matrix/js/MatrixUtil.js

8ab6afc0ff1f6b225e52d7489864024d814b37fcTrippvar MatrixUtil = {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Used as value for the _rounding method.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @property _rounder
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @private
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        _rounder: 100000,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Rounds values
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method _round
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @private
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        _round: function(val) {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            val = Math.round(val * MatrixUtil._rounder) / MatrixUtil._rounder;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return val;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Converts a radian value to a degree.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method rad2deg
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Number} rad Radian value to be converted.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Number
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        rad2deg: function(rad) {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var deg = rad * (180 / Math.PI);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return deg;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Converts a degree value to a radian.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method deg2rad
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Number} deg Degree value to be converted to radian.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Number
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        deg2rad: function(deg) {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var rad = deg * (Math.PI / 180);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return rad;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Converts an angle to a radian
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method angle2rad
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Objecxt} val Value to be converted to radian.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Number
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        angle2rad: function(val) {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            if (typeof val === 'string' && val.indexOf('rad') > -1) {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                val = parseFloat(val);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            } else { // default to deg
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                val = MatrixUtil.deg2rad(parseFloat(val));
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return val;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Converts a transform object to an array of column vectors.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * /                                             \
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * | matrix[0][0]   matrix[1][0]    matrix[2][0] |
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * | matrix[0][1]   matrix[1][1]    matrix[2][1] |
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * | matrix[0][2]   matrix[1][2]    matrix[2][2] |
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * \                                             /
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method getnxn
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Array
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        convertTransformToArray: function(matrix)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var matrixArray = [
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    [matrix.a, matrix.c, matrix.dx],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    [matrix.b, matrix.d, matrix.dy],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    [0, 0, 1]
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                ];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return matrixArray;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Returns the determinant of a given matrix.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * /                                             \
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * | matrix[0][0]   matrix[1][0]    matrix[2][0] |
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * | matrix[0][1]   matrix[1][1]    matrix[2][1] |
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * | matrix[0][2]   matrix[1][2]    matrix[2][2] |
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * | matrix[0][3]   matrix[1][3]    matrix[2][3] |
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * \                                             /
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method getDeterminant
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Array} matrix An nxn matrix represented an array of vector (column) arrays. Each vector array has index for each row.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Number
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        getDeterminant: function(matrix)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var determinant = 0,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                len = matrix.length,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                i = 0,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                multiplier;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            if(len == 2)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                return matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            for(; i < len; ++i)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                multiplier = matrix[i][0];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                if(i % 2 === 0 || i === 0)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    determinant += multiplier * MatrixUtil.getDeterminant(MatrixUtil.getMinors(matrix, i, 0));
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                else
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    determinant -= multiplier * MatrixUtil.getDeterminant(MatrixUtil.getMinors(matrix, i, 0));
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return determinant;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Returns the inverse of a matrix
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method inverse
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param Array matrix An array representing an nxn matrix
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Array
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * /                                             \
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * | matrix[0][0]   matrix[1][0]    matrix[2][0] |
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * | matrix[0][1]   matrix[1][1]    matrix[2][1] |
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * | matrix[0][2]   matrix[1][2]    matrix[2][2] |
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * | matrix[0][3]   matrix[1][3]    matrix[2][3] |
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * \                                             /
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        inverse: function(matrix)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var determinant = 0,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                len = matrix.length,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                i = 0,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                j,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                inverse,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                adjunct = [],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                //vector representing 2x2 matrix
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                minor = [],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                multiplier;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            if(len === 2)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                determinant = matrix[0][0] * matrix[1][1] - matrix[0][1] * matrix[1][0];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                inverse = [
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    [matrix[1][1] * determinant, -matrix[1][0] * determinant],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    [-matrix[0][1] * determinant, matrix[0][0] * determinant]
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                ];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            else
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                determinant = MatrixUtil.getDeterminant(matrix);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                for(; i < len; ++i)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    adjunct[i] = [];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    for(j = 0; j < len; ++j)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        minor = MatrixUtil.getMinors(matrix, j, i);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        adjunct[i][j] = MatrixUtil.getDeterminant(minor);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        if((i + j) % 2 !== 0 && (i + j) !== 0)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                            adjunct[i][j] *= -1;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                inverse = MatrixUtil.scalarMultiply(adjunct, 1/determinant);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return inverse;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Multiplies a matrix by a numeric value.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method scalarMultiply
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Array} matrix The matrix to be altered.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Number} multiplier The number to multiply against the matrix.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Array
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        scalarMultiply: function(matrix, multiplier)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var i = 0,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                j,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                len = matrix.length;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            for(; i < len; ++i)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                for(j = 0; j < len; ++j)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    matrix[i][j] = MatrixUtil._round(matrix[i][j] * multiplier);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return matrix;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Returns the transpose for an nxn matrix.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method transpose
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param matrix An nxn matrix represented by an array of vector arrays.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Array
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        transpose: function(matrix)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var len = matrix.length,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                i = 0,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                j = 0,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                transpose = [];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            for(; i < len; ++i)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                transpose[i] = [];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                for(j = 0; j < len; ++j)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    transpose[i].push(matrix[j][i]);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return transpose;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Returns a matrix of minors based on a matrix, column index and row index.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method getMinors
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Array} matrix The matrix from which to extract the matrix of minors.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Number} columnIndex A zero-based index representing the specified column to exclude.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Number} rowIndex A zero-based index represeenting the specified row to exclude.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Array
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        getMinors: function(matrix, columnIndex, rowIndex)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var minors = [],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                len = matrix.length,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                i = 0,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                j,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                column;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            for(; i < len; ++i)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                if(i !== columnIndex)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    column = [];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    for(j = 0; j < len; ++j)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        if(j !== rowIndex)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                            column.push(matrix[i][j]);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    minors.push(column);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return minors;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Returns the sign of value
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method sign
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Number} val value to be interpreted
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Number
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        sign: function(val)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return val === 0 ? 1 : val/Math.abs(val);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Multiplies a vector and a matrix
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method vectorMatrixProduct
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Array} vector Array representing a column vector
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Array} matrix Array representing an nxn matrix
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Array
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        vectorMatrixProduct: function(vector, matrix)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var i,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                j,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                len = vector.length,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                product = [],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                rowProduct;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            for(i = 0; i < len; ++i)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                rowProduct = 0;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                for(j = 0; j < len; ++j)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    rowProduct += vector[i] * matrix[i][j];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                product[i] = rowProduct;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return product;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Breaks up a 2d transform matrix into a series of transform operations.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method decompose
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Array} 3x3 matrix array
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Array
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        decompose: function(matrix)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var a = matrix[0][0],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                b = matrix[1][0],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                c = matrix[0][1],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                d = matrix[1][1],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                dx = matrix[0][2],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                dy = matrix[1][2],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                translate = [dx, dy],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                rotate,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                sx,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                sy,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                sign = sign,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                shear;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            if((a * d - b * c) === 0)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                return false;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            //get length of vector(ab)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            sx = MatrixUtil._round(Math.sqrt(a * a + b * b));
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            //normalize components of vector(ab)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            a /= sx;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            b /= sx;
83e1c423e969705408dfcf7d94c7cd3c762e18f8Tripp            shear = MatrixUtil._round(a * c + b * d);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            c -= a * shear;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            d -= b * shear;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            //get length of vector(cd)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            sy = MatrixUtil._round(Math.sqrt(c * c + d * d));
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            //normalize components of vector(cd)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            c /= sy;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            d /= sy;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            shear /=sy;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            if(a * b < c * d)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                a = -a;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                b = -b;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                c = -c;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                d = -d;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                shear = -shear;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                sx = -sx;
83e1c423e969705408dfcf7d94c7cd3c762e18f8Tripp                sy = -sy;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
83e1c423e969705408dfcf7d94c7cd3c762e18f8Tripp            shear = MatrixUtil._round(MatrixUtil.rad2deg(Math.atan(shear)));
83e1c423e969705408dfcf7d94c7cd3c762e18f8Tripp            rotate = MatrixUtil._round(MatrixUtil.rad2deg(Math.atan2(matrix[1][0], matrix[0][0])));
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return [
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                ["translate", dx, dy],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                ["rotate", rotate],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                ["skewX", shear],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                ["scale", sx, sy]
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            ];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Parses a transform string and returns an array of transform arrays.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method getTransformArray
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {String} val A transform string
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Array
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        getTransformArray: function(transform) {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var re = /\s*([a-z]*)\(([\w,\.,\-,\s]*)\)/gi,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                transforms = [],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                args,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                m,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                decomp,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                methods = MatrixUtil.transformMethods;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            while ((m = re.exec(transform))) {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                if (methods.hasOwnProperty(m[1]))
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    args = m[2].split(',');
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    args.unshift(m[1]);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    transforms.push(args);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                else if(m[1] == "matrix")
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    args = m[2].split(',');
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    decomp = MatrixUtil.decompose([
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        [args[0], args[2], args[4]],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        [args[1], args[3], args[5]],
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        [0, 0, 1]
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    ]);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    transforms.push(decomp[0]);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    transforms.push(decomp[1]);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    transforms.push(decomp[2]);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    transforms.push(decomp[3]);
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return transforms;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Returns an array of transform arrays representing transform functions and arguments.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method getTransformFunctionArray
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Array
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        getTransformFunctionArray: function(transform) {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var list;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            switch(transform)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                case "skew" :
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    list = [transform, 0, 0];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                break;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                case "scale" :
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    list = [transform, 1, 1];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                break;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                case "scaleX" :
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    list = [transform, 1];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                break;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                case "scaleY" :
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    list = [transform, 1];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                break;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                case "translate" :
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    list = [transform, 0, 0];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                break;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                default :
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    list = [transform, 0];
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                break;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return list;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Compares to arrays or transform functions to ensure both contain the same functions in the same
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * order.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @method compareTransformSequence
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Array} list1 Array to compare
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @param {Array} list2 Array to compare
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @return Boolean
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        compareTransformSequence: function(list1, list2)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            var i = 0,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                len = list1.length,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                len2 = list2.length,
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                isEqual = len === len2;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            if(isEqual)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                for(; i < len; ++i)
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    if(list1[i][0] != list2[i][0])
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        isEqual = false;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                        break;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                    }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp                }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            return isEqual;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        },
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        /**
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * Mapping of possible transform method names.
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         *
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @property transformMethods
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         * @type Object
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp         */
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        transformMethods: {
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            rotate: "rotate",
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            skew: "skew",
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            skewX: "skewX",
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            skewY: "skewY",
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            translate: "translate",
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            translateX: "translateX",
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            translateY: "tranlsateY",
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            scale: "scale",
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            scaleX: "scaleX",
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp            scaleY: "scaleY"
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp        }
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp};
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp
8ab6afc0ff1f6b225e52d7489864024d814b37fcTrippY.MatrixUtil = MatrixUtil;
8ab6afc0ff1f6b225e52d7489864024d814b37fcTripp