972 lines
30 KiB
JavaScript
972 lines
30 KiB
JavaScript
'use strict';
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exports.type = 'perItem';
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exports.active = true;
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exports.description = 'optimizes path data: writes in shorter form, applies transformations';
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exports.params = {
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applyTransforms: true,
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applyTransformsStroked: true,
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makeArcs: {
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threshold: 2.5, // coefficient of rounding error
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tolerance: 0.5 // percentage of radius
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},
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straightCurves: true,
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lineShorthands: true,
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curveSmoothShorthands: true,
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floatPrecision: 3,
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transformPrecision: 5,
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removeUseless: true,
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collapseRepeated: true,
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utilizeAbsolute: true,
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leadingZero: true,
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negativeExtraSpace: true,
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noSpaceAfterFlags: true,
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forceAbsolutePath: false
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};
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var pathElems = require('./_collections.js').pathElems,
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path2js = require('./_path.js').path2js,
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js2path = require('./_path.js').js2path,
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applyTransforms = require('./_path.js').applyTransforms,
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cleanupOutData = require('../lib/svgo/tools').cleanupOutData,
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roundData,
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precision,
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error,
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arcThreshold,
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arcTolerance,
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hasMarkerMid,
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hasStrokeLinecap;
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/**
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* Convert absolute Path to relative,
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* collapse repeated instructions,
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* detect and convert Lineto shorthands,
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* remove useless instructions like "l0,0",
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* trim useless delimiters and leading zeros,
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* decrease accuracy of floating-point numbers.
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*
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* @see http://www.w3.org/TR/SVG/paths.html#PathData
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*
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* @param {Object} item current iteration item
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* @param {Object} params plugin params
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* @return {Boolean} if false, item will be filtered out
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*
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* @author Kir Belevich
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*/
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exports.fn = function(item, params) {
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if (item.isElem(pathElems) && item.hasAttr('d')) {
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precision = params.floatPrecision;
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error = precision !== false ? +Math.pow(.1, precision).toFixed(precision) : 1e-2;
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roundData = precision > 0 && precision < 20 ? strongRound : round;
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if (params.makeArcs) {
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arcThreshold = params.makeArcs.threshold;
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arcTolerance = params.makeArcs.tolerance;
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}
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hasMarkerMid = item.hasAttr('marker-mid');
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var stroke = item.computedAttr('stroke'),
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strokeLinecap = item.computedAttr('stroke');
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hasStrokeLinecap = stroke && stroke != 'none' && strokeLinecap && strokeLinecap != 'butt';
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var data = path2js(item);
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// TODO: get rid of functions returns
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if (data.length) {
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convertToRelative(data);
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if (params.applyTransforms) {
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data = applyTransforms(item, data, params);
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}
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data = filters(data, params);
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if (params.utilizeAbsolute) {
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data = convertToMixed(data, params);
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}
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js2path(item, data, params);
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}
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}
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};
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/**
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* Convert absolute path data coordinates to relative.
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*
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* @param {Array} path input path data
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* @param {Object} params plugin params
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* @return {Array} output path data
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*/
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function convertToRelative(path) {
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var point = [0, 0],
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subpathPoint = [0, 0],
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baseItem;
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path.forEach(function(item, index) {
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var instruction = item.instruction,
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data = item.data;
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// data !== !z
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if (data) {
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// already relative
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// recalculate current point
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if ('mcslqta'.indexOf(instruction) > -1) {
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point[0] += data[data.length - 2];
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point[1] += data[data.length - 1];
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if (instruction === 'm') {
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subpathPoint[0] = point[0];
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subpathPoint[1] = point[1];
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baseItem = item;
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}
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} else if (instruction === 'h') {
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point[0] += data[0];
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} else if (instruction === 'v') {
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point[1] += data[0];
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}
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// convert absolute path data coordinates to relative
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// if "M" was not transformed from "m"
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// M → m
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if (instruction === 'M') {
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if (index > 0) instruction = 'm';
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data[0] -= point[0];
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data[1] -= point[1];
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subpathPoint[0] = point[0] += data[0];
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subpathPoint[1] = point[1] += data[1];
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baseItem = item;
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}
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// L → l
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// T → t
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else if ('LT'.indexOf(instruction) > -1) {
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instruction = instruction.toLowerCase();
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// x y
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// 0 1
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data[0] -= point[0];
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data[1] -= point[1];
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point[0] += data[0];
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point[1] += data[1];
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// C → c
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} else if (instruction === 'C') {
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instruction = 'c';
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// x1 y1 x2 y2 x y
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// 0 1 2 3 4 5
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data[0] -= point[0];
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data[1] -= point[1];
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data[2] -= point[0];
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data[3] -= point[1];
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data[4] -= point[0];
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data[5] -= point[1];
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point[0] += data[4];
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point[1] += data[5];
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// S → s
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// Q → q
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} else if ('SQ'.indexOf(instruction) > -1) {
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instruction = instruction.toLowerCase();
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// x1 y1 x y
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// 0 1 2 3
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data[0] -= point[0];
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data[1] -= point[1];
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data[2] -= point[0];
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data[3] -= point[1];
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point[0] += data[2];
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point[1] += data[3];
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// A → a
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} else if (instruction === 'A') {
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instruction = 'a';
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// rx ry x-axis-rotation large-arc-flag sweep-flag x y
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// 0 1 2 3 4 5 6
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data[5] -= point[0];
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data[6] -= point[1];
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point[0] += data[5];
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point[1] += data[6];
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// H → h
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} else if (instruction === 'H') {
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instruction = 'h';
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data[0] -= point[0];
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point[0] += data[0];
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// V → v
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} else if (instruction === 'V') {
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instruction = 'v';
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data[0] -= point[1];
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point[1] += data[0];
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}
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item.instruction = instruction;
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item.data = data;
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// store absolute coordinates for later use
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item.coords = point.slice(-2);
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}
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// !data === z, reset current point
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else if (instruction == 'z') {
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if (baseItem) {
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item.coords = baseItem.coords;
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}
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point[0] = subpathPoint[0];
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point[1] = subpathPoint[1];
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}
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item.base = index > 0 ? path[index - 1].coords : [0, 0];
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});
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return path;
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}
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/**
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* Main filters loop.
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*
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* @param {Array} path input path data
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* @param {Object} params plugin params
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* @return {Array} output path data
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*/
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function filters(path, params) {
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var stringify = data2Path.bind(null, params),
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relSubpoint = [0, 0],
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pathBase = [0, 0],
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prev = {};
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path = path.filter(function(item, index, path) {
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var instruction = item.instruction,
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data = item.data,
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next = path[index + 1];
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if (data) {
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var sdata = data,
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circle;
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if (instruction === 's') {
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sdata = [0, 0].concat(data);
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if ('cs'.indexOf(prev.instruction) > -1) {
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var pdata = prev.data,
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n = pdata.length;
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// (-x, -y) of the prev tangent point relative to the current point
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sdata[0] = pdata[n - 2] - pdata[n - 4];
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sdata[1] = pdata[n - 1] - pdata[n - 3];
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}
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}
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// convert curves to arcs if possible
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if (
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params.makeArcs &&
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(instruction == 'c' || instruction == 's') &&
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isConvex(sdata) &&
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(circle = findCircle(sdata))
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) {
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var r = roundData([circle.radius])[0],
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angle = findArcAngle(sdata, circle),
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sweep = sdata[5] * sdata[0] - sdata[4] * sdata[1] > 0 ? 1 : 0,
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arc = {
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instruction: 'a',
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data: [r, r, 0, 0, sweep, sdata[4], sdata[5]],
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coords: item.coords.slice(),
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base: item.base
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},
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output = [arc],
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// relative coordinates to adjust the found circle
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relCenter = [circle.center[0] - sdata[4], circle.center[1] - sdata[5]],
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relCircle = { center: relCenter, radius: circle.radius },
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arcCurves = [item],
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hasPrev = 0,
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suffix = '',
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nextLonghand;
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if (
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prev.instruction == 'c' && isConvex(prev.data) && isArcPrev(prev.data, circle) ||
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prev.instruction == 'a' && prev.sdata && isArcPrev(prev.sdata, circle)
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) {
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arcCurves.unshift(prev);
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arc.base = prev.base;
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arc.data[5] = arc.coords[0] - arc.base[0];
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arc.data[6] = arc.coords[1] - arc.base[1];
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var prevData = prev.instruction == 'a' ? prev.sdata : prev.data;
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var prevAngle = findArcAngle(prevData,
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{
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center: [prevData[4] + circle.center[0], prevData[5] + circle.center[1]],
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radius: circle.radius
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}
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);
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angle += prevAngle;
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if (angle > Math.PI) arc.data[3] = 1;
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hasPrev = 1;
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}
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// check if next curves are fitting the arc
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for (var j = index; (next = path[++j]) && ~'cs'.indexOf(next.instruction);) {
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var nextData = next.data;
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if (next.instruction == 's') {
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nextLonghand = makeLonghand({instruction: 's', data: next.data.slice() },
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path[j - 1].data);
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nextData = nextLonghand.data;
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nextLonghand.data = nextData.slice(0, 2);
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suffix = stringify([nextLonghand]);
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}
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if (isConvex(nextData) && isArc(nextData, relCircle)) {
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angle += findArcAngle(nextData, relCircle);
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if (angle - 2 * Math.PI > 1e-3) break; // more than 360°
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if (angle > Math.PI) arc.data[3] = 1;
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arcCurves.push(next);
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if (2 * Math.PI - angle > 1e-3) { // less than 360°
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arc.coords = next.coords;
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arc.data[5] = arc.coords[0] - arc.base[0];
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arc.data[6] = arc.coords[1] - arc.base[1];
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} else {
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// full circle, make a half-circle arc and add a second one
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arc.data[5] = 2 * (relCircle.center[0] - nextData[4]);
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arc.data[6] = 2 * (relCircle.center[1] - nextData[5]);
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arc.coords = [arc.base[0] + arc.data[5], arc.base[1] + arc.data[6]];
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arc = {
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instruction: 'a',
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data: [r, r, 0, 0, sweep,
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next.coords[0] - arc.coords[0], next.coords[1] - arc.coords[1]],
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coords: next.coords,
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base: arc.coords
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};
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output.push(arc);
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j++;
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break;
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}
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relCenter[0] -= nextData[4];
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relCenter[1] -= nextData[5];
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} else break;
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}
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if ((stringify(output) + suffix).length < stringify(arcCurves).length) {
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if (path[j] && path[j].instruction == 's') {
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makeLonghand(path[j], path[j - 1].data);
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}
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if (hasPrev) {
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var prevArc = output.shift();
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roundData(prevArc.data);
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relSubpoint[0] += prevArc.data[5] - prev.data[prev.data.length - 2];
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relSubpoint[1] += prevArc.data[6] - prev.data[prev.data.length - 1];
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prev.instruction = 'a';
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prev.data = prevArc.data;
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item.base = prev.coords = prevArc.coords;
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}
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arc = output.shift();
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if (arcCurves.length == 1) {
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item.sdata = sdata.slice(); // preserve curve data for future checks
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} else if (arcCurves.length - 1 - hasPrev > 0) {
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// filter out consumed next items
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path.splice.apply(path, [index + 1, arcCurves.length - 1 - hasPrev].concat(output));
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}
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if (!arc) return false;
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instruction = 'a';
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data = arc.data;
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item.coords = arc.coords;
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}
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}
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// Rounding relative coordinates, taking in account accummulating error
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// to get closer to absolute coordinates. Sum of rounded value remains same:
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// l .25 3 .25 2 .25 3 .25 2 -> l .3 3 .2 2 .3 3 .2 2
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if (precision !== false) {
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if ('mltqsc'.indexOf(instruction) > -1) {
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for (var i = data.length; i--;) {
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data[i] += item.base[i % 2] - relSubpoint[i % 2];
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}
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} else if (instruction == 'h') {
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data[0] += item.base[0] - relSubpoint[0];
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} else if (instruction == 'v') {
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data[0] += item.base[1] - relSubpoint[1];
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} else if (instruction == 'a') {
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data[5] += item.base[0] - relSubpoint[0];
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data[6] += item.base[1] - relSubpoint[1];
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}
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roundData(data);
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if (instruction == 'h') relSubpoint[0] += data[0];
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else if (instruction == 'v') relSubpoint[1] += data[0];
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else {
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relSubpoint[0] += data[data.length - 2];
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relSubpoint[1] += data[data.length - 1];
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}
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roundData(relSubpoint);
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if (instruction.toLowerCase() == 'm') {
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pathBase[0] = relSubpoint[0];
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pathBase[1] = relSubpoint[1];
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}
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}
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// convert straight curves into lines segments
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if (params.straightCurves) {
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if (
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instruction === 'c' &&
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isCurveStraightLine(data) ||
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instruction === 's' &&
|
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isCurveStraightLine(sdata)
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) {
|
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if (next && next.instruction == 's')
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makeLonghand(next, data); // fix up next curve
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instruction = 'l';
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data = data.slice(-2);
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}
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else if (
|
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instruction === 'q' &&
|
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isCurveStraightLine(data)
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) {
|
||
if (next && next.instruction == 't')
|
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makeLonghand(next, data); // fix up next curve
|
||
instruction = 'l';
|
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data = data.slice(-2);
|
||
}
|
||
|
||
else if (
|
||
instruction === 't' &&
|
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prev.instruction !== 'q' &&
|
||
prev.instruction !== 't'
|
||
) {
|
||
instruction = 'l';
|
||
data = data.slice(-2);
|
||
}
|
||
|
||
else if (
|
||
instruction === 'a' &&
|
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(data[0] === 0 || data[1] === 0)
|
||
) {
|
||
instruction = 'l';
|
||
data = data.slice(-2);
|
||
}
|
||
}
|
||
|
||
// horizontal and vertical line shorthands
|
||
// l 50 0 → h 50
|
||
// l 0 50 → v 50
|
||
if (
|
||
params.lineShorthands &&
|
||
instruction === 'l'
|
||
) {
|
||
if (data[1] === 0) {
|
||
instruction = 'h';
|
||
data.pop();
|
||
} else if (data[0] === 0) {
|
||
instruction = 'v';
|
||
data.shift();
|
||
}
|
||
}
|
||
|
||
// collapse repeated commands
|
||
// h 20 h 30 -> h 50
|
||
if (
|
||
params.collapseRepeated &&
|
||
!hasMarkerMid &&
|
||
('mhv'.indexOf(instruction) > -1) &&
|
||
prev.instruction &&
|
||
instruction == prev.instruction.toLowerCase() &&
|
||
(
|
||
(instruction != 'h' && instruction != 'v') ||
|
||
(prev.data[0] >= 0) == (item.data[0] >= 0)
|
||
)) {
|
||
prev.data[0] += data[0];
|
||
if (instruction != 'h' && instruction != 'v') {
|
||
prev.data[1] += data[1];
|
||
}
|
||
prev.coords = item.coords;
|
||
path[index] = prev;
|
||
return false;
|
||
}
|
||
|
||
// convert curves into smooth shorthands
|
||
if (params.curveSmoothShorthands && prev.instruction) {
|
||
|
||
// curveto
|
||
if (instruction === 'c') {
|
||
|
||
// c + c → c + s
|
||
if (
|
||
prev.instruction === 'c' &&
|
||
data[0] === -(prev.data[2] - prev.data[4]) &&
|
||
data[1] === -(prev.data[3] - prev.data[5])
|
||
) {
|
||
instruction = 's';
|
||
data = data.slice(2);
|
||
}
|
||
|
||
// s + c → s + s
|
||
else if (
|
||
prev.instruction === 's' &&
|
||
data[0] === -(prev.data[0] - prev.data[2]) &&
|
||
data[1] === -(prev.data[1] - prev.data[3])
|
||
) {
|
||
instruction = 's';
|
||
data = data.slice(2);
|
||
}
|
||
|
||
// [^cs] + c → [^cs] + s
|
||
else if (
|
||
'cs'.indexOf(prev.instruction) === -1 &&
|
||
data[0] === 0 &&
|
||
data[1] === 0
|
||
) {
|
||
instruction = 's';
|
||
data = data.slice(2);
|
||
}
|
||
|
||
}
|
||
|
||
// quadratic Bézier curveto
|
||
else if (instruction === 'q') {
|
||
|
||
// q + q → q + t
|
||
if (
|
||
prev.instruction === 'q' &&
|
||
data[0] === (prev.data[2] - prev.data[0]) &&
|
||
data[1] === (prev.data[3] - prev.data[1])
|
||
) {
|
||
instruction = 't';
|
||
data = data.slice(2);
|
||
}
|
||
|
||
// t + q → t + t
|
||
else if (
|
||
prev.instruction === 't' &&
|
||
data[2] === prev.data[0] &&
|
||
data[3] === prev.data[1]
|
||
) {
|
||
instruction = 't';
|
||
data = data.slice(2);
|
||
}
|
||
|
||
}
|
||
|
||
}
|
||
|
||
// remove useless non-first path segments
|
||
if (params.removeUseless && !hasStrokeLinecap) {
|
||
|
||
// l 0,0 / h 0 / v 0 / q 0,0 0,0 / t 0,0 / c 0,0 0,0 0,0 / s 0,0 0,0
|
||
if (
|
||
(
|
||
'lhvqtcs'.indexOf(instruction) > -1
|
||
) &&
|
||
data.every(function(i) { return i === 0; })
|
||
) {
|
||
path[index] = prev;
|
||
return false;
|
||
}
|
||
|
||
// a 25,25 -30 0,1 0,0
|
||
if (
|
||
instruction === 'a' &&
|
||
data[5] === 0 &&
|
||
data[6] === 0
|
||
) {
|
||
path[index] = prev;
|
||
return false;
|
||
}
|
||
|
||
}
|
||
|
||
item.instruction = instruction;
|
||
item.data = data;
|
||
|
||
prev = item;
|
||
|
||
} else {
|
||
|
||
// z resets coordinates
|
||
relSubpoint[0] = pathBase[0];
|
||
relSubpoint[1] = pathBase[1];
|
||
if (prev.instruction == 'z') return false;
|
||
prev = item;
|
||
|
||
}
|
||
|
||
return true;
|
||
|
||
});
|
||
|
||
return path;
|
||
|
||
}
|
||
|
||
/**
|
||
* Writes data in shortest form using absolute or relative coordinates.
|
||
*
|
||
* @param {Array} data input path data
|
||
* @return {Boolean} output
|
||
*/
|
||
function convertToMixed(path, params) {
|
||
|
||
var prev = path[0];
|
||
|
||
path = path.filter(function(item, index) {
|
||
|
||
if (index == 0) return true;
|
||
if (!item.data) {
|
||
prev = item;
|
||
return true;
|
||
}
|
||
|
||
var instruction = item.instruction,
|
||
data = item.data,
|
||
adata = data && data.slice(0);
|
||
|
||
if ('mltqsc'.indexOf(instruction) > -1) {
|
||
for (var i = adata.length; i--;) {
|
||
adata[i] += item.base[i % 2];
|
||
}
|
||
} else if (instruction == 'h') {
|
||
adata[0] += item.base[0];
|
||
} else if (instruction == 'v') {
|
||
adata[0] += item.base[1];
|
||
} else if (instruction == 'a') {
|
||
adata[5] += item.base[0];
|
||
adata[6] += item.base[1];
|
||
}
|
||
|
||
roundData(adata);
|
||
|
||
var absoluteDataStr = cleanupOutData(adata, params),
|
||
relativeDataStr = cleanupOutData(data, params);
|
||
|
||
// Convert to absolute coordinates if it's shorter or forceAbsolutePath is true.
|
||
// v-20 -> V0
|
||
// Don't convert if it fits following previous instruction.
|
||
// l20 30-10-50 instead of l20 30L20 30
|
||
if (
|
||
params.forceAbsolutePath || (
|
||
absoluteDataStr.length < relativeDataStr.length &&
|
||
!(
|
||
params.negativeExtraSpace &&
|
||
instruction == prev.instruction &&
|
||
prev.instruction.charCodeAt(0) > 96 &&
|
||
absoluteDataStr.length == relativeDataStr.length - 1 &&
|
||
(data[0] < 0 || /^0\./.test(data[0]) && prev.data[prev.data.length - 1] % 1)
|
||
))
|
||
) {
|
||
item.instruction = instruction.toUpperCase();
|
||
item.data = adata;
|
||
}
|
||
|
||
prev = item;
|
||
|
||
return true;
|
||
|
||
});
|
||
|
||
return path;
|
||
|
||
}
|
||
|
||
/**
|
||
* Checks if curve is convex. Control points of such a curve must form
|
||
* a convex quadrilateral with diagonals crosspoint inside of it.
|
||
*
|
||
* @param {Array} data input path data
|
||
* @return {Boolean} output
|
||
*/
|
||
function isConvex(data) {
|
||
|
||
var center = getIntersection([0, 0, data[2], data[3], data[0], data[1], data[4], data[5]]);
|
||
|
||
return center &&
|
||
(data[2] < center[0] == center[0] < 0) &&
|
||
(data[3] < center[1] == center[1] < 0) &&
|
||
(data[4] < center[0] == center[0] < data[0]) &&
|
||
(data[5] < center[1] == center[1] < data[1]);
|
||
|
||
}
|
||
|
||
/**
|
||
* Computes lines equations by two points and returns their intersection point.
|
||
*
|
||
* @param {Array} coords 8 numbers for 4 pairs of coordinates (x,y)
|
||
* @return {Array|undefined} output coordinate of lines' crosspoint
|
||
*/
|
||
function getIntersection(coords) {
|
||
|
||
// Prev line equation parameters.
|
||
var a1 = coords[1] - coords[3], // y1 - y2
|
||
b1 = coords[2] - coords[0], // x2 - x1
|
||
c1 = coords[0] * coords[3] - coords[2] * coords[1], // x1 * y2 - x2 * y1
|
||
|
||
// Next line equation parameters
|
||
a2 = coords[5] - coords[7], // y1 - y2
|
||
b2 = coords[6] - coords[4], // x2 - x1
|
||
c2 = coords[4] * coords[7] - coords[5] * coords[6], // x1 * y2 - x2 * y1
|
||
denom = (a1 * b2 - a2 * b1);
|
||
|
||
if (!denom) return; // parallel lines havn't an intersection
|
||
|
||
var cross = [
|
||
(b1 * c2 - b2 * c1) / denom,
|
||
(a1 * c2 - a2 * c1) / -denom
|
||
];
|
||
if (
|
||
!isNaN(cross[0]) && !isNaN(cross[1]) &&
|
||
isFinite(cross[0]) && isFinite(cross[1])
|
||
) {
|
||
return cross;
|
||
}
|
||
|
||
}
|
||
|
||
/**
|
||
* Decrease accuracy of floating-point numbers
|
||
* in path data keeping a specified number of decimals.
|
||
* Smart rounds values like 2.3491 to 2.35 instead of 2.349.
|
||
* Doesn't apply "smartness" if the number precision fits already.
|
||
*
|
||
* @param {Array} data input data array
|
||
* @return {Array} output data array
|
||
*/
|
||
function strongRound(data) {
|
||
for (var i = data.length; i-- > 0;) {
|
||
if (data[i].toFixed(precision) != data[i]) {
|
||
var rounded = +data[i].toFixed(precision - 1);
|
||
data[i] = +Math.abs(rounded - data[i]).toFixed(precision + 1) >= error ?
|
||
+data[i].toFixed(precision) :
|
||
rounded;
|
||
}
|
||
}
|
||
return data;
|
||
}
|
||
|
||
/**
|
||
* Simple rounding function if precision is 0.
|
||
*
|
||
* @param {Array} data input data array
|
||
* @return {Array} output data array
|
||
*/
|
||
function round(data) {
|
||
for (var i = data.length; i-- > 0;) {
|
||
data[i] = Math.round(data[i]);
|
||
}
|
||
return data;
|
||
}
|
||
|
||
/**
|
||
* Checks if a curve is a straight line by measuring distance
|
||
* from middle points to the line formed by end points.
|
||
*
|
||
* @param {Array} xs array of curve points x-coordinates
|
||
* @param {Array} ys array of curve points y-coordinates
|
||
* @return {Boolean}
|
||
*/
|
||
|
||
function isCurveStraightLine(data) {
|
||
|
||
// Get line equation a·x + b·y + c = 0 coefficients a, b (c = 0) by start and end points.
|
||
var i = data.length - 2,
|
||
a = -data[i + 1], // y1 − y2 (y1 = 0)
|
||
b = data[i], // x2 − x1 (x1 = 0)
|
||
d = 1 / (a * a + b * b); // same part for all points
|
||
|
||
if (i <= 1 || !isFinite(d)) return false; // curve that ends at start point isn't the case
|
||
|
||
// Distance from point (x0, y0) to the line is sqrt((c − a·x0 − b·y0)² / (a² + b²))
|
||
while ((i -= 2) >= 0) {
|
||
if (Math.sqrt(Math.pow(a * data[i] + b * data[i + 1], 2) * d) > error)
|
||
return false;
|
||
}
|
||
|
||
return true;
|
||
|
||
}
|
||
|
||
/**
|
||
* Converts next curve from shorthand to full form using the current curve data.
|
||
*
|
||
* @param {Object} item curve to convert
|
||
* @param {Array} data current curve data
|
||
*/
|
||
|
||
function makeLonghand(item, data) {
|
||
switch (item.instruction) {
|
||
case 's': item.instruction = 'c'; break;
|
||
case 't': item.instruction = 'q'; break;
|
||
}
|
||
item.data.unshift(data[data.length - 2] - data[data.length - 4], data[data.length - 1] - data[data.length - 3]);
|
||
return item;
|
||
}
|
||
|
||
/**
|
||
* Returns distance between two points
|
||
*
|
||
* @param {Array} point1 first point coordinates
|
||
* @param {Array} point2 second point coordinates
|
||
* @return {Number} distance
|
||
*/
|
||
|
||
function getDistance(point1, point2) {
|
||
return Math.hypot(point1[0] - point2[0], point1[1] - point2[1]);
|
||
}
|
||
|
||
/**
|
||
* Returns coordinates of the curve point corresponding to the certain t
|
||
* a·(1 - t)³·p1 + b·(1 - t)²·t·p2 + c·(1 - t)·t²·p3 + d·t³·p4,
|
||
* where pN are control points and p1 is zero due to relative coordinates.
|
||
*
|
||
* @param {Array} curve array of curve points coordinates
|
||
* @param {Number} t parametric position from 0 to 1
|
||
* @return {Array} Point coordinates
|
||
*/
|
||
|
||
function getCubicBezierPoint(curve, t) {
|
||
var sqrT = t * t,
|
||
cubT = sqrT * t,
|
||
mt = 1 - t,
|
||
sqrMt = mt * mt;
|
||
|
||
return [
|
||
3 * sqrMt * t * curve[0] + 3 * mt * sqrT * curve[2] + cubT * curve[4],
|
||
3 * sqrMt * t * curve[1] + 3 * mt * sqrT * curve[3] + cubT * curve[5]
|
||
];
|
||
}
|
||
|
||
/**
|
||
* Finds circle by 3 points of the curve and checks if the curve fits the found circle.
|
||
*
|
||
* @param {Array} curve
|
||
* @return {Object|undefined} circle
|
||
*/
|
||
|
||
function findCircle(curve) {
|
||
var midPoint = getCubicBezierPoint(curve, 1/2),
|
||
m1 = [midPoint[0] / 2, midPoint[1] / 2],
|
||
m2 = [(midPoint[0] + curve[4]) / 2, (midPoint[1] + curve[5]) / 2],
|
||
center = getIntersection([
|
||
m1[0], m1[1],
|
||
m1[0] + m1[1], m1[1] - m1[0],
|
||
m2[0], m2[1],
|
||
m2[0] + (m2[1] - midPoint[1]), m2[1] - (m2[0] - midPoint[0])
|
||
]),
|
||
radius = center && getDistance([0, 0], center),
|
||
tolerance = Math.min(arcThreshold * error, arcTolerance * radius / 100);
|
||
|
||
if (center && radius < 1e15 &&
|
||
[1/4, 3/4].every(function(point) {
|
||
return Math.abs(getDistance(getCubicBezierPoint(curve, point), center) - radius) <= tolerance;
|
||
}))
|
||
return { center: center, radius: radius};
|
||
}
|
||
|
||
/**
|
||
* Checks if a curve fits the given circle.
|
||
*
|
||
* @param {Object} circle
|
||
* @param {Array} curve
|
||
* @return {Boolean}
|
||
*/
|
||
|
||
function isArc(curve, circle) {
|
||
var tolerance = Math.min(arcThreshold * error, arcTolerance * circle.radius / 100);
|
||
|
||
return [0, 1/4, 1/2, 3/4, 1].every(function(point) {
|
||
return Math.abs(getDistance(getCubicBezierPoint(curve, point), circle.center) - circle.radius) <= tolerance;
|
||
});
|
||
}
|
||
|
||
/**
|
||
* Checks if a previous curve fits the given circle.
|
||
*
|
||
* @param {Object} circle
|
||
* @param {Array} curve
|
||
* @return {Boolean}
|
||
*/
|
||
|
||
function isArcPrev(curve, circle) {
|
||
return isArc(curve, {
|
||
center: [circle.center[0] + curve[4], circle.center[1] + curve[5]],
|
||
radius: circle.radius
|
||
});
|
||
}
|
||
|
||
/**
|
||
* Finds angle of a curve fitting the given arc.
|
||
|
||
* @param {Array} curve
|
||
* @param {Object} relCircle
|
||
* @return {Number} angle
|
||
*/
|
||
|
||
function findArcAngle(curve, relCircle) {
|
||
var x1 = -relCircle.center[0],
|
||
y1 = -relCircle.center[1],
|
||
x2 = curve[4] - relCircle.center[0],
|
||
y2 = curve[5] - relCircle.center[1];
|
||
|
||
return Math.acos(
|
||
(x1 * x2 + y1 * y2) /
|
||
Math.sqrt((x1 * x1 + y1 * y1) * (x2 * x2 + y2 * y2))
|
||
);
|
||
}
|
||
|
||
/**
|
||
* Converts given path data to string.
|
||
*
|
||
* @param {Object} params
|
||
* @param {Array} pathData
|
||
* @return {String}
|
||
*/
|
||
|
||
function data2Path(params, pathData) {
|
||
return pathData.reduce(function(pathString, item) {
|
||
var strData = '';
|
||
if (item.data) {
|
||
strData = cleanupOutData(roundData(item.data.slice()), params);
|
||
}
|
||
return pathString + item.instruction + strData;
|
||
}, '');
|
||
}
|