380 lines
10 KiB
JavaScript
380 lines
10 KiB
JavaScript
'use strict';
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const regTransformTypes = /matrix|translate|scale|rotate|skewX|skewY/;
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const regTransformSplit =
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/\s*(matrix|translate|scale|rotate|skewX|skewY)\s*\(\s*(.+?)\s*\)[\s,]*/;
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const regNumericValues = /[-+]?(?:\d*\.\d+|\d+\.?)(?:[eE][-+]?\d+)?/g;
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/**
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* @typedef {{ name: string, data: Array<number> }} TransformItem
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*/
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/**
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* Convert transform string to JS representation.
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*
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* @type {(transformString: string) => Array<TransformItem>}
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*/
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exports.transform2js = (transformString) => {
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// JS representation of the transform data
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/**
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* @type {Array<TransformItem>}
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*/
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const transforms = [];
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// current transform context
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/**
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* @type {null | TransformItem}
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*/
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let current = null;
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// split value into ['', 'translate', '10 50', '', 'scale', '2', '', 'rotate', '-45', '']
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for (const item of transformString.split(regTransformSplit)) {
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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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current = { name: item, data: [] };
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transforms.push(current);
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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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// eslint-disable-next-line no-cond-assign
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while ((num = regNumericValues.exec(item))) {
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num = Number(num);
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if (current != null) {
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current.data.push(num);
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}
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}
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}
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}
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}
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// return empty array if broken transform (no data)
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return current == null || current.data.length == 0 ? [] : 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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* @type {(transforms: Array<TransformItem>) => TransformItem}
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*/
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exports.transformsMultiply = (transforms) => {
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// convert transforms objects to the matrices
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const matrixData = transforms.map((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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const matrixTransform = {
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name: 'matrix',
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data:
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matrixData.length > 0 ? matrixData.reduce(multiplyTransformMatrices) : [],
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};
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return matrixTransform;
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};
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/**
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* math utilities in radians.
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*/
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const mth = {
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/**
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* @type {(deg: number) => number}
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*/
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rad: (deg) => {
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return (deg * Math.PI) / 180;
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},
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/**
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* @type {(rad: number) => number}
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*/
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deg: (rad) => {
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return (rad * 180) / Math.PI;
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},
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/**
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* @type {(deg: number) => number}
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*/
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cos: (deg) => {
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return Math.cos(mth.rad(deg));
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},
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/**
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* @type {(val: number, floatPrecision: number) => number}
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*/
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acos: (val, floatPrecision) => {
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return Number(mth.deg(Math.acos(val)).toFixed(floatPrecision));
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},
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/**
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* @type {(deg: number) => number}
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*/
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sin: (deg) => {
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return Math.sin(mth.rad(deg));
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},
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/**
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* @type {(val: number, floatPrecision: number) => number}
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*/
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asin: (val, floatPrecision) => {
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return Number(mth.deg(Math.asin(val)).toFixed(floatPrecision));
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},
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/**
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* @type {(deg: number) => number}
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*/
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tan: (deg) => {
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return Math.tan(mth.rad(deg));
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},
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/**
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* @type {(val: number, floatPrecision: number) => number}
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*/
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atan: (val, floatPrecision) => {
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return Number(mth.deg(Math.atan(val)).toFixed(floatPrecision));
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},
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};
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/**
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* @typedef {{
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* convertToShorts: boolean,
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* floatPrecision: number,
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* transformPrecision: number,
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* matrixToTransform: boolean,
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* shortTranslate: boolean,
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* shortScale: boolean,
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* shortRotate: boolean,
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* removeUseless: boolean,
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* collapseIntoOne: boolean,
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* leadingZero: boolean,
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* negativeExtraSpace: boolean,
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* }} TransformParams
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*/
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/**
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* Decompose matrix into simple transforms. See
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* https://frederic-wang.fr/decomposition-of-2d-transform-matrices.html
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*
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* @type {(transform: TransformItem, params: TransformParams) => Array<TransformItem>}
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*/
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exports.matrixToTransform = (transform, params) => {
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let floatPrecision = params.floatPrecision;
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let data = transform.data;
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let transforms = [];
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let sx = Number(
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Math.hypot(data[0], data[1]).toFixed(params.transformPrecision)
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);
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let sy = Number(
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((data[0] * data[3] - data[1] * data[2]) / sx).toFixed(
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params.transformPrecision
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)
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);
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let colsSum = data[0] * data[2] + data[1] * data[3];
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let rowsSum = data[0] * data[1] + data[2] * data[3];
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let scaleBefore = rowsSum != 0 || 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({
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name: 'translate',
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data: data.slice(4, data[5] ? 6 : 5),
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});
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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({
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name: 'skewX',
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data: [mth.atan(data[2] / sy, floatPrecision)],
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});
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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({
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name: 'skewY',
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data: [mth.atan(data[1] / data[0], floatPrecision)],
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});
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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.hypot(data[0], data[2]);
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sy = (data[3] < 0 ? -1 : 1) * Math.hypot(data[1], data[3]);
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transforms.push({ name: 'scale', data: [sx, sy] });
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}
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var angle = Math.min(Math.max(-1, data[0] / sx), 1),
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rotate = [
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mth.acos(angle, floatPrecision) *
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((scaleBefore ? 1 : sy) * data[1] < 0 ? -1 : 1),
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];
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if (rotate[0]) transforms.push({ name: 'rotate', data: rotate });
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if (rowsSum && colsSum)
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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 ? 1 : sy),
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y = data[5] * (scaleBefore ? 1 : sx),
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denom =
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(Math.pow(1 - cos, 2) + Math.pow(sin, 2)) *
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(scaleBefore ? 1 : 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)
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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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* @type {(transform: TransformItem) => Array<number> }
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*/
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const transformToMatrix = (transform) => {
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if (transform.name === 'matrix') {
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return transform.data;
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}
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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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return [1, 0, 0, 1, transform.data[0], transform.data[1] || 0];
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case 'scale':
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// [sx, 0, 0, sy, 0, 0]
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return [
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transform.data[0],
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0,
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0,
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transform.data[1] || transform.data[0],
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0,
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0,
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];
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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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return [
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cos,
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sin,
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-sin,
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cos,
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(1 - cos) * cx + sin * cy,
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(1 - cos) * cy - sin * cx,
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];
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case 'skewX':
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// [1, 0, tan(a), 1, 0, 0]
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return [1, 0, mth.tan(transform.data[0]), 1, 0, 0];
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case 'skewY':
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// [1, tan(a), 0, 1, 0, 0]
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return [1, mth.tan(transform.data[0]), 0, 1, 0, 0];
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default:
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throw Error(`Unknown transform ${transform.name}`);
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}
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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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* @type {(
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* cursor: [x: number, y: number],
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* arc: Array<number>,
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* transform: Array<number>
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* ) => Array<number>}
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*/
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exports.transformArc = (cursor, arc, transform) => {
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const x = arc[5] - cursor[0];
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const y = arc[6] - cursor[1];
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let a = arc[0];
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let b = arc[1];
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const rot = (arc[2] * Math.PI) / 180;
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const cos = Math.cos(rot);
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const sin = Math.sin(rot);
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// skip if radius is 0
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if (a > 0 && b > 0) {
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let h =
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Math.pow(x * cos + y * sin, 2) / (4 * a * a) +
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Math.pow(y * cos - x * 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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}
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const ellipse = [a * cos, a * sin, -b * sin, b * cos, 0, 0];
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const m = multiplyTransformMatrices(transform, ellipse);
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// Decompose the new ellipse matrix
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const lastCol = m[2] * m[2] + m[3] * m[3];
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const squareSum = m[0] * m[0] + m[1] * m[1] + lastCol;
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const root =
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Math.hypot(m[0] - m[3], m[1] + m[2]) * Math.hypot(m[0] + m[3], m[1] - m[2]);
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if (!root) {
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// 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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const majorAxisSqr = (squareSum + root) / 2;
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const minorAxisSqr = (squareSum - root) / 2;
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const major = Math.abs(majorAxisSqr - lastCol) > 1e-6;
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const sub = (major ? majorAxisSqr : minorAxisSqr) - lastCol;
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const rowsSum = m[0] * m[2] + m[1] * m[3];
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const term1 = m[0] * sub + m[2] * rowsSum;
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const 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] =
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(((major ? term2 < 0 : term1 > 0) ? -1 : 1) *
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Math.acos((major ? term1 : term2) / Math.hypot(term1, term2)) *
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180) /
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Math.PI;
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}
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if (transform[0] < 0 !== transform[3] < 0) {
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// Flip the sweep flag if coordinates are being flipped horizontally XOR vertically
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arc[4] = 1 - arc[4];
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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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* @type {(a: Array<number>, b: Array<number>) => Array<number>}
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*/
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const 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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