1 | 'use strict';
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2 |
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3 | const regTransformTypes = /matrix|translate|scale|rotate|skewX|skewY/;
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4 | const regTransformSplit =
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5 | /\s*(matrix|translate|scale|rotate|skewX|skewY)\s*\(\s*(.+?)\s*\)[\s,]*/;
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6 | const regNumericValues = /[-+]?(?:\d*\.\d+|\d+\.?)(?:[eE][-+]?\d+)?/g;
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7 |
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8 | /**
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9 | * @typedef {{ name: string, data: Array<number> }} TransformItem
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10 | */
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11 |
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12 | /**
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13 | * Convert transform string to JS representation.
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14 | *
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15 | * @type {(transformString: string) => Array<TransformItem>}
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16 | */
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17 | exports.transform2js = (transformString) => {
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18 | // JS representation of the transform data
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19 | /**
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20 | * @type {Array<TransformItem>}
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21 | */
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22 | const transforms = [];
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23 | // current transform context
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24 | /**
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25 | * @type {null | TransformItem}
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26 | */
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27 | let current = null;
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28 | // split value into ['', 'translate', '10 50', '', 'scale', '2', '', 'rotate', '-45', '']
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29 | for (const item of transformString.split(regTransformSplit)) {
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30 | var num;
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31 | if (item) {
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32 | // if item is a translate function
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33 | if (regTransformTypes.test(item)) {
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34 | // then collect it and change current context
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35 | current = { name: item, data: [] };
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36 | transforms.push(current);
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37 | // else if item is data
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38 | } else {
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39 | // then split it into [10, 50] and collect as context.data
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40 | // eslint-disable-next-line no-cond-assign
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41 | while ((num = regNumericValues.exec(item))) {
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42 | num = Number(num);
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43 | if (current != null) {
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44 | current.data.push(num);
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45 | }
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46 | }
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47 | }
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48 | }
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49 | }
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50 | // return empty array if broken transform (no data)
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51 | return current == null || current.data.length == 0 ? [] : transforms;
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52 | };
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53 |
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54 | /**
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55 | * Multiply transforms into one.
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56 | *
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57 | * @type {(transforms: Array<TransformItem>) => TransformItem}
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58 | */
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59 | exports.transformsMultiply = (transforms) => {
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60 | // convert transforms objects to the matrices
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61 | const matrixData = transforms.map((transform) => {
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62 | if (transform.name === 'matrix') {
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63 | return transform.data;
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64 | }
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65 | return transformToMatrix(transform);
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66 | });
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67 | // multiply all matrices into one
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68 | const matrixTransform = {
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69 | name: 'matrix',
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70 | data:
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71 | matrixData.length > 0 ? matrixData.reduce(multiplyTransformMatrices) : [],
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72 | };
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73 | return matrixTransform;
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74 | };
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75 |
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76 | /**
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77 | * math utilities in radians.
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78 | */
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79 | const mth = {
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80 | /**
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81 | * @type {(deg: number) => number}
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82 | */
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83 | rad: (deg) => {
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84 | return (deg * Math.PI) / 180;
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85 | },
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86 |
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87 | /**
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88 | * @type {(rad: number) => number}
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89 | */
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90 | deg: (rad) => {
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91 | return (rad * 180) / Math.PI;
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92 | },
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93 |
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94 | /**
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95 | * @type {(deg: number) => number}
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96 | */
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97 | cos: (deg) => {
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98 | return Math.cos(mth.rad(deg));
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99 | },
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100 |
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101 | /**
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102 | * @type {(val: number, floatPrecision: number) => number}
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103 | */
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104 | acos: (val, floatPrecision) => {
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105 | return Number(mth.deg(Math.acos(val)).toFixed(floatPrecision));
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106 | },
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107 |
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108 | /**
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109 | * @type {(deg: number) => number}
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110 | */
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111 | sin: (deg) => {
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112 | return Math.sin(mth.rad(deg));
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113 | },
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114 |
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115 | /**
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116 | * @type {(val: number, floatPrecision: number) => number}
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117 | */
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118 | asin: (val, floatPrecision) => {
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119 | return Number(mth.deg(Math.asin(val)).toFixed(floatPrecision));
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120 | },
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121 |
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122 | /**
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123 | * @type {(deg: number) => number}
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124 | */
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125 | tan: (deg) => {
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126 | return Math.tan(mth.rad(deg));
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127 | },
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128 |
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129 | /**
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130 | * @type {(val: number, floatPrecision: number) => number}
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131 | */
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132 | atan: (val, floatPrecision) => {
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133 | return Number(mth.deg(Math.atan(val)).toFixed(floatPrecision));
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134 | },
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135 | };
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136 |
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137 | /**
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138 | * @typedef {{
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139 | * convertToShorts: boolean,
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140 | * floatPrecision: number,
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141 | * transformPrecision: number,
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142 | * matrixToTransform: boolean,
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143 | * shortTranslate: boolean,
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144 | * shortScale: boolean,
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145 | * shortRotate: boolean,
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146 | * removeUseless: boolean,
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147 | * collapseIntoOne: boolean,
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148 | * leadingZero: boolean,
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149 | * negativeExtraSpace: boolean,
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150 | * }} TransformParams
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151 | */
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152 |
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153 | /**
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154 | * Decompose matrix into simple transforms. See
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155 | * https://frederic-wang.fr/decomposition-of-2d-transform-matrices.html
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156 | *
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157 | * @type {(transform: TransformItem, params: TransformParams) => Array<TransformItem>}
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158 | */
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159 | exports.matrixToTransform = (transform, params) => {
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160 | let floatPrecision = params.floatPrecision;
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161 | let data = transform.data;
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162 | let transforms = [];
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163 | let sx = Number(
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164 | Math.hypot(data[0], data[1]).toFixed(params.transformPrecision)
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165 | );
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166 | let sy = Number(
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167 | ((data[0] * data[3] - data[1] * data[2]) / sx).toFixed(
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168 | params.transformPrecision
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169 | )
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170 | );
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171 | let colsSum = data[0] * data[2] + data[1] * data[3];
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172 | let rowsSum = data[0] * data[1] + data[2] * data[3];
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173 | let scaleBefore = rowsSum != 0 || sx == sy;
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174 |
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175 | // [..., ..., ..., ..., tx, ty] → translate(tx, ty)
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176 | if (data[4] || data[5]) {
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177 | transforms.push({
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178 | name: 'translate',
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179 | data: data.slice(4, data[5] ? 6 : 5),
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180 | });
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181 | }
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182 |
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183 | // [sx, 0, tan(a)·sy, sy, 0, 0] → skewX(a)·scale(sx, sy)
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184 | if (!data[1] && data[2]) {
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185 | transforms.push({
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186 | name: 'skewX',
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187 | data: [mth.atan(data[2] / sy, floatPrecision)],
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188 | });
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189 |
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190 | // [sx, sx·tan(a), 0, sy, 0, 0] → skewY(a)·scale(sx, sy)
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191 | } else if (data[1] && !data[2]) {
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192 | transforms.push({
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193 | name: 'skewY',
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194 | data: [mth.atan(data[1] / data[0], floatPrecision)],
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195 | });
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196 | sx = data[0];
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197 | sy = data[3];
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198 |
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199 | // [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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200 | // [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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201 | } else if (!colsSum || (sx == 1 && sy == 1) || !scaleBefore) {
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202 | if (!scaleBefore) {
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203 | sx = (data[0] < 0 ? -1 : 1) * Math.hypot(data[0], data[2]);
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204 | sy = (data[3] < 0 ? -1 : 1) * Math.hypot(data[1], data[3]);
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205 | transforms.push({ name: 'scale', data: [sx, sy] });
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206 | }
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207 | var angle = Math.min(Math.max(-1, data[0] / sx), 1),
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208 | rotate = [
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209 | mth.acos(angle, floatPrecision) *
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210 | ((scaleBefore ? 1 : sy) * data[1] < 0 ? -1 : 1),
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211 | ];
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212 |
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213 | if (rotate[0]) transforms.push({ name: 'rotate', data: rotate });
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214 |
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215 | if (rowsSum && colsSum)
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216 | transforms.push({
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217 | name: 'skewX',
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218 | data: [mth.atan(colsSum / (sx * sx), floatPrecision)],
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219 | });
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220 |
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221 | // rotate(a, cx, cy) can consume translate() within optional arguments cx, cy (rotation point)
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222 | if (rotate[0] && (data[4] || data[5])) {
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223 | transforms.shift();
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224 | var cos = data[0] / sx,
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225 | sin = data[1] / (scaleBefore ? sx : sy),
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226 | x = data[4] * (scaleBefore ? 1 : sy),
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227 | y = data[5] * (scaleBefore ? 1 : sx),
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228 | denom =
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229 | (Math.pow(1 - cos, 2) + Math.pow(sin, 2)) *
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230 | (scaleBefore ? 1 : sx * sy);
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231 | rotate.push(((1 - cos) * x - sin * y) / denom);
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232 | rotate.push(((1 - cos) * y + sin * x) / denom);
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233 | }
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234 |
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235 | // Too many transformations, return original matrix if it isn't just a scale/translate
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236 | } else if (data[1] || data[2]) {
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237 | return [transform];
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238 | }
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239 |
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240 | if ((scaleBefore && (sx != 1 || sy != 1)) || !transforms.length)
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241 | transforms.push({
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242 | name: 'scale',
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243 | data: sx == sy ? [sx] : [sx, sy],
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244 | });
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245 |
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246 | return transforms;
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247 | };
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248 |
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249 | /**
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250 | * Convert transform to the matrix data.
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251 | *
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252 | * @type {(transform: TransformItem) => Array<number> }
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253 | */
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254 | const transformToMatrix = (transform) => {
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255 | if (transform.name === 'matrix') {
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256 | return transform.data;
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257 | }
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258 | switch (transform.name) {
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259 | case 'translate':
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260 | // [1, 0, 0, 1, tx, ty]
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261 | return [1, 0, 0, 1, transform.data[0], transform.data[1] || 0];
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262 | case 'scale':
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263 | // [sx, 0, 0, sy, 0, 0]
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264 | return [
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265 | transform.data[0],
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266 | 0,
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267 | 0,
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268 | transform.data[1] || transform.data[0],
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269 | 0,
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270 | 0,
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271 | ];
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272 | case 'rotate':
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273 | // [cos(a), sin(a), -sin(a), cos(a), x, y]
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274 | var cos = mth.cos(transform.data[0]),
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275 | sin = mth.sin(transform.data[0]),
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276 | cx = transform.data[1] || 0,
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277 | cy = transform.data[2] || 0;
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278 | return [
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279 | cos,
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280 | sin,
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281 | -sin,
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282 | cos,
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283 | (1 - cos) * cx + sin * cy,
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284 | (1 - cos) * cy - sin * cx,
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285 | ];
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286 | case 'skewX':
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287 | // [1, 0, tan(a), 1, 0, 0]
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288 | return [1, 0, mth.tan(transform.data[0]), 1, 0, 0];
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289 | case 'skewY':
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290 | // [1, tan(a), 0, 1, 0, 0]
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291 | return [1, mth.tan(transform.data[0]), 0, 1, 0, 0];
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292 | default:
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293 | throw Error(`Unknown transform ${transform.name}`);
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294 | }
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295 | };
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296 |
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297 | /**
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298 | * Applies transformation to an arc. To do so, we represent ellipse as a matrix, multiply it
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299 | * by the transformation matrix and use a singular value decomposition to represent in a form
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300 | * rotate(θ)·scale(a b)·rotate(φ). This gives us new ellipse params a, b and θ.
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301 | * SVD is being done with the formulae provided by Wolffram|Alpha (svd {{m0, m2}, {m1, m3}})
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302 | *
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303 | * @type {(
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304 | * cursor: [x: number, y: number],
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305 | * arc: Array<number>,
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306 | * transform: Array<number>
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307 | * ) => Array<number>}
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308 | */
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309 | exports.transformArc = (cursor, arc, transform) => {
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310 | const x = arc[5] - cursor[0];
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311 | const y = arc[6] - cursor[1];
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312 | let a = arc[0];
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313 | let b = arc[1];
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314 | const rot = (arc[2] * Math.PI) / 180;
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315 | const cos = Math.cos(rot);
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316 | const sin = Math.sin(rot);
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317 | // skip if radius is 0
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318 | if (a > 0 && b > 0) {
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319 | let h =
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320 | Math.pow(x * cos + y * sin, 2) / (4 * a * a) +
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321 | Math.pow(y * cos - x * sin, 2) / (4 * b * b);
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322 | if (h > 1) {
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323 | h = Math.sqrt(h);
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324 | a *= h;
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325 | b *= h;
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326 | }
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327 | }
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328 | const ellipse = [a * cos, a * sin, -b * sin, b * cos, 0, 0];
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329 | const m = multiplyTransformMatrices(transform, ellipse);
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330 | // Decompose the new ellipse matrix
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331 | const lastCol = m[2] * m[2] + m[3] * m[3];
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332 | const squareSum = m[0] * m[0] + m[1] * m[1] + lastCol;
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333 | const root =
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334 | Math.hypot(m[0] - m[3], m[1] + m[2]) * Math.hypot(m[0] + m[3], m[1] - m[2]);
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335 |
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336 | if (!root) {
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337 | // circle
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338 | arc[0] = arc[1] = Math.sqrt(squareSum / 2);
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339 | arc[2] = 0;
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340 | } else {
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341 | const majorAxisSqr = (squareSum + root) / 2;
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342 | const minorAxisSqr = (squareSum - root) / 2;
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343 | const major = Math.abs(majorAxisSqr - lastCol) > 1e-6;
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344 | const sub = (major ? majorAxisSqr : minorAxisSqr) - lastCol;
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345 | const rowsSum = m[0] * m[2] + m[1] * m[3];
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346 | const term1 = m[0] * sub + m[2] * rowsSum;
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347 | const term2 = m[1] * sub + m[3] * rowsSum;
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348 | arc[0] = Math.sqrt(majorAxisSqr);
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349 | arc[1] = Math.sqrt(minorAxisSqr);
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350 | arc[2] =
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351 | (((major ? term2 < 0 : term1 > 0) ? -1 : 1) *
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352 | Math.acos((major ? term1 : term2) / Math.hypot(term1, term2)) *
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353 | 180) /
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354 | Math.PI;
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355 | }
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356 |
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357 | if (transform[0] < 0 !== transform[3] < 0) {
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358 | // Flip the sweep flag if coordinates are being flipped horizontally XOR vertically
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359 | arc[4] = 1 - arc[4];
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360 | }
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361 |
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362 | return arc;
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363 | };
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364 |
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365 | /**
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366 | * Multiply transformation matrices.
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367 | *
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368 | * @type {(a: Array<number>, b: Array<number>) => Array<number>}
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369 | */
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370 | const multiplyTransformMatrices = (a, b) => {
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371 | return [
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372 | a[0] * b[0] + a[2] * b[1],
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373 | a[1] * b[0] + a[3] * b[1],
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374 | a[0] * b[2] + a[2] * b[3],
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375 | a[1] * b[2] + a[3] * b[3],
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376 | a[0] * b[4] + a[2] * b[5] + a[4],
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377 | a[1] * b[4] + a[3] * b[5] + a[5],
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378 | ];
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379 | };
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