| 1 | 'use strict';
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| 2 |
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| 3 | var regTransformTypes = /matrix|translate|scale|rotate|skewX|skewY/,
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| 4 | regTransformSplit = /\s*(matrix|translate|scale|rotate|skewX|skewY)\s*\(\s*(.+?)\s*\)[\s,]*/,
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| 5 | regNumericValues = /[-+]?(?:\d*\.\d+|\d+\.?)(?:[eE][-+]?\d+)?/g;
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| 6 |
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| 7 | /**
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| 8 | * Convert transform string to JS representation.
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| 9 | *
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| 10 | * @param {String} transformString input string
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| 11 | * @param {Object} params plugin params
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| 12 | * @return {Array} output array
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| 13 | */
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| 14 | exports.transform2js = function(transformString) {
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| 15 |
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| 16 | // JS representation of the transform data
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| 17 | var transforms = [],
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| 18 | // current transform context
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| 19 | current;
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| 20 |
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| 21 | // split value into ['', 'translate', '10 50', '', 'scale', '2', '', 'rotate', '-45', '']
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| 22 | transformString.split(regTransformSplit).forEach(function(item) {
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| 23 | /*jshint -W084 */
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| 24 | var num;
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| 25 |
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| 26 | if (item) {
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| 27 | // if item is a translate function
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| 28 | if (regTransformTypes.test(item)) {
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| 29 | // then collect it and change current context
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| 30 | transforms.push(current = { name: item });
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| 31 | // else if item is data
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| 32 | } else {
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| 33 | // then split it into [10, 50] and collect as context.data
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| 34 | while (num = regNumericValues.exec(item)) {
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| 35 | num = Number(num);
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| 36 | if (current.data)
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| 37 | current.data.push(num);
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| 38 | else
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| 39 | current.data = [num];
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| 40 | }
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| 41 | }
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| 42 | }
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| 43 | });
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| 44 |
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| 45 | // return empty array if broken transform (no data)
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| 46 | return current && current.data ? transforms : [];
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| 47 | };
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| 48 |
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| 49 | /**
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| 50 | * Multiply transforms into one.
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| 51 | *
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| 52 | * @param {Array} input transforms array
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| 53 | * @return {Array} output matrix array
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| 54 | */
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| 55 | exports.transformsMultiply = function(transforms) {
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| 56 |
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| 57 | // convert transforms objects to the matrices
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| 58 | transforms = transforms.map(function(transform) {
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| 59 | if (transform.name === 'matrix') {
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| 60 | return transform.data;
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| 61 | }
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| 62 | return transformToMatrix(transform);
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| 63 | });
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| 64 |
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| 65 | // multiply all matrices into one
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| 66 | transforms = {
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| 67 | name: 'matrix',
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| 68 | data: transforms.length > 0 ? transforms.reduce(multiplyTransformMatrices) : []
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| 69 | };
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| 70 |
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| 71 | return transforms;
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| 72 |
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| 73 | };
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| 74 |
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| 75 | /**
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| 76 | * Do math like a schoolgirl.
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| 77 | *
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| 78 | * @type {Object}
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| 79 | */
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| 80 | var mth = exports.mth = {
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| 81 |
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| 82 | rad: function(deg) {
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| 83 | return deg * Math.PI / 180;
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| 84 | },
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| 85 |
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| 86 | deg: function(rad) {
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| 87 | return rad * 180 / Math.PI;
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| 88 | },
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| 89 |
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| 90 | cos: function(deg) {
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| 91 | return Math.cos(this.rad(deg));
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| 92 | },
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| 93 |
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| 94 | acos: function(val, floatPrecision) {
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| 95 | return +(this.deg(Math.acos(val)).toFixed(floatPrecision));
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| 96 | },
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| 97 |
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| 98 | sin: function(deg) {
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| 99 | return Math.sin(this.rad(deg));
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| 100 | },
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| 101 |
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| 102 | asin: function(val, floatPrecision) {
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| 103 | return +(this.deg(Math.asin(val)).toFixed(floatPrecision));
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| 104 | },
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| 105 |
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| 106 | tan: function(deg) {
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| 107 | return Math.tan(this.rad(deg));
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| 108 | },
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| 109 |
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| 110 | atan: function(val, floatPrecision) {
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| 111 | return +(this.deg(Math.atan(val)).toFixed(floatPrecision));
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| 112 | }
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| 113 |
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| 114 | };
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| 115 |
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| 116 | /**
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| 117 | * Decompose matrix into simple transforms. See
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| 118 | * http://frederic-wang.fr/decomposition-of-2d-transform-matrices.html
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| 119 | *
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| 120 | * @param {Object} data matrix transform object
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| 121 | * @return {Object|Array} transforms array or original transform object
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| 122 | */
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| 123 | exports.matrixToTransform = function(transform, params) {
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| 124 | var floatPrecision = params.floatPrecision,
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| 125 | data = transform.data,
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| 126 | transforms = [],
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| 127 | sx = +Math.hypot(data[0], data[1]).toFixed(params.transformPrecision),
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| 128 | sy = +((data[0] * data[3] - data[1] * data[2]) / sx).toFixed(params.transformPrecision),
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| 129 | colsSum = data[0] * data[2] + data[1] * data[3],
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| 130 | rowsSum = data[0] * data[1] + data[2] * data[3],
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| 131 | scaleBefore = rowsSum != 0 || sx == sy;
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| 132 |
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| 133 | // [..., ..., ..., ..., tx, ty] → translate(tx, ty)
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| 134 | if (data[4] || data[5]) {
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| 135 | transforms.push({ name: 'translate', data: data.slice(4, data[5] ? 6 : 5) });
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| 136 | }
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| 137 |
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| 138 | // [sx, 0, tan(a)·sy, sy, 0, 0] → skewX(a)·scale(sx, sy)
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| 139 | if (!data[1] && data[2]) {
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| 140 | transforms.push({ name: 'skewX', data: [mth.atan(data[2] / sy, floatPrecision)] });
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| 141 |
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| 142 | // [sx, sx·tan(a), 0, sy, 0, 0] → skewY(a)·scale(sx, sy)
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| 143 | } else if (data[1] && !data[2]) {
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| 144 | transforms.push({ name: 'skewY', data: [mth.atan(data[1] / data[0], floatPrecision)] });
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| 145 | sx = data[0];
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| 146 | sy = data[3];
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| 147 |
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| 148 | // [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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| 149 | // [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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| 150 | } else if (!colsSum || (sx == 1 && sy == 1) || !scaleBefore) {
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| 151 | if (!scaleBefore) {
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| 152 | sx = (data[0] < 0 ? -1 : 1) * Math.hypot(data[0], data[2]);
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| 153 | sy = (data[3] < 0 ? -1 : 1) * Math.hypot(data[1], data[3]);
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| 154 | transforms.push({ name: 'scale', data: [sx, sy] });
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| 155 | }
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| 156 | var angle = Math.min(Math.max(-1, data[0] / sx), 1),
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| 157 | rotate = [mth.acos(angle, floatPrecision) * ((scaleBefore ? 1 : sy) * data[1] < 0 ? -1 : 1)];
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| 158 |
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| 159 | if (rotate[0]) transforms.push({ name: 'rotate', data: rotate });
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| 160 |
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| 161 | if (rowsSum && colsSum) transforms.push({
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| 162 | name: 'skewX',
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| 163 | data: [mth.atan(colsSum / (sx * sx), floatPrecision)]
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| 164 | });
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| 165 |
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| 166 | // rotate(a, cx, cy) can consume translate() within optional arguments cx, cy (rotation point)
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| 167 | if (rotate[0] && (data[4] || data[5])) {
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| 168 | transforms.shift();
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| 169 | var cos = data[0] / sx,
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| 170 | sin = data[1] / (scaleBefore ? sx : sy),
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| 171 | x = data[4] * (scaleBefore || sy),
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| 172 | y = data[5] * (scaleBefore || sx),
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| 173 | denom = (Math.pow(1 - cos, 2) + Math.pow(sin, 2)) * (scaleBefore || sx * sy);
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| 174 | rotate.push(((1 - cos) * x - sin * y) / denom);
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| 175 | rotate.push(((1 - cos) * y + sin * x) / denom);
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| 176 | }
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| 177 |
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| 178 | // Too many transformations, return original matrix if it isn't just a scale/translate
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| 179 | } else if (data[1] || data[2]) {
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| 180 | return transform;
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| 181 | }
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| 182 |
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| 183 | if (scaleBefore && (sx != 1 || sy != 1) || !transforms.length) transforms.push({
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| 184 | name: 'scale',
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| 185 | data: sx == sy ? [sx] : [sx, sy]
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| 186 | });
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| 187 |
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| 188 | return transforms;
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| 189 | };
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| 190 |
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| 191 | /**
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| 192 | * Convert transform to the matrix data.
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| 193 | *
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| 194 | * @param {Object} transform transform object
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| 195 | * @return {Array} matrix data
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| 196 | */
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| 197 | function transformToMatrix(transform) {
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| 198 |
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| 199 | if (transform.name === 'matrix') return transform.data;
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| 200 |
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| 201 | var matrix;
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| 202 |
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| 203 | switch (transform.name) {
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| 204 | case 'translate':
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| 205 | // [1, 0, 0, 1, tx, ty]
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| 206 | matrix = [1, 0, 0, 1, transform.data[0], transform.data[1] || 0];
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| 207 | break;
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| 208 | case 'scale':
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| 209 | // [sx, 0, 0, sy, 0, 0]
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| 210 | matrix = [transform.data[0], 0, 0, transform.data[1] || transform.data[0], 0, 0];
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| 211 | break;
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| 212 | case 'rotate':
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| 213 | // [cos(a), sin(a), -sin(a), cos(a), x, y]
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| 214 | var cos = mth.cos(transform.data[0]),
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| 215 | sin = mth.sin(transform.data[0]),
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| 216 | cx = transform.data[1] || 0,
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| 217 | cy = transform.data[2] || 0;
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| 218 |
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| 219 | matrix = [cos, sin, -sin, cos, (1 - cos) * cx + sin * cy, (1 - cos) * cy - sin * cx];
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| 220 | break;
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| 221 | case 'skewX':
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| 222 | // [1, 0, tan(a), 1, 0, 0]
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| 223 | matrix = [1, 0, mth.tan(transform.data[0]), 1, 0, 0];
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| 224 | break;
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| 225 | case 'skewY':
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| 226 | // [1, tan(a), 0, 1, 0, 0]
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| 227 | matrix = [1, mth.tan(transform.data[0]), 0, 1, 0, 0];
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| 228 | break;
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| 229 | }
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| 230 |
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| 231 | return matrix;
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| 232 |
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| 233 | }
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| 234 |
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| 235 | /**
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| 236 | * Applies transformation to an arc. To do so, we represent ellipse as a matrix, multiply it
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| 237 | * by the transformation matrix and use a singular value decomposition to represent in a form
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| 238 | * rotate(θ)·scale(a b)·rotate(φ). This gives us new ellipse params a, b and θ.
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| 239 | * SVD is being done with the formulae provided by Wolffram|Alpha (svd {{m0, m2}, {m1, m3}})
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| 240 | *
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| 241 | * @param {Array} arc [a, b, rotation in deg]
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| 242 | * @param {Array} transform transformation matrix
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| 243 | * @return {Array} arc transformed input arc
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| 244 | */
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| 245 | exports.transformArc = function(arc, transform) {
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| 246 |
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| 247 | var a = arc[0],
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| 248 | b = arc[1],
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| 249 | rot = arc[2] * Math.PI / 180,
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| 250 | cos = Math.cos(rot),
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| 251 | sin = Math.sin(rot),
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| 252 | h = Math.pow(arc[5] * cos + arc[6] * sin, 2) / (4 * a * a) +
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| 253 | Math.pow(arc[6] * cos - arc[5] * sin, 2) / (4 * b * b);
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| 254 | if (h > 1) {
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| 255 | h = Math.sqrt(h);
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| 256 | a *= h;
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| 257 | b *= h;
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| 258 | }
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| 259 | var ellipse = [a * cos, a * sin, -b * sin, b * cos, 0, 0],
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| 260 | m = multiplyTransformMatrices(transform, ellipse),
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| 261 | // Decompose the new ellipse matrix
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| 262 | lastCol = m[2] * m[2] + m[3] * m[3],
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| 263 | squareSum = m[0] * m[0] + m[1] * m[1] + lastCol,
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| 264 | root = Math.hypot(m[0] - m[3], m[1] + m[2]) * Math.hypot(m[0] + m[3], m[1] - m[2]);
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| 265 |
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| 266 | if (!root) { // circle
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| 267 | arc[0] = arc[1] = Math.sqrt(squareSum / 2);
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| 268 | arc[2] = 0;
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| 269 | } else {
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| 270 | var majorAxisSqr = (squareSum + root) / 2,
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| 271 | minorAxisSqr = (squareSum - root) / 2,
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| 272 | major = Math.abs(majorAxisSqr - lastCol) > 1e-6,
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| 273 | sub = (major ? majorAxisSqr : minorAxisSqr) - lastCol,
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| 274 | rowsSum = m[0] * m[2] + m[1] * m[3],
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| 275 | term1 = m[0] * sub + m[2] * rowsSum,
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| 276 | term2 = m[1] * sub + m[3] * rowsSum;
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| 277 | arc[0] = Math.sqrt(majorAxisSqr);
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| 278 | arc[1] = Math.sqrt(minorAxisSqr);
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| 279 | arc[2] = ((major ? term2 < 0 : term1 > 0) ? -1 : 1) *
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| 280 | Math.acos((major ? term1 : term2) / Math.hypot(term1, term2)) * 180 / Math.PI;
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| 281 | }
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| 282 |
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| 283 | if ((transform[0] < 0) !== (transform[3] < 0)) {
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| 284 | // Flip the sweep flag if coordinates are being flipped horizontally XOR vertically
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| 285 | arc[4] = 1 - arc[4];
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| 286 | }
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| 287 |
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| 288 | return arc;
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| 289 |
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| 290 | };
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| 291 |
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| 292 | /**
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| 293 | * Multiply transformation matrices.
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| 294 | *
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| 295 | * @param {Array} a matrix A data
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| 296 | * @param {Array} b matrix B data
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| 297 | * @return {Array} result
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| 298 | */
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| 299 | function multiplyTransformMatrices(a, b) {
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| 300 |
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| 301 | return [
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| 302 | a[0] * b[0] + a[2] * b[1],
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| 303 | a[1] * b[0] + a[3] * b[1],
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| 304 | a[0] * b[2] + a[2] * b[3],
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| 305 | a[1] * b[2] + a[3] * b[3],
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| 306 | a[0] * b[4] + a[2] * b[5] + a[4],
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| 307 | a[1] * b[4] + a[3] * b[5] + a[5]
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| 308 | ];
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| 309 |
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| 310 | }
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