309 lines
9.9 KiB
JavaScript
309 lines
9.9 KiB
JavaScript
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'use strict';
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var regTransformTypes = /matrix|translate|scale|rotate|skewX|skewY/,
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regTransformSplit = /\s*(matrix|translate|scale|rotate|skewX|skewY)\s*\(\s*(.+?)\s*\)[\s,]*/,
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regNumericValues = /[-+]?(?:\d*\.\d+|\d+\.?)(?:[eE][-+]?\d+)?/g;
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/**
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* Convert transform string to JS representation.
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*
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* @param {String} transformString input string
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* @param {Object} params plugin params
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* @return {Array} output array
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*/
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exports.transform2js = function(transformString) {
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// JS representation of the transform data
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var transforms = [],
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// current transform context
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current;
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// split value into ['', 'translate', '10 50', '', 'scale', '2', '', 'rotate', '-45', '']
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transformString.split(regTransformSplit).forEach(function(item) {
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/*jshint -W084 */
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var num;
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if (item) {
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// if item is a translate function
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if (regTransformTypes.test(item)) {
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// then collect it and change current context
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transforms.push(current = { name: item });
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// else if item is data
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} else {
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// then split it into [10, 50] and collect as context.data
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while (num = regNumericValues.exec(item)) {
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num = Number(num);
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if (current.data)
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current.data.push(num);
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else
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current.data = [num];
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}
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}
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}
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});
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return transforms;
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};
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/**
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* Multiply transforms into one.
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*
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* @param {Array} input transforms array
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* @return {Array} output matrix array
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*/
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exports.transformsMultiply = function(transforms) {
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// convert transforms objects to the matrices
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transforms = transforms.map(function(transform) {
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if (transform.name === 'matrix') {
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return transform.data;
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}
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return transformToMatrix(transform);
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});
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// multiply all matrices into one
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transforms = {
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name: 'matrix',
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data: transforms.reduce(function(a, b) {
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return multiplyTransformMatrices(a, b);
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})
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};
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return transforms;
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};
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/**
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* Do math like a schoolgirl.
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*
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* @type {Object}
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*/
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var mth = exports.mth = {
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rad: function(deg) {
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return deg * Math.PI / 180;
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},
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deg: function(rad) {
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return rad * 180 / Math.PI;
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},
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cos: function(deg) {
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return Math.cos(this.rad(deg));
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},
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acos: function(val, floatPrecision) {
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return +(this.deg(Math.acos(val)).toFixed(floatPrecision));
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},
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sin: function(deg) {
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return Math.sin(this.rad(deg));
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},
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asin: function(val, floatPrecision) {
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return +(this.deg(Math.asin(val)).toFixed(floatPrecision));
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},
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tan: function(deg) {
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return Math.tan(this.rad(deg));
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},
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atan: function(val, floatPrecision) {
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return +(this.deg(Math.atan(val)).toFixed(floatPrecision));
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}
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};
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/**
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* Decompose matrix into simple transforms. See
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* http://www.maths-informatique-jeux.com/blog/frederic/?post/2013/12/01/Decomposition-of-2D-transform-matrices
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*
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* @param {Object} data matrix transform object
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* @return {Object|Array} transforms array or original transform object
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*/
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exports.matrixToTransform = function(transform, params) {
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var floatPrecision = params.floatPrecision,
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data = transform.data,
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transforms = [],
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sx = +Math.sqrt(data[0] * data[0] + data[1] * data[1]).toFixed(params.transformPrecision),
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sy = +((data[0] * data[3] - data[1] * data[2]) / sx).toFixed(params.transformPrecision),
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colsSum = data[0] * data[2] + data[1] * data[3],
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rowsSum = data[0] * data[1] + data[2] * data[3],
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scaleBefore = rowsSum || +(sx == sy);
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// [..., ..., ..., ..., tx, ty] → translate(tx, ty)
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if (data[4] || data[5]) {
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transforms.push({ name: 'translate', data: data.slice(4, data[5] ? 6 : 5) });
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}
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// [sx, 0, tan(a)·sy, sy, 0, 0] → skewX(a)·scale(sx, sy)
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if (!data[1] && data[2]) {
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transforms.push({ name: 'skewX', data: [mth.atan(data[2] / sy, floatPrecision)] });
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// [sx, sx·tan(a), 0, sy, 0, 0] → skewY(a)·scale(sx, sy)
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} else if (data[1] && !data[2]) {
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transforms.push({ name: 'skewY', data: [mth.atan(data[1] / data[0], floatPrecision)] });
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sx = data[0];
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sy = data[3];
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// [sx·cos(a), sx·sin(a), sy·-sin(a), sy·cos(a), x, y] → rotate(a[, cx, cy])·(scale or skewX) or
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// [sx·cos(a), sy·sin(a), sx·-sin(a), sy·cos(a), x, y] → scale(sx, sy)·rotate(a[, cx, cy]) (if !scaleBefore)
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} else if (!colsSum || (sx == 1 && sy == 1) || !scaleBefore) {
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if (!scaleBefore) {
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sx = (data[0] < 0 ? -1 : 1) * Math.sqrt(data[0] * data[0] + data[2] * data[2]);
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sy = (data[3] < 0 ? -1 : 1) * Math.sqrt(data[1] * data[1] + data[3] * data[3]);
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transforms.push({ name: 'scale', data: [sx, sy] });
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}
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var rotate = [mth.acos(data[0] / sx, floatPrecision) * (data[1] * sy < 0 ? -1 : 1)];
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if (rotate[0]) transforms.push({ name: 'rotate', data: rotate });
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if (rowsSum && colsSum) transforms.push({
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name: 'skewX',
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data: [mth.atan(colsSum / (sx * sx), floatPrecision)]
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});
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// rotate(a, cx, cy) can consume translate() within optional arguments cx, cy (rotation point)
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if (rotate[0] && (data[4] || data[5])) {
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transforms.shift();
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var cos = data[0] / sx,
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sin = data[1] / (scaleBefore ? sx : sy),
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x = data[4] * (scaleBefore || sy),
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y = data[5] * (scaleBefore || sx),
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denom = (Math.pow(1 - cos, 2) + Math.pow(sin, 2)) * (scaleBefore || sx * sy);
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rotate.push(((1 - cos) * x - sin * y) / denom);
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rotate.push(((1 - cos) * y + sin * x) / denom);
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}
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// Too many transformations, return original matrix if it isn't just a scale/translate
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} else if (data[1] || data[2]) {
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return transform;
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}
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if (scaleBefore && (sx != 1 || sy != 1) || !transforms.length) transforms.push({
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name: 'scale',
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data: sx == sy ? [sx] : [sx, sy]
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});
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return transforms;
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};
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/**
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* Convert transform to the matrix data.
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*
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* @param {Object} transform transform object
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* @return {Array} matrix data
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*/
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function transformToMatrix(transform) {
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if (transform.name === 'matrix') return transform.data;
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var matrix;
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switch (transform.name) {
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case 'translate':
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// [1, 0, 0, 1, tx, ty]
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matrix = [1, 0, 0, 1, transform.data[0], transform.data[1] || 0];
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break;
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case 'scale':
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// [sx, 0, 0, sy, 0, 0]
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matrix = [transform.data[0], 0, 0, transform.data[1] || transform.data[0], 0, 0];
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break;
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case 'rotate':
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// [cos(a), sin(a), -sin(a), cos(a), x, y]
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var cos = mth.cos(transform.data[0]),
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sin = mth.sin(transform.data[0]),
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cx = transform.data[1] || 0,
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cy = transform.data[2] || 0;
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matrix = [cos, sin, -sin, cos, (1 - cos) * cx + sin * cy, (1 - cos) * cy - sin * cx];
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break;
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case 'skewX':
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// [1, 0, tan(a), 1, 0, 0]
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matrix = [1, 0, mth.tan(transform.data[0]), 1, 0, 0];
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break;
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case 'skewY':
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// [1, tan(a), 0, 1, 0, 0]
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matrix = [1, mth.tan(transform.data[0]), 0, 1, 0, 0];
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break;
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}
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return matrix;
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}
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/**
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* Applies transformation to an arc. To do so, we represent ellipse as a matrix, multiply it
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* by the transformation matrix and use a singular value decomposition to represent in a form
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* rotate(θ)·scale(a b)·rotate(φ). This gives us new ellipse params a, b and θ.
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* SVD is being done with the formulae provided by Wolffram|Alpha (svd {{m0, m2}, {m1, m3}})
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*
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* @param {Array} arc [a, b, rotation in deg]
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* @param {Array} transform transformation matrix
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* @return {Array} arc transformed input arc
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*/
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exports.transformArc = function(arc, transform) {
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var a = arc[0],
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b = arc[1],
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rot = arc[2] * Math.PI / 180,
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cos = Math.cos(rot),
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sin = Math.sin(rot),
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h = Math.pow(arc[5] * cos + arc[6] * sin, 2) / (4 * a * a) +
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Math.pow(arc[6] * cos - arc[5] * sin, 2) / (4 * b * b);
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if (h > 1) {
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h = Math.sqrt(h);
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a *= h;
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b *= h;
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}
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var ellipse = [a * cos, a * sin, -b * sin, b * cos, 0, 0],
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m = multiplyTransformMatrices(transform, ellipse),
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// Decompose the new ellipse matrix
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lastCol = m[2] * m[2] + m[3] * m[3],
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squareSum = m[0] * m[0] + m[1] * m[1] + lastCol,
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root = Math.sqrt(
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(Math.pow(m[0] - m[3], 2) + Math.pow(m[1] + m[2], 2)) *
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(Math.pow(m[0] + m[3], 2) + Math.pow(m[1] - m[2], 2))
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);
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if (!root) { // circle
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arc[0] = arc[1] = Math.sqrt(squareSum / 2);
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arc[2] = 0;
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} else {
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var majorAxisSqr = (squareSum + root) / 2,
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minorAxisSqr = (squareSum - root) / 2,
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major = Math.abs(majorAxisSqr - lastCol) > 1e-6,
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sub = (major ? majorAxisSqr : minorAxisSqr) - lastCol,
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rowsSum = m[0] * m[2] + m[1] * m[3],
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term1 = m[0] * sub + m[2] * rowsSum,
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term2 = m[1] * sub + m[3] * rowsSum;
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arc[0] = Math.sqrt(majorAxisSqr);
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arc[1] = Math.sqrt(minorAxisSqr);
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arc[2] = ((major ? term2 < 0 : term1 > 0) ? -1 : 1) *
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Math.acos((major ? term1 : term2) / Math.sqrt(term1 * term1 + term2 * term2)) * 180 / Math.PI;
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}
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return arc;
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};
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/**
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* Multiply transformation matrices.
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*
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* @param {Array} a matrix A data
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* @param {Array} b matrix B data
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* @return {Array} result
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*/
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function multiplyTransformMatrices(a, b) {
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return [
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a[0] * b[0] + a[2] * b[1],
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a[1] * b[0] + a[3] * b[1],
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a[0] * b[2] + a[2] * b[3],
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a[1] * b[2] + a[3] * b[3],
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a[0] * b[4] + a[2] * b[5] + a[4],
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a[1] * b[4] + a[3] * b[5] + a[5]
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];
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}
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