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989 lines
31 KiB
989 lines
31 KiB
2 years ago
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/* global a2c */
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'use strict';
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var rNumber = String.raw`[-+]?(?:\d*\.\d+|\d+\.?)(?:[eE][-+]?\d+)?\s*`,
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rCommaWsp = String.raw`(?:\s,?\s*|,\s*)`,
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rNumberCommaWsp = `(${rNumber})` + rCommaWsp,
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rFlagCommaWsp = `([01])${rCommaWsp}?`,
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rCoordinatePair = String.raw`(${rNumber})${rCommaWsp}?(${rNumber})`,
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rArcSeq = (rNumberCommaWsp + '?').repeat(2) + rNumberCommaWsp + rFlagCommaWsp.repeat(2) + rCoordinatePair;
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var regPathInstructions = /([MmLlHhVvCcSsQqTtAaZz])\s*/,
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regCoordinateSequence = new RegExp(rNumber, 'g'),
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regArcArgumentSequence = new RegExp(rArcSeq, 'g'),
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regNumericValues = /[-+]?(\d*\.\d+|\d+\.?)(?:[eE][-+]?\d+)?/,
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transform2js = require('./_transforms').transform2js,
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transformsMultiply = require('./_transforms').transformsMultiply,
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transformArc = require('./_transforms').transformArc,
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collections = require('./_collections.js'),
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referencesProps = collections.referencesProps,
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defaultStrokeWidth = collections.attrsGroupsDefaults.presentation['stroke-width'],
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cleanupOutData = require('../lib/svgo/tools').cleanupOutData,
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removeLeadingZero = require('../lib/svgo/tools').removeLeadingZero,
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prevCtrlPoint;
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/**
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* Convert path string to JS representation.
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*
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* @param {String} pathString 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.path2js = function(path) {
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if (path.pathJS) return path.pathJS;
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var paramsLength = { // Number of parameters of every path command
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H: 1, V: 1, M: 2, L: 2, T: 2, Q: 4, S: 4, C: 6, A: 7,
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h: 1, v: 1, m: 2, l: 2, t: 2, q: 4, s: 4, c: 6, a: 7
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},
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pathData = [], // JS representation of the path data
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instruction, // current instruction context
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startMoveto = false;
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// splitting path string into array like ['M', '10 50', 'L', '20 30']
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path.attr('d').value.split(regPathInstructions).forEach(function(data) {
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if (!data) return;
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if (!startMoveto) {
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if (data == 'M' || data == 'm') {
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startMoveto = true;
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} else return;
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}
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// instruction item
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if (regPathInstructions.test(data)) {
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instruction = data;
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// z - instruction w/o data
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if (instruction == 'Z' || instruction == 'z') {
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pathData.push({
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instruction: 'z'
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});
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}
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// data item
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} else {
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/* jshint boss: true */
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if (instruction == 'A' || instruction == 'a') {
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var newData = [];
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for (var args; (args = regArcArgumentSequence.exec(data));) {
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for (var i = 1; i < args.length; i++) {
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newData.push(args[i]);
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}
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}
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data = newData;
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} else {
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data = data.match(regCoordinateSequence);
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}
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if (!data) return;
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data = data.map(Number);
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// Subsequent moveto pairs of coordinates are threated as implicit lineto commands
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// http://www.w3.org/TR/SVG/paths.html#PathDataMovetoCommands
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if (instruction == 'M' || instruction == 'm') {
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pathData.push({
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instruction: pathData.length == 0 ? 'M' : instruction,
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data: data.splice(0, 2)
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});
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instruction = instruction == 'M' ? 'L' : 'l';
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}
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for (var pair = paramsLength[instruction]; data.length;) {
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pathData.push({
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instruction: instruction,
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data: data.splice(0, pair)
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});
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}
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}
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});
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// First moveto is actually absolute. Subsequent coordinates were separated above.
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if (pathData.length && pathData[0].instruction == 'm') {
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pathData[0].instruction = 'M';
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}
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path.pathJS = pathData;
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return pathData;
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};
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/**
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* Convert relative Path data to absolute.
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*
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* @param {Array} data input data
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* @return {Array} output data
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*/
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var relative2absolute = exports.relative2absolute = function(data) {
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var currentPoint = [0, 0],
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subpathPoint = [0, 0],
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i;
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return data.map(function(item) {
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var instruction = item.instruction,
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itemData = item.data && item.data.slice();
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if (instruction == 'M') {
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set(currentPoint, itemData);
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set(subpathPoint, itemData);
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} else if ('mlcsqt'.indexOf(instruction) > -1) {
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for (i = 0; i < itemData.length; i++) {
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itemData[i] += currentPoint[i % 2];
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}
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set(currentPoint, itemData);
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if (instruction == 'm') {
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set(subpathPoint, itemData);
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}
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} else if (instruction == 'a') {
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itemData[5] += currentPoint[0];
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itemData[6] += currentPoint[1];
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set(currentPoint, itemData);
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} else if (instruction == 'h') {
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itemData[0] += currentPoint[0];
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currentPoint[0] = itemData[0];
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} else if (instruction == 'v') {
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itemData[0] += currentPoint[1];
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currentPoint[1] = itemData[0];
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} else if ('MZLCSQTA'.indexOf(instruction) > -1) {
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set(currentPoint, itemData);
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} else if (instruction == 'H') {
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currentPoint[0] = itemData[0];
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} else if (instruction == 'V') {
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currentPoint[1] = itemData[0];
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} else if (instruction == 'z') {
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set(currentPoint, subpathPoint);
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}
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return instruction == 'z' ?
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{ instruction: 'z' } :
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{
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instruction: instruction.toUpperCase(),
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data: itemData
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};
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});
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};
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/**
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* Apply transformation(s) to the Path data.
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*
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* @param {Object} elem current element
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* @param {Array} path input path data
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* @param {Object} params whether to apply transforms to stroked lines and transform precision (used for stroke width)
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* @return {Array} output path data
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*/
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exports.applyTransforms = function(elem, path, params) {
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// if there are no 'stroke' attr and references to other objects such as
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// gradiends or clip-path which are also subjects to transform.
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if (!elem.hasAttr('transform') || !elem.attr('transform').value ||
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elem.someAttr(function(attr) {
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return ~referencesProps.indexOf(attr.name) && ~attr.value.indexOf('url(');
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}))
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return path;
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var matrix = transformsMultiply(transform2js(elem.attr('transform').value)),
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stroke = elem.computedAttr('stroke'),
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id = elem.computedAttr('id'),
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transformPrecision = params.transformPrecision,
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newPoint, scale;
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if (stroke && stroke != 'none') {
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if (!params.applyTransformsStroked ||
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(matrix.data[0] != matrix.data[3] || matrix.data[1] != -matrix.data[2]) &&
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(matrix.data[0] != -matrix.data[3] || matrix.data[1] != matrix.data[2]))
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return path;
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// "stroke-width" should be inside the part with ID, otherwise it can be overrided in <use>
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if (id) {
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var idElem = elem,
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hasStrokeWidth = false;
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do {
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if (idElem.hasAttr('stroke-width')) hasStrokeWidth = true;
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} while (!idElem.hasAttr('id', id) && !hasStrokeWidth && (idElem = idElem.parentNode));
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if (!hasStrokeWidth) return path;
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}
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scale = +Math.sqrt(matrix.data[0] * matrix.data[0] + matrix.data[1] * matrix.data[1]).toFixed(transformPrecision);
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if (scale !== 1) {
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var strokeWidth = elem.computedAttr('stroke-width') || defaultStrokeWidth;
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if (!elem.hasAttr('vector-effect') || elem.attr('vector-effect').value !== 'non-scaling-stroke') {
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if (elem.hasAttr('stroke-width')) {
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elem.attrs['stroke-width'].value = elem.attrs['stroke-width'].value.trim()
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.replace(regNumericValues, function(num) {
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return removeLeadingZero(num * scale);
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});
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} else {
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elem.addAttr({
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name: 'stroke-width',
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prefix: '',
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local: 'stroke-width',
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value: strokeWidth.replace(regNumericValues, function(num) {
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return removeLeadingZero(num * scale);
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})
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});
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}
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}
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}
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} else if (id) { // Stroke and stroke-width can be redefined with <use>
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return path;
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}
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path.forEach(function(pathItem) {
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if (pathItem.data) {
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// h -> l
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if (pathItem.instruction === 'h') {
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pathItem.instruction = 'l';
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pathItem.data[1] = 0;
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// v -> l
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} else if (pathItem.instruction === 'v') {
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pathItem.instruction = 'l';
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pathItem.data[1] = pathItem.data[0];
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pathItem.data[0] = 0;
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}
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// if there is a translate() transform
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if (pathItem.instruction === 'M' &&
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(matrix.data[4] !== 0 ||
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matrix.data[5] !== 0)
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) {
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// then apply it only to the first absoluted M
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newPoint = transformPoint(matrix.data, pathItem.data[0], pathItem.data[1]);
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set(pathItem.data, newPoint);
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set(pathItem.coords, newPoint);
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// clear translate() data from transform matrix
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matrix.data[4] = 0;
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matrix.data[5] = 0;
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} else {
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if (pathItem.instruction == 'a') {
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transformArc(pathItem.data, matrix.data);
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// reduce number of digits in rotation angle
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if (Math.abs(pathItem.data[2]) > 80) {
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var a = pathItem.data[0],
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rotation = pathItem.data[2];
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pathItem.data[0] = pathItem.data[1];
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pathItem.data[1] = a;
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pathItem.data[2] = rotation + (rotation > 0 ? -90 : 90);
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}
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newPoint = transformPoint(matrix.data, pathItem.data[5], pathItem.data[6]);
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pathItem.data[5] = newPoint[0];
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pathItem.data[6] = newPoint[1];
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} else {
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for (var i = 0; i < pathItem.data.length; i += 2) {
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newPoint = transformPoint(matrix.data, pathItem.data[i], pathItem.data[i + 1]);
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pathItem.data[i] = newPoint[0];
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pathItem.data[i + 1] = newPoint[1];
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}
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}
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pathItem.coords[0] = pathItem.base[0] + pathItem.data[pathItem.data.length - 2];
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pathItem.coords[1] = pathItem.base[1] + pathItem.data[pathItem.data.length - 1];
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}
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}
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});
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// remove transform attr
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elem.removeAttr('transform');
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return path;
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};
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/**
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* Apply transform 3x3 matrix to x-y point.
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*
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* @param {Array} matrix transform 3x3 matrix
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* @param {Array} point x-y point
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* @return {Array} point with new coordinates
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*/
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function transformPoint(matrix, x, y) {
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return [
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matrix[0] * x + matrix[2] * y + matrix[4],
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matrix[1] * x + matrix[3] * y + matrix[5]
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];
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}
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/**
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* Compute Cubic Bézie bounding box.
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*
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* @see http://processingjs.nihongoresources.com/bezierinfo/
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*
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* @param {Float} xa
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* @param {Float} ya
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* @param {Float} xb
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* @param {Float} yb
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* @param {Float} xc
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* @param {Float} yc
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* @param {Float} xd
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* @param {Float} yd
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*
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* @return {Object}
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*/
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exports.computeCubicBoundingBox = function(xa, ya, xb, yb, xc, yc, xd, yd) {
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var minx = Number.POSITIVE_INFINITY,
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miny = Number.POSITIVE_INFINITY,
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maxx = Number.NEGATIVE_INFINITY,
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maxy = Number.NEGATIVE_INFINITY,
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ts,
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t,
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x,
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y,
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i;
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// X
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if (xa < minx) { minx = xa; }
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if (xa > maxx) { maxx = xa; }
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if (xd < minx) { minx= xd; }
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if (xd > maxx) { maxx = xd; }
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|
|
ts = computeCubicFirstDerivativeRoots(xa, xb, xc, xd);
|
||
|
|
|
||
|
|
for (i = 0; i < ts.length; i++) {
|
||
|
|
|
||
|
|
t = ts[i];
|
||
|
|
|
||
|
|
if (t >= 0 && t <= 1) {
|
||
|
|
x = computeCubicBaseValue(t, xa, xb, xc, xd);
|
||
|
|
// y = computeCubicBaseValue(t, ya, yb, yc, yd);
|
||
|
|
|
||
|
|
if (x < minx) { minx = x; }
|
||
|
|
if (x > maxx) { maxx = x; }
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
// Y
|
||
|
|
if (ya < miny) { miny = ya; }
|
||
|
|
if (ya > maxy) { maxy = ya; }
|
||
|
|
if (yd < miny) { miny = yd; }
|
||
|
|
if (yd > maxy) { maxy = yd; }
|
||
|
|
|
||
|
|
ts = computeCubicFirstDerivativeRoots(ya, yb, yc, yd);
|
||
|
|
|
||
|
|
for (i = 0; i < ts.length; i++) {
|
||
|
|
|
||
|
|
t = ts[i];
|
||
|
|
|
||
|
|
if (t >= 0 && t <= 1) {
|
||
|
|
// x = computeCubicBaseValue(t, xa, xb, xc, xd);
|
||
|
|
y = computeCubicBaseValue(t, ya, yb, yc, yd);
|
||
|
|
|
||
|
|
if (y < miny) { miny = y; }
|
||
|
|
if (y > maxy) { maxy = y; }
|
||
|
|
}
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
return {
|
||
|
|
minx: minx,
|
||
|
|
miny: miny,
|
||
|
|
maxx: maxx,
|
||
|
|
maxy: maxy
|
||
|
|
};
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
// compute the value for the cubic bezier function at time=t
|
||
|
|
function computeCubicBaseValue(t, a, b, c, d) {
|
||
|
|
|
||
|
|
var mt = 1 - t;
|
||
|
|
|
||
|
|
return mt * mt * mt * a + 3 * mt * mt * t * b + 3 * mt * t * t * c + t * t * t * d;
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
// compute the value for the first derivative of the cubic bezier function at time=t
|
||
|
|
function computeCubicFirstDerivativeRoots(a, b, c, d) {
|
||
|
|
|
||
|
|
var result = [-1, -1],
|
||
|
|
tl = -a + 2 * b - c,
|
||
|
|
tr = -Math.sqrt(-a * (c - d) + b * b - b * (c + d) + c * c),
|
||
|
|
dn = -a + 3 * b - 3 * c + d;
|
||
|
|
|
||
|
|
if (dn !== 0) {
|
||
|
|
result[0] = (tl + tr) / dn;
|
||
|
|
result[1] = (tl - tr) / dn;
|
||
|
|
}
|
||
|
|
|
||
|
|
return result;
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Compute Quadratic Bézier bounding box.
|
||
|
|
*
|
||
|
|
* @see http://processingjs.nihongoresources.com/bezierinfo/
|
||
|
|
*
|
||
|
|
* @param {Float} xa
|
||
|
|
* @param {Float} ya
|
||
|
|
* @param {Float} xb
|
||
|
|
* @param {Float} yb
|
||
|
|
* @param {Float} xc
|
||
|
|
* @param {Float} yc
|
||
|
|
*
|
||
|
|
* @return {Object}
|
||
|
|
*/
|
||
|
|
exports.computeQuadraticBoundingBox = function(xa, ya, xb, yb, xc, yc) {
|
||
|
|
|
||
|
|
var minx = Number.POSITIVE_INFINITY,
|
||
|
|
miny = Number.POSITIVE_INFINITY,
|
||
|
|
maxx = Number.NEGATIVE_INFINITY,
|
||
|
|
maxy = Number.NEGATIVE_INFINITY,
|
||
|
|
t,
|
||
|
|
x,
|
||
|
|
y;
|
||
|
|
|
||
|
|
// X
|
||
|
|
if (xa < minx) { minx = xa; }
|
||
|
|
if (xa > maxx) { maxx = xa; }
|
||
|
|
if (xc < minx) { minx = xc; }
|
||
|
|
if (xc > maxx) { maxx = xc; }
|
||
|
|
|
||
|
|
t = computeQuadraticFirstDerivativeRoot(xa, xb, xc);
|
||
|
|
|
||
|
|
if (t >= 0 && t <= 1) {
|
||
|
|
x = computeQuadraticBaseValue(t, xa, xb, xc);
|
||
|
|
// y = computeQuadraticBaseValue(t, ya, yb, yc);
|
||
|
|
|
||
|
|
if (x < minx) { minx = x; }
|
||
|
|
if (x > maxx) { maxx = x; }
|
||
|
|
}
|
||
|
|
|
||
|
|
// Y
|
||
|
|
if (ya < miny) { miny = ya; }
|
||
|
|
if (ya > maxy) { maxy = ya; }
|
||
|
|
if (yc < miny) { miny = yc; }
|
||
|
|
if (yc > maxy) { maxy = yc; }
|
||
|
|
|
||
|
|
t = computeQuadraticFirstDerivativeRoot(ya, yb, yc);
|
||
|
|
|
||
|
|
if (t >= 0 && t <=1 ) {
|
||
|
|
// x = computeQuadraticBaseValue(t, xa, xb, xc);
|
||
|
|
y = computeQuadraticBaseValue(t, ya, yb, yc);
|
||
|
|
|
||
|
|
if (y < miny) { miny = y; }
|
||
|
|
if (y > maxy) { maxy = y ; }
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
return {
|
||
|
|
minx: minx,
|
||
|
|
miny: miny,
|
||
|
|
maxx: maxx,
|
||
|
|
maxy: maxy
|
||
|
|
};
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
// compute the value for the quadratic bezier function at time=t
|
||
|
|
function computeQuadraticBaseValue(t, a, b, c) {
|
||
|
|
|
||
|
|
var mt = 1 - t;
|
||
|
|
|
||
|
|
return mt * mt * a + 2 * mt * t * b + t * t * c;
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
// compute the value for the first derivative of the quadratic bezier function at time=t
|
||
|
|
function computeQuadraticFirstDerivativeRoot(a, b, c) {
|
||
|
|
|
||
|
|
var t = -1,
|
||
|
|
denominator = a - 2 * b + c;
|
||
|
|
|
||
|
|
if (denominator !== 0) {
|
||
|
|
t = (a - b) / denominator;
|
||
|
|
}
|
||
|
|
|
||
|
|
return t;
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Convert path array to string.
|
||
|
|
*
|
||
|
|
* @param {Array} path input path data
|
||
|
|
* @param {Object} params plugin params
|
||
|
|
* @return {String} output path string
|
||
|
|
*/
|
||
|
|
exports.js2path = function(path, data, params) {
|
||
|
|
|
||
|
|
path.pathJS = data;
|
||
|
|
|
||
|
|
if (params.collapseRepeated) {
|
||
|
|
data = collapseRepeated(data);
|
||
|
|
}
|
||
|
|
|
||
|
|
path.attr('d').value = data.reduce(function(pathString, item) {
|
||
|
|
var strData = '';
|
||
|
|
if (item.data) {
|
||
|
|
strData = cleanupOutData(item.data, params, item.instruction);
|
||
|
|
}
|
||
|
|
return pathString += item.instruction + strData;
|
||
|
|
}, '');
|
||
|
|
|
||
|
|
};
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Collapse repeated instructions data
|
||
|
|
*
|
||
|
|
* @param {Array} path input path data
|
||
|
|
* @return {Array} output path data
|
||
|
|
*/
|
||
|
|
function collapseRepeated(data) {
|
||
|
|
|
||
|
|
var prev,
|
||
|
|
prevIndex;
|
||
|
|
|
||
|
|
// copy an array and modifieds item to keep original data untouched
|
||
|
|
data = data.reduce(function(newPath, item) {
|
||
|
|
if (
|
||
|
|
prev && item.data &&
|
||
|
|
item.instruction == prev.instruction
|
||
|
|
) {
|
||
|
|
// concat previous data with current
|
||
|
|
if (item.instruction != 'M') {
|
||
|
|
prev = newPath[prevIndex] = {
|
||
|
|
instruction: prev.instruction,
|
||
|
|
data: prev.data.concat(item.data),
|
||
|
|
coords: item.coords,
|
||
|
|
base: prev.base
|
||
|
|
};
|
||
|
|
} else {
|
||
|
|
prev.data = item.data;
|
||
|
|
prev.coords = item.coords;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
newPath.push(item);
|
||
|
|
prev = item;
|
||
|
|
prevIndex = newPath.length - 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
return newPath;
|
||
|
|
}, []);
|
||
|
|
|
||
|
|
return data;
|
||
|
|
|
||
|
|
}
|
||
|
|
|
||
|
|
function set(dest, source) {
|
||
|
|
dest[0] = source[source.length - 2];
|
||
|
|
dest[1] = source[source.length - 1];
|
||
|
|
return dest;
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Checks if two paths have an intersection by checking convex hulls
|
||
|
|
* collision using Gilbert-Johnson-Keerthi distance algorithm
|
||
|
|
* http://entropyinteractive.com/2011/04/gjk-algorithm/
|
||
|
|
*
|
||
|
|
* @param {Array} path1 JS path representation
|
||
|
|
* @param {Array} path2 JS path representation
|
||
|
|
* @return {Boolean}
|
||
|
|
*/
|
||
|
|
exports.intersects = function(path1, path2) {
|
||
|
|
if (path1.length < 3 || path2.length < 3) return false; // nothing to fill
|
||
|
|
|
||
|
|
// Collect points of every subpath.
|
||
|
|
var points1 = relative2absolute(path1).reduce(gatherPoints, []),
|
||
|
|
points2 = relative2absolute(path2).reduce(gatherPoints, []);
|
||
|
|
|
||
|
|
// Axis-aligned bounding box check.
|
||
|
|
if (points1.maxX <= points2.minX || points2.maxX <= points1.minX ||
|
||
|
|
points1.maxY <= points2.minY || points2.maxY <= points1.minY ||
|
||
|
|
points1.every(function (set1) {
|
||
|
|
return points2.every(function (set2) {
|
||
|
|
return set1[set1.maxX][0] <= set2[set2.minX][0] ||
|
||
|
|
set2[set2.maxX][0] <= set1[set1.minX][0] ||
|
||
|
|
set1[set1.maxY][1] <= set2[set2.minY][1] ||
|
||
|
|
set2[set2.maxY][1] <= set1[set1.minY][1];
|
||
|
|
});
|
||
|
|
})
|
||
|
|
) return false;
|
||
|
|
|
||
|
|
// Get a convex hull from points of each subpath. Has the most complexity O(n·log n).
|
||
|
|
var hullNest1 = points1.map(convexHull),
|
||
|
|
hullNest2 = points2.map(convexHull);
|
||
|
|
|
||
|
|
// Check intersection of every subpath of the first path with every subpath of the second.
|
||
|
|
return hullNest1.some(function(hull1) {
|
||
|
|
if (hull1.length < 3) return false;
|
||
|
|
|
||
|
|
return hullNest2.some(function(hull2) {
|
||
|
|
if (hull2.length < 3) return false;
|
||
|
|
|
||
|
|
var simplex = [getSupport(hull1, hull2, [1, 0])], // create the initial simplex
|
||
|
|
direction = minus(simplex[0]); // set the direction to point towards the origin
|
||
|
|
|
||
|
|
var iterations = 1e4; // infinite loop protection, 10 000 iterations is more than enough
|
||
|
|
while (true) {
|
||
|
|
if (iterations-- == 0) {
|
||
|
|
console.error('Error: infinite loop while processing mergePaths plugin.');
|
||
|
|
return true; // true is the safe value that means “do nothing with paths”
|
||
|
|
}
|
||
|
|
// add a new point
|
||
|
|
simplex.push(getSupport(hull1, hull2, direction));
|
||
|
|
// see if the new point was on the correct side of the origin
|
||
|
|
if (dot(direction, simplex[simplex.length - 1]) <= 0) return false;
|
||
|
|
// process the simplex
|
||
|
|
if (processSimplex(simplex, direction)) return true;
|
||
|
|
}
|
||
|
|
});
|
||
|
|
});
|
||
|
|
|
||
|
|
function getSupport(a, b, direction) {
|
||
|
|
return sub(supportPoint(a, direction), supportPoint(b, minus(direction)));
|
||
|
|
}
|
||
|
|
|
||
|
|
// Computes farthest polygon point in particular direction.
|
||
|
|
// Thanks to knowledge of min/max x and y coordinates we can choose a quadrant to search in.
|
||
|
|
// Since we're working on convex hull, the dot product is increasing until we find the farthest point.
|
||
|
|
function supportPoint(polygon, direction) {
|
||
|
|
var index = direction[1] >= 0 ?
|
||
|
|
direction[0] < 0 ? polygon.maxY : polygon.maxX :
|
||
|
|
direction[0] < 0 ? polygon.minX : polygon.minY,
|
||
|
|
max = -Infinity,
|
||
|
|
value;
|
||
|
|
while ((value = dot(polygon[index], direction)) > max) {
|
||
|
|
max = value;
|
||
|
|
index = ++index % polygon.length;
|
||
|
|
}
|
||
|
|
return polygon[(index || polygon.length) - 1];
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
function processSimplex(simplex, direction) {
|
||
|
|
/* jshint -W004 */
|
||
|
|
|
||
|
|
// we only need to handle to 1-simplex and 2-simplex
|
||
|
|
if (simplex.length == 2) { // 1-simplex
|
||
|
|
var a = simplex[1],
|
||
|
|
b = simplex[0],
|
||
|
|
AO = minus(simplex[1]),
|
||
|
|
AB = sub(b, a);
|
||
|
|
// AO is in the same direction as AB
|
||
|
|
if (dot(AO, AB) > 0) {
|
||
|
|
// get the vector perpendicular to AB facing O
|
||
|
|
set(direction, orth(AB, a));
|
||
|
|
} else {
|
||
|
|
set(direction, AO);
|
||
|
|
// only A remains in the simplex
|
||
|
|
simplex.shift();
|
||
|
|
}
|
||
|
|
} else { // 2-simplex
|
||
|
|
var a = simplex[2], // [a, b, c] = simplex
|
||
|
|
b = simplex[1],
|
||
|
|
c = simplex[0],
|
||
|
|
AB = sub(b, a),
|
||
|
|
AC = sub(c, a),
|
||
|
|
AO = minus(a),
|
||
|
|
ACB = orth(AB, AC), // the vector perpendicular to AB facing away from C
|
||
|
|
ABC = orth(AC, AB); // the vector perpendicular to AC facing away from B
|
||
|
|
|
||
|
|
if (dot(ACB, AO) > 0) {
|
||
|
|
if (dot(AB, AO) > 0) { // region 4
|
||
|
|
set(direction, ACB);
|
||
|
|
simplex.shift(); // simplex = [b, a]
|
||
|
|
} else { // region 5
|
||
|
|
set(direction, AO);
|
||
|
|
simplex.splice(0, 2); // simplex = [a]
|
||
|
|
}
|
||
|
|
} else if (dot(ABC, AO) > 0) {
|
||
|
|
if (dot(AC, AO) > 0) { // region 6
|
||
|
|
set(direction, ABC);
|
||
|
|
simplex.splice(1, 1); // simplex = [c, a]
|
||
|
|
} else { // region 5 (again)
|
||
|
|
set(direction, AO);
|
||
|
|
simplex.splice(0, 2); // simplex = [a]
|
||
|
|
}
|
||
|
|
} else // region 7
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
function minus(v) {
|
||
|
|
return [-v[0], -v[1]];
|
||
|
|
}
|
||
|
|
|
||
|
|
function sub(v1, v2) {
|
||
|
|
return [v1[0] - v2[0], v1[1] - v2[1]];
|
||
|
|
}
|
||
|
|
|
||
|
|
function dot(v1, v2) {
|
||
|
|
return v1[0] * v2[0] + v1[1] * v2[1];
|
||
|
|
}
|
||
|
|
|
||
|
|
function orth(v, from) {
|
||
|
|
var o = [-v[1], v[0]];
|
||
|
|
return dot(o, minus(from)) < 0 ? minus(o) : o;
|
||
|
|
}
|
||
|
|
|
||
|
|
function gatherPoints(points, item, index, path) {
|
||
|
|
|
||
|
|
var subPath = points.length && points[points.length - 1],
|
||
|
|
prev = index && path[index - 1],
|
||
|
|
basePoint = subPath.length && subPath[subPath.length - 1],
|
||
|
|
data = item.data,
|
||
|
|
ctrlPoint = basePoint;
|
||
|
|
|
||
|
|
switch (item.instruction) {
|
||
|
|
case 'M':
|
||
|
|
points.push(subPath = []);
|
||
|
|
break;
|
||
|
|
case 'H':
|
||
|
|
addPoint(subPath, [data[0], basePoint[1]]);
|
||
|
|
break;
|
||
|
|
case 'V':
|
||
|
|
addPoint(subPath, [basePoint[0], data[0]]);
|
||
|
|
break;
|
||
|
|
case 'Q':
|
||
|
|
addPoint(subPath, data.slice(0, 2));
|
||
|
|
prevCtrlPoint = [data[2] - data[0], data[3] - data[1]]; // Save control point for shorthand
|
||
|
|
break;
|
||
|
|
case 'T':
|
||
|
|
if (prev.instruction == 'Q' || prev.instruction == 'T') {
|
||
|
|
ctrlPoint = [basePoint[0] + prevCtrlPoint[0], basePoint[1] + prevCtrlPoint[1]];
|
||
|
|
addPoint(subPath, ctrlPoint);
|
||
|
|
prevCtrlPoint = [data[0] - ctrlPoint[0], data[1] - ctrlPoint[1]];
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
case 'C':
|
||
|
|
// Approximate quibic Bezier curve with middle points between control points
|
||
|
|
addPoint(subPath, [.5 * (basePoint[0] + data[0]), .5 * (basePoint[1] + data[1])]);
|
||
|
|
addPoint(subPath, [.5 * (data[0] + data[2]), .5 * (data[1] + data[3])]);
|
||
|
|
addPoint(subPath, [.5 * (data[2] + data[4]), .5 * (data[3] + data[5])]);
|
||
|
|
prevCtrlPoint = [data[4] - data[2], data[5] - data[3]]; // Save control point for shorthand
|
||
|
|
break;
|
||
|
|
case 'S':
|
||
|
|
if (prev.instruction == 'C' || prev.instruction == 'S') {
|
||
|
|
addPoint(subPath, [basePoint[0] + .5 * prevCtrlPoint[0], basePoint[1] + .5 * prevCtrlPoint[1]]);
|
||
|
|
ctrlPoint = [basePoint[0] + prevCtrlPoint[0], basePoint[1] + prevCtrlPoint[1]];
|
||
|
|
}
|
||
|
|
addPoint(subPath, [.5 * (ctrlPoint[0] + data[0]), .5 * (ctrlPoint[1]+ data[1])]);
|
||
|
|
addPoint(subPath, [.5 * (data[0] + data[2]), .5 * (data[1] + data[3])]);
|
||
|
|
prevCtrlPoint = [data[2] - data[0], data[3] - data[1]];
|
||
|
|
break;
|
||
|
|
case 'A':
|
||
|
|
// Convert the arc to bezier curves and use the same approximation
|
||
|
|
var curves = a2c.apply(0, basePoint.concat(data));
|
||
|
|
for (var cData; (cData = curves.splice(0,6).map(toAbsolute)).length;) {
|
||
|
|
addPoint(subPath, [.5 * (basePoint[0] + cData[0]), .5 * (basePoint[1] + cData[1])]);
|
||
|
|
addPoint(subPath, [.5 * (cData[0] + cData[2]), .5 * (cData[1] + cData[3])]);
|
||
|
|
addPoint(subPath, [.5 * (cData[2] + cData[4]), .5 * (cData[3] + cData[5])]);
|
||
|
|
if (curves.length) addPoint(subPath, basePoint = cData.slice(-2));
|
||
|
|
}
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
// Save final command coordinates
|
||
|
|
if (data && data.length >= 2) addPoint(subPath, data.slice(-2));
|
||
|
|
return points;
|
||
|
|
|
||
|
|
function toAbsolute(n, i) { return n + basePoint[i % 2] }
|
||
|
|
|
||
|
|
// Writes data about the extreme points on each axle
|
||
|
|
function addPoint(path, point) {
|
||
|
|
if (!path.length || point[1] > path[path.maxY][1]) {
|
||
|
|
path.maxY = path.length;
|
||
|
|
points.maxY = points.length ? Math.max(point[1], points.maxY) : point[1];
|
||
|
|
}
|
||
|
|
if (!path.length || point[0] > path[path.maxX][0]) {
|
||
|
|
path.maxX = path.length;
|
||
|
|
points.maxX = points.length ? Math.max(point[0], points.maxX) : point[0];
|
||
|
|
}
|
||
|
|
if (!path.length || point[1] < path[path.minY][1]) {
|
||
|
|
path.minY = path.length;
|
||
|
|
points.minY = points.length ? Math.min(point[1], points.minY) : point[1];
|
||
|
|
}
|
||
|
|
if (!path.length || point[0] < path[path.minX][0]) {
|
||
|
|
path.minX = path.length;
|
||
|
|
points.minX = points.length ? Math.min(point[0], points.minX) : point[0];
|
||
|
|
}
|
||
|
|
path.push(point);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/**
|
||
|
|
* Forms a convex hull from set of points of every subpath using monotone chain convex hull algorithm.
|
||
|
|
* http://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain
|
||
|
|
*
|
||
|
|
* @param points An array of [X, Y] coordinates
|
||
|
|
*/
|
||
|
|
function convexHull(points) {
|
||
|
|
/* jshint -W004 */
|
||
|
|
|
||
|
|
points.sort(function(a, b) {
|
||
|
|
return a[0] == b[0] ? a[1] - b[1] : a[0] - b[0];
|
||
|
|
});
|
||
|
|
|
||
|
|
var lower = [],
|
||
|
|
minY = 0,
|
||
|
|
bottom = 0;
|
||
|
|
for (var i = 0; i < points.length; i++) {
|
||
|
|
while (lower.length >= 2 && cross(lower[lower.length - 2], lower[lower.length - 1], points[i]) <= 0) {
|
||
|
|
lower.pop();
|
||
|
|
}
|
||
|
|
if (points[i][1] < points[minY][1]) {
|
||
|
|
minY = i;
|
||
|
|
bottom = lower.length;
|
||
|
|
}
|
||
|
|
lower.push(points[i]);
|
||
|
|
}
|
||
|
|
|
||
|
|
var upper = [],
|
||
|
|
maxY = points.length - 1,
|
||
|
|
top = 0;
|
||
|
|
for (var i = points.length; i--;) {
|
||
|
|
while (upper.length >= 2 && cross(upper[upper.length - 2], upper[upper.length - 1], points[i]) <= 0) {
|
||
|
|
upper.pop();
|
||
|
|
}
|
||
|
|
if (points[i][1] > points[maxY][1]) {
|
||
|
|
maxY = i;
|
||
|
|
top = upper.length;
|
||
|
|
}
|
||
|
|
upper.push(points[i]);
|
||
|
|
}
|
||
|
|
|
||
|
|
// last points are equal to starting points of the other part
|
||
|
|
upper.pop();
|
||
|
|
lower.pop();
|
||
|
|
|
||
|
|
var hull = lower.concat(upper);
|
||
|
|
|
||
|
|
hull.minX = 0; // by sorting
|
||
|
|
hull.maxX = lower.length;
|
||
|
|
hull.minY = bottom;
|
||
|
|
hull.maxY = (lower.length + top) % hull.length;
|
||
|
|
|
||
|
|
return hull;
|
||
|
|
}
|
||
|
|
|
||
|
|
function cross(o, a, b) {
|
||
|
|
return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0]);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* Based on code from Snap.svg (Apache 2 license). http://snapsvg.io/
|
||
|
|
* Thanks to Dmitry Baranovskiy for his great work!
|
||
|
|
*/
|
||
|
|
|
||
|
|
// jshint ignore: start
|
||
|
|
function a2c(x1, y1, rx, ry, angle, large_arc_flag, sweep_flag, x2, y2, recursive) {
|
||
|
|
// for more information of where this Math came from visit:
|
||
|
|
// http://www.w3.org/TR/SVG11/implnote.html#ArcImplementationNotes
|
||
|
|
var _120 = Math.PI * 120 / 180,
|
||
|
|
rad = Math.PI / 180 * (+angle || 0),
|
||
|
|
res = [],
|
||
|
|
rotateX = function(x, y, rad) { return x * Math.cos(rad) - y * Math.sin(rad) },
|
||
|
|
rotateY = function(x, y, rad) { return x * Math.sin(rad) + y * Math.cos(rad) };
|
||
|
|
if (!recursive) {
|
||
|
|
x1 = rotateX(x1, y1, -rad);
|
||
|
|
y1 = rotateY(x1, y1, -rad);
|
||
|
|
x2 = rotateX(x2, y2, -rad);
|
||
|
|
y2 = rotateY(x2, y2, -rad);
|
||
|
|
var x = (x1 - x2) / 2,
|
||
|
|
y = (y1 - y2) / 2;
|
||
|
|
var h = (x * x) / (rx * rx) + (y * y) / (ry * ry);
|
||
|
|
if (h > 1) {
|
||
|
|
h = Math.sqrt(h);
|
||
|
|
rx = h * rx;
|
||
|
|
ry = h * ry;
|
||
|
|
}
|
||
|
|
var rx2 = rx * rx,
|
||
|
|
ry2 = ry * ry,
|
||
|
|
k = (large_arc_flag == sweep_flag ? -1 : 1) *
|
||
|
|
Math.sqrt(Math.abs((rx2 * ry2 - rx2 * y * y - ry2 * x * x) / (rx2 * y * y + ry2 * x * x))),
|
||
|
|
cx = k * rx * y / ry + (x1 + x2) / 2,
|
||
|
|
cy = k * -ry * x / rx + (y1 + y2) / 2,
|
||
|
|
f1 = Math.asin(((y1 - cy) / ry).toFixed(9)),
|
||
|
|
f2 = Math.asin(((y2 - cy) / ry).toFixed(9));
|
||
|
|
|
||
|
|
f1 = x1 < cx ? Math.PI - f1 : f1;
|
||
|
|
f2 = x2 < cx ? Math.PI - f2 : f2;
|
||
|
|
f1 < 0 && (f1 = Math.PI * 2 + f1);
|
||
|
|
f2 < 0 && (f2 = Math.PI * 2 + f2);
|
||
|
|
if (sweep_flag && f1 > f2) {
|
||
|
|
f1 = f1 - Math.PI * 2;
|
||
|
|
}
|
||
|
|
if (!sweep_flag && f2 > f1) {
|
||
|
|
f2 = f2 - Math.PI * 2;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
f1 = recursive[0];
|
||
|
|
f2 = recursive[1];
|
||
|
|
cx = recursive[2];
|
||
|
|
cy = recursive[3];
|
||
|
|
}
|
||
|
|
var df = f2 - f1;
|
||
|
|
if (Math.abs(df) > _120) {
|
||
|
|
var f2old = f2,
|
||
|
|
x2old = x2,
|
||
|
|
y2old = y2;
|
||
|
|
f2 = f1 + _120 * (sweep_flag && f2 > f1 ? 1 : -1);
|
||
|
|
x2 = cx + rx * Math.cos(f2);
|
||
|
|
y2 = cy + ry * Math.sin(f2);
|
||
|
|
res = a2c(x2, y2, rx, ry, angle, 0, sweep_flag, x2old, y2old, [f2, f2old, cx, cy]);
|
||
|
|
}
|
||
|
|
df = f2 - f1;
|
||
|
|
var c1 = Math.cos(f1),
|
||
|
|
s1 = Math.sin(f1),
|
||
|
|
c2 = Math.cos(f2),
|
||
|
|
s2 = Math.sin(f2),
|
||
|
|
t = Math.tan(df / 4),
|
||
|
|
hx = 4 / 3 * rx * t,
|
||
|
|
hy = 4 / 3 * ry * t,
|
||
|
|
m = [
|
||
|
|
- hx * s1, hy * c1,
|
||
|
|
x2 + hx * s2 - x1, y2 - hy * c2 - y1,
|
||
|
|
x2 - x1, y2 - y1
|
||
|
|
];
|
||
|
|
if (recursive) {
|
||
|
|
return m.concat(res);
|
||
|
|
} else {
|
||
|
|
res = m.concat(res);
|
||
|
|
var newres = [];
|
||
|
|
for (var i = 0, n = res.length; i < n; i++) {
|
||
|
|
newres[i] = i % 2 ? rotateY(res[i - 1], res[i], rad) : rotateX(res[i], res[i + 1], rad);
|
||
|
|
}
|
||
|
|
return newres;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
// jshint ignore: end
|