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+'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
+};
+
+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;
+
+/**
+ * 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 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) {
+
+ // 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.
+ // v-20 -> V0
+ // Don't convert if it fits following previous instruction.
+ // l20 30-10-50 instead of l20 30L20 30
+ if (
+ 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.sqrt(Math.pow(point1[0] - point2[0], 2) + Math.pow(point1[1] - point2[1], 2));
+}
+
+/**
+ * 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 && [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 circe.
+ *
+ * @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 previos curve fits the given circe.
+ *
+ * @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) : '');
+ }, '');
+}
generated by cgit v1.2.3 (git 2.25.1) at 2026-10-08 00:02:59 +0000