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+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; var prevAngle = findArcAngle(prevData, { center: [prevData[4] + circle.center[0], prevData[5] + circle.center[1]], radius: circle.radius } ); angle += prevAngle; 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) { var strData = ''; if (item.data) { strData = cleanupOutData(roundData(item.data.slice()), params); } return pathString + item.instruction + strData; }, ''); }