| 'use strict'; |
| |
| exports.type = 'perItem'; |
| |
| exports.active = true; |
| |
| exports.description = 'optimizes path data: writes in shorter form, applies transformations'; |
| |
| exports.params = { |
| applyTransforms: true, |
| applyTransformsStroked: true, |
| makeArcs: { |
| threshold: 2.5, // coefficient of rounding error |
| tolerance: 0.5 // percentage of radius |
| }, |
| straightCurves: true, |
| lineShorthands: true, |
| curveSmoothShorthands: true, |
| floatPrecision: 3, |
| transformPrecision: 5, |
| removeUseless: true, |
| collapseRepeated: true, |
| utilizeAbsolute: true, |
| leadingZero: true, |
| negativeExtraSpace: true, |
| forceAbsolutePath: false |
| }; |
| |
| var pathElems = require('./_collections.js').pathElems, |
| path2js = require('./_path.js').path2js, |
| js2path = require('./_path.js').js2path, |
| applyTransforms = require('./_path.js').applyTransforms, |
| cleanupOutData = require('../lib/svgo/tools').cleanupOutData, |
| roundData, |
| precision, |
| error, |
| arcThreshold, |
| arcTolerance, |
| hasMarkerMid, |
| hasStrokeLinecap; |
| |
| /** |
| * Convert absolute Path to relative, |
| * collapse repeated instructions, |
| * detect and convert Lineto shorthands, |
| * remove useless instructions like "l0,0", |
| * trim useless delimiters and leading zeros, |
| * decrease accuracy of floating-point numbers. |
| * |
| * @see http://www.w3.org/TR/SVG/paths.html#PathData |
| * |
| * @param {Object} item current iteration item |
| * @param {Object} params plugin params |
| * @return {Boolean} if false, item will be filtered out |
| * |
| * @author Kir Belevich |
| */ |
| exports.fn = function(item, params) { |
| |
| if (item.isElem(pathElems) && item.hasAttr('d')) { |
| |
| precision = params.floatPrecision; |
| error = precision !== false ? +Math.pow(.1, precision).toFixed(precision) : 1e-2; |
| roundData = precision > 0 && precision < 20 ? strongRound : round; |
| if (params.makeArcs) { |
| arcThreshold = params.makeArcs.threshold; |
| arcTolerance = params.makeArcs.tolerance; |
| } |
| hasMarkerMid = item.hasAttr('marker-mid'); |
| |
| var stroke = item.computedAttr('stroke'), |
| strokeLinecap = item.computedAttr('stroke'); |
| hasStrokeLinecap = stroke && stroke != 'none' && strokeLinecap && strokeLinecap != 'butt'; |
| |
| var data = path2js(item); |
| |
| // TODO: get rid of functions returns |
| if (data.length) { |
| convertToRelative(data); |
| |
| if (params.applyTransforms) { |
| data = applyTransforms(item, data, params); |
| } |
| |
| data = filters(data, params); |
| |
| if (params.utilizeAbsolute) { |
| data = convertToMixed(data, params); |
| } |
| |
| js2path(item, data, params); |
| } |
| |
| } |
| |
| }; |
| |
| /** |
| * Convert absolute path data coordinates to relative. |
| * |
| * @param {Array} path input path data |
| * @param {Object} params plugin params |
| * @return {Array} output path data |
| */ |
| function convertToRelative(path) { |
| |
| var point = [0, 0], |
| subpathPoint = [0, 0], |
| baseItem; |
| |
| path.forEach(function(item, index) { |
| |
| var instruction = item.instruction, |
| data = item.data; |
| |
| // data !== !z |
| if (data) { |
| |
| // already relative |
| // recalculate current point |
| if ('mcslqta'.indexOf(instruction) > -1) { |
| |
| point[0] += data[data.length - 2]; |
| point[1] += data[data.length - 1]; |
| |
| if (instruction === 'm') { |
| subpathPoint[0] = point[0]; |
| subpathPoint[1] = point[1]; |
| baseItem = item; |
| } |
| |
| } else if (instruction === 'h') { |
| |
| point[0] += data[0]; |
| |
| } else if (instruction === 'v') { |
| |
| point[1] += data[0]; |
| |
| } |
| |
| // convert absolute path data coordinates to relative |
| // if "M" was not transformed from "m" |
| // M → m |
| if (instruction === 'M') { |
| |
| if (index > 0) instruction = 'm'; |
| |
| data[0] -= point[0]; |
| data[1] -= point[1]; |
| |
| subpathPoint[0] = point[0] += data[0]; |
| subpathPoint[1] = point[1] += data[1]; |
| |
| baseItem = item; |
| |
| } |
| |
| // L → l |
| // T → t |
| else if ('LT'.indexOf(instruction) > -1) { |
| |
| instruction = instruction.toLowerCase(); |
| |
| // x y |
| // 0 1 |
| data[0] -= point[0]; |
| data[1] -= point[1]; |
| |
| point[0] += data[0]; |
| point[1] += data[1]; |
| |
| // C → c |
| } else if (instruction === 'C') { |
| |
| instruction = 'c'; |
| |
| // x1 y1 x2 y2 x y |
| // 0 1 2 3 4 5 |
| data[0] -= point[0]; |
| data[1] -= point[1]; |
| data[2] -= point[0]; |
| data[3] -= point[1]; |
| data[4] -= point[0]; |
| data[5] -= point[1]; |
| |
| point[0] += data[4]; |
| point[1] += data[5]; |
| |
| // S → s |
| // Q → q |
| } else if ('SQ'.indexOf(instruction) > -1) { |
| |
| instruction = instruction.toLowerCase(); |
| |
| // x1 y1 x y |
| // 0 1 2 3 |
| data[0] -= point[0]; |
| data[1] -= point[1]; |
| data[2] -= point[0]; |
| data[3] -= point[1]; |
| |
| point[0] += data[2]; |
| point[1] += data[3]; |
| |
| // A → a |
| } else if (instruction === 'A') { |
| |
| instruction = 'a'; |
| |
| // rx ry x-axis-rotation large-arc-flag sweep-flag x y |
| // 0 1 2 3 4 5 6 |
| data[5] -= point[0]; |
| data[6] -= point[1]; |
| |
| point[0] += data[5]; |
| point[1] += data[6]; |
| |
| // H → h |
| } else if (instruction === 'H') { |
| |
| instruction = 'h'; |
| |
| data[0] -= point[0]; |
| |
| point[0] += data[0]; |
| |
| // V → v |
| } else if (instruction === 'V') { |
| |
| instruction = 'v'; |
| |
| data[0] -= point[1]; |
| |
| point[1] += data[0]; |
| |
| } |
| |
| item.instruction = instruction; |
| item.data = data; |
| |
| // store absolute coordinates for later use |
| item.coords = point.slice(-2); |
| |
| } |
| |
| // !data === z, reset current point |
| else if (instruction == 'z') { |
| if (baseItem) { |
| item.coords = baseItem.coords; |
| } |
| point[0] = subpathPoint[0]; |
| point[1] = subpathPoint[1]; |
| } |
| |
| item.base = index > 0 ? path[index - 1].coords : [0, 0]; |
| |
| }); |
| |
| return path; |
| |
| } |
| |
| /** |
| * Main filters loop. |
| * |
| * @param {Array} path input path data |
| * @param {Object} params plugin params |
| * @return {Array} output path data |
| */ |
| function filters(path, params) { |
| |
| var stringify = data2Path.bind(null, params), |
| relSubpoint = [0, 0], |
| pathBase = [0, 0], |
| prev = {}; |
| |
| path = path.filter(function(item, index, path) { |
| |
| var instruction = item.instruction, |
| data = item.data, |
| next = path[index + 1]; |
| |
| if (data) { |
| |
| var sdata = data, |
| circle; |
| |
| if (instruction === 's') { |
| sdata = [0, 0].concat(data); |
| |
| if ('cs'.indexOf(prev.instruction) > -1) { |
| var pdata = prev.data, |
| n = pdata.length; |
| |
| // (-x, -y) of the prev tangent point relative to the current point |
| sdata[0] = pdata[n - 2] - pdata[n - 4]; |
| sdata[1] = pdata[n - 1] - pdata[n - 3]; |
| } |
| |
| } |
| |
| // convert curves to arcs if possible |
| if ( |
| params.makeArcs && |
| (instruction == 'c' || instruction == 's') && |
| isConvex(sdata) && |
| (circle = findCircle(sdata)) |
| ) { |
| var r = roundData([circle.radius])[0], |
| angle = findArcAngle(sdata, circle), |
| sweep = sdata[5] * sdata[0] - sdata[4] * sdata[1] > 0 ? 1 : 0, |
| arc = { |
| instruction: 'a', |
| data: [r, r, 0, 0, sweep, sdata[4], sdata[5]], |
| coords: item.coords.slice(), |
| base: item.base |
| }, |
| output = [arc], |
| // relative coordinates to adjust the found circle |
| relCenter = [circle.center[0] - sdata[4], circle.center[1] - sdata[5]], |
| relCircle = { center: relCenter, radius: circle.radius }, |
| arcCurves = [item], |
| hasPrev = 0, |
| suffix = '', |
| nextLonghand; |
| |
| if ( |
| prev.instruction == 'c' && isConvex(prev.data) && isArcPrev(prev.data, circle) || |
| prev.instruction == 'a' && prev.sdata && isArcPrev(prev.sdata, circle) |
| ) { |
| arcCurves.unshift(prev); |
| arc.base = prev.base; |
| arc.data[5] = arc.coords[0] - arc.base[0]; |
| arc.data[6] = arc.coords[1] - arc.base[1]; |
| var prevData = prev.instruction == 'a' ? prev.sdata : prev.data; |
| angle += findArcAngle(prevData, |
| { |
| center: [prevData[4] + relCenter[0], prevData[5] + relCenter[1]], |
| radius: circle.radius |
| } |
| ); |
| if (angle > Math.PI) arc.data[3] = 1; |
| hasPrev = 1; |
| } |
| |
| // check if next curves are fitting the arc |
| for (var j = index; (next = path[++j]) && ~'cs'.indexOf(next.instruction);) { |
| var nextData = next.data; |
| if (next.instruction == 's') { |
| nextLonghand = makeLonghand({instruction: 's', data: next.data.slice() }, |
| path[j - 1].data); |
| nextData = nextLonghand.data; |
| nextLonghand.data = nextData.slice(0, 2); |
| suffix = stringify([nextLonghand]); |
| } |
| if (isConvex(nextData) && isArc(nextData, relCircle)) { |
| angle += findArcAngle(nextData, relCircle); |
| if (angle - 2 * Math.PI > 1e-3) break; // more than 360° |
| if (angle > Math.PI) arc.data[3] = 1; |
| arcCurves.push(next); |
| if (2 * Math.PI - angle > 1e-3) { // less than 360° |
| arc.coords = next.coords; |
| arc.data[5] = arc.coords[0] - arc.base[0]; |
| arc.data[6] = arc.coords[1] - arc.base[1]; |
| } else { |
| // full circle, make a half-circle arc and add a second one |
| arc.data[5] = 2 * (relCircle.center[0] - nextData[4]); |
| arc.data[6] = 2 * (relCircle.center[1] - nextData[5]); |
| arc.coords = [arc.base[0] + arc.data[5], arc.base[1] + arc.data[6]]; |
| arc = { |
| instruction: 'a', |
| data: [r, r, 0, 0, sweep, |
| next.coords[0] - arc.coords[0], next.coords[1] - arc.coords[1]], |
| coords: next.coords, |
| base: arc.coords |
| }; |
| output.push(arc); |
| j++; |
| break; |
| } |
| relCenter[0] -= nextData[4]; |
| relCenter[1] -= nextData[5]; |
| } else break; |
| } |
| |
| if ((stringify(output) + suffix).length < stringify(arcCurves).length) { |
| if (path[j] && path[j].instruction == 's') { |
| makeLonghand(path[j], path[j - 1].data); |
| } |
| if (hasPrev) { |
| var prevArc = output.shift(); |
| roundData(prevArc.data); |
| relSubpoint[0] += prevArc.data[5] - prev.data[prev.data.length - 2]; |
| relSubpoint[1] += prevArc.data[6] - prev.data[prev.data.length - 1]; |
| prev.instruction = 'a'; |
| prev.data = prevArc.data; |
| item.base = prev.coords = prevArc.coords; |
| } |
| arc = output.shift(); |
| if (arcCurves.length == 1) { |
| item.sdata = sdata.slice(); // preserve curve data for future checks |
| } else if (arcCurves.length - 1 - hasPrev > 0) { |
| // filter out consumed next items |
| path.splice.apply(path, [index + 1, arcCurves.length - 1 - hasPrev].concat(output)); |
| } |
| if (!arc) return false; |
| instruction = 'a'; |
| data = arc.data; |
| item.coords = arc.coords; |
| } |
| } |
| |
| // Rounding relative coordinates, taking in account accummulating error |
| // to get closer to absolute coordinates. Sum of rounded value remains same: |
| // l .25 3 .25 2 .25 3 .25 2 -> l .3 3 .2 2 .3 3 .2 2 |
| if (precision !== false) { |
| if ('mltqsc'.indexOf(instruction) > -1) { |
| for (var i = data.length; i--;) { |
| data[i] += item.base[i % 2] - relSubpoint[i % 2]; |
| } |
| } else if (instruction == 'h') { |
| data[0] += item.base[0] - relSubpoint[0]; |
| } else if (instruction == 'v') { |
| data[0] += item.base[1] - relSubpoint[1]; |
| } else if (instruction == 'a') { |
| data[5] += item.base[0] - relSubpoint[0]; |
| data[6] += item.base[1] - relSubpoint[1]; |
| } |
| roundData(data); |
| |
| if (instruction == 'h') relSubpoint[0] += data[0]; |
| else if (instruction == 'v') relSubpoint[1] += data[0]; |
| else { |
| relSubpoint[0] += data[data.length - 2]; |
| relSubpoint[1] += data[data.length - 1]; |
| } |
| roundData(relSubpoint); |
| |
| if (instruction.toLowerCase() == 'm') { |
| pathBase[0] = relSubpoint[0]; |
| pathBase[1] = relSubpoint[1]; |
| } |
| } |
| |
| // convert straight curves into lines segments |
| if (params.straightCurves) { |
| |
| if ( |
| instruction === 'c' && |
| isCurveStraightLine(data) || |
| instruction === 's' && |
| isCurveStraightLine(sdata) |
| ) { |
| if (next && next.instruction == 's') |
| makeLonghand(next, data); // fix up next curve |
| instruction = 'l'; |
| data = data.slice(-2); |
| } |
| |
| else if ( |
| instruction === 'q' && |
| isCurveStraightLine(data) |
| ) { |
| if (next && next.instruction == 't') |
| makeLonghand(next, data); // fix up next curve |
| instruction = 'l'; |
| data = data.slice(-2); |
| } |
| |
| else if ( |
| instruction === 't' && |
| prev.instruction !== 'q' && |
| prev.instruction !== 't' |
| ) { |
| instruction = 'l'; |
| data = data.slice(-2); |
| } |
| |
| else if ( |
| instruction === 'a' && |
| (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) { |
| return pathString + item.instruction + (item.data ? cleanupOutData(roundData(item.data.slice()), params) : ''); |
| }, ''); |
| } |
