * @returns {mat3} out
 */
mat3.rotate = function (out, a, rad) {
    var a00 = a[0], a01 = a[1], a02 = a[2],
        a10 = a[3], a11 = a[4], a12 = a[5],
        a20 = a[6], a21 = a[7], a22 = a[8],

        s = Math.sin(rad),
        c = Math.cos(rad);

    out[0] = c * a00 + s * a10;
    out[1] = c * a01 + s * a11;
    out[2] = c * a02 + s * a12;

    out[3] = c * a10 - s * a00;
    out[4] = c * a11 - s * a01;
    out[5] = c * a12 - s * a02;

    out[6] = a20;
    out[7] = a21;
    out[8] = a22;
    return out;
};

/**
 * Scales the mat3 by the dimensions in the given vec2
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to rotate
 * @param {vec2} v the vec2 to scale the matrix by
 * @returns {mat3} out
 **/
mat3.scale = function(out, a, v) {
    var x = v[0], y = v[1];

    out[0] = x * a[0];
    out[1] = x * a[1];
    out[2] = x * a[2];

    out[3] = y * a[3];
    out[4] = y * a[4];
    out[5] = y * a[5];

    out[6] = a[6];
    out[7] = a[7];
    out[8] = a[8];
    return out;
};

/**
 * Creates a matrix from a vector translation
 * This is equivalent to (but much faster than):
 *
 *     mat3.identity(dest);
 *     mat3.translate(dest, dest, vec);
 *
 * @param {mat3} out mat3 receiving operation result
 * @param {vec2} v Translation vector
 * @returns {mat3} out
 */
mat3.fromTranslation = function(out, v) {
    out[0] = 1;
    out[1] = 0;
    out[2] = 0;
    out[3] = 0;
    out[4] = 1;
    out[5] = 0;
    out[6] = v[0];
    out[7] = v[1];
    out[8] = 1;
    return out;
}

/**
 * Creates a matrix from a given angle
 * This is equivalent to (but much faster than):
 *
 *     mat3.identity(dest);
 *     mat3.rotate(dest, dest, rad);
 *
 * @param {mat3} out mat3 receiving operation result
 * @param {Number} rad the angle to rotate the matrix by
 * @returns {mat3} out
 */
mat3.fromRotation = function(out, rad) {
    var s = Math.sin(rad), c = Math.cos(rad);

    out[0] = c;
    out[1] = s;
    out[2] = 0;

    out[3] = -s;
    out[4] = c;
    out[5] = 0;

    out[6] = 0;
    out[7] = 0;
    out[8] = 1;
    return out;
}

/**
 * Creates a matrix from a vector scaling
 * This is equivalent to (but much faster than):
 *
 *     mat3.identity(dest);
 *     mat3.scale(dest, dest, vec);
 *
 * @param {mat3} out mat3 receiving operation result
 * @param {vec2} v Scaling vector
 * @returns {mat3} out
 */
mat3.fromScaling = function(out, v) {
    out[0] = v[0];
    out[1] = 0;
    out[2] = 0;

    out[3] = 0;
    out[4] = v[1];
    out[5] = 0;

    out[6] = 0;
    out[7] = 0;
    out[8] = 1;
    return out;
}

/**
 * Copies the values from a mat2d into a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat2d} a the matrix to copy
 * @returns {mat3} out
 **/
mat3.fromMat2d = function(out, a) {
    out[0] = a[0];
    out[1] = a[1];
    out[2] = 0;

    out[3] = a[2];
    out[4] = a[3];
    out[5] = 0;

    out[6] = a[4];
    out[7] = a[5];
    out[8] = 1;
    return out;
};

/**
* Calculates a 3x3 matrix from the given quaternion
*
* @param {mat3} out mat3 receiving operation result
* @param {quat} q Quaternion to create matrix from
*
* @returns {mat3} out
*/
mat3.fromQuat = function (out, q) {
    var x = q[0], y = q[1], z = q[2], w = q[3],
        x2 = x + x,
        y2 = y + y,
        z2 = z + z,

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

    out[0] = 1 - yy - zz;
    out[3] = yx - wz;
    out[6] = zx + wy;

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

    out[2] = zx - wy;
    out[5] = zy + wx;
    out[8] = 1 - xx - yy;

    return out;
};

/**
* Calculates a 3x3 normal matrix (transpose inverse) from the 4x4 matrix
*
* @param {mat3} out mat3 receiving operation result
* @param {mat4} a Mat4 to derive the normal matrix from
*
* @returns {mat3} out
*/
mat3.normalFromMat4 = function (out, a) {
    var 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],
        a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[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,

        // Calculate the determinant
        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] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
    out[2] = (a10 * b10 - a11 * b08 + a13 * b06) * det;

    out[3] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
    out[4] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
    out[5] = (a01 * b08 - a00 * b10 - a03 * b06) * det;

    out[6] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
    out[7] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
    out[8] = (a30 * b04 - a31 * b02 + a33 * b00) * det;

    return out;
};

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

/**
 * Returns Frobenius norm of a mat3
 *
 * @param {mat3} a the matrix to calculate Frobenius norm of
 * @returns {Number} Frobenius norm
 */
mat3.frob = function (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)))
};


module.exports = mat3;