Check path intersection while merging.

Fixes #253, resolves #260, fixes #298.

plugins/_path.js

@@ -9,7 +9,8 @@ var regPathInstructions = /([MmLlHhVvCcSsQqTtAaZz])\s*/,
     referencesProps = collections.referencesProps,
     defaultStrokeWidth = collections.attrsGroupsDefaults.presentation['stroke-width'],
     cleanupOutData = require('../lib/svgo/tools').cleanupOutData,
-    removeLeadingZero = require('../lib/svgo/tools').removeLeadingZero;
+    removeLeadingZero = require('../lib/svgo/tools').removeLeadingZero,
+    prevCtrlPoint;
 
 /**
  * Convert path string to JS representation.
@@ -311,7 +312,6 @@ exports.applyTransforms = function(elem, path, applyTransformsStroked, floatPrec
     elem.removeAttr('transform');
 
     return path;
-
 };
 
 /**
@@ -590,6 +590,290 @@ function set(dest, source) {
     return dest;
 }
 
+/**
+ * Checks if two paths have an intersection by checking convex hulls
+ * collision using Gilbert-Johnson-Keerthi distance algorithm
+ * http://entropyinteractive.com/2011/04/gjk-algorithm/
+ *
+ * @param {Array} path1 JS path representation
+ * @param {Array} path2 JS path representation
+ * @return {Boolean}
+ */
+exports.interesects = function(path1, path2) {
+    if (path1.length < 3 || path2.length < 3) return false; // nothing to fill
+
+    // Collect points of every subpath.
+    var points1 = relative2absolute(path1).reduce(gatherPoints, []),
+        points2 = relative2absolute(path2).reduce(gatherPoints, []);
+
+    // Axis-aligned bounding box check.
+    if (points1.maxX <= points2.minX || points2.maxX <= points1.minX ||
+        points1.maxY <= points2.minY || points2.maxY <= points1.minY ||
+        points1.every(function (set1) {
+            return points2.every(function (set2) {
+                return set1[set1.maxX][0] <= set2[set2.minX][0] ||
+                    set2[set2.maxX][0] <= set1[set1.minX][0] ||
+                    set1[set1.maxY][1] <= set2[set2.minY][1] ||
+                    set2[set2.maxY][1] <= set1[set1.minY][1];
+            });
+        })
+    ) return false;
+
+    // Get a convex hull from points of each subpath. Has the most complexity O(n·log n).
+    var hullNest1 = points1.map(convexHull),
+        hullNest2 = points2.map(convexHull);
+
+    // Check intersection of every subpath of the first path with every subpath of the second.
+    return hullNest1.some(function(hull1) {
+        if (hull1.length < 3) return false;
+
+        return hullNest2.some(function(hull2) {
+            if (hull2.length < 3) return false;
+
+            var simplex = [getSupport(hull1, hull2, [1, 0])], // create the initial simplex
+                direction = minus(simplex[0]); // set the direction to point towards the origin
+
+            var iterations = 1e4; // infinite loop protection, 10 000 iterations is more than enough
+            while (true) {
+                if (iterations-- == 0) {
+                    console.error('Error: infinite loop while processing mergePaths plugin.');
+                    return true; // true is the safe value that means “do nothing with paths”
+                }
+                // add a new point
+                simplex.push(getSupport(hull1, hull2, direction));
+                // see if the new point was on the correct side of the origin
+                if (dot(direction, simplex[simplex.length - 1]) <= 0) return false;
+                // process the simplex
+                if (processSimplex(simplex, direction)) return true;
+            }
+        });
+    });
+
+    function getSupport(a, b, direction) {
+        return sub(supportPoint(a, direction), supportPoint(b, minus(direction)));
+    }
+
+    // Compute farthest polygon point in particular direction.
+    function supportPoint(polygon, direction) {
+        // Choose a quadrant to search in. In the worst case only one quadrant would be iterated.
+        var index = direction[1] >= 0 ?
+                direction[0] < 0 ? polygon.maxY : polygon.maxX : // [1, 0] lands right on maxX
+                direction[0] < 0 ? polygon.minX : polygon.minY,
+            max = dot(polygon[index], direction);
+
+        for (var i = index; i < polygon.length; i++) {
+            var value = dot(polygon[i], direction);
+            if (value >= max) {
+                index = i;
+                max = value;
+            } else break; // surely we've found the maximum since we've choosen a quadrant
+        }
+        return polygon[index];
+    }
+};
+
+function processSimplex(simplex, direction) {
+    // we only need to handle to 1-simplex and 2-simplex
+    if (simplex.length == 2) { // 1-simplex
+        var a = simplex[1],
+            b = simplex[0],
+            AO = minus(simplex[1]),
+            AB = sub(b, a);
+        // AO is in the same direction as AB
+        if (dot(AO, AB) > 0) {
+            // get the vector perpendicular to AB facing O
+            set(direction, orth(AB, a));
+        } else {
+            set(direction, AO);
+            // only A remains in the simplex
+            simplex.shift();
+        }
+    } else { // 2-simplex
+        var a = simplex[2], // [a, b, c] = simplex
+            b = simplex[1],
+            c = simplex[0],
+            AB = sub(b, a),
+            AC = sub(c, a),
+            AO = minus(a),
+            ACB = orth(AB, AC), // the vector perpendicular to AB facing away from C
+            ABC = orth(AC, AB); // the vector perpendicular to AC facing away from B
+
+        if (dot(ACB, AO) > 0) {
+            if (dot(AB, AO) > 0) { // region 4
+                set(direction, ACB);
+                simplex.shift(); // simplex = [b, a]
+            } else { // region 5
+                set(direction, AO);
+                simplex.splice(0, 2); // simplex = [a]
+            }
+        } else if (dot(ABC, AO) > 0) {
+            if (dot(AC, AO) > 0) { // region 6
+                set(direction, ABC);
+                simplex.splice(1, 1); // simplex = [c, a]
+            } else { // region 5 (again)
+                set(direction, AO);
+                simplex.splice(0, 2); // simplex = [a]
+            }
+        } else // region 7
+            return true;
+    }
+    return false;
+}
+
+function minus(v) {
+    return [-v[0], -v[1]];
+}
+
+function sub(v1, v2) {
+    return [v1[0] - v2[0], v1[1] - v2[1]];
+}
+
+function dot(v1, v2) {
+    return v1[0] * v2[0] + v1[1] * v2[1];
+}
+
+function orth(v, from) {
+    var o = [-v[1], v[0]];
+    return dot(o, minus(from)) < 0 ? minus(o) : o;
+}
+
+function gatherPoints(points, item, index, path) {
+
+    var subPath = points.length && points[points.length - 1],
+        prev = index && path[index - 1],
+        basePoint = subPath.length && subPath[subPath.length - 1],
+        data = item.data,
+        ctrlPoint = basePoint;
+
+    switch (item.instruction) {
+        case 'M':
+            points.push(subPath = []);
+            break;
+        case 'H':
+            addPoint(subPath, [data[0], basePoint[1]]);
+            break;
+        case 'V':
+            addPoint(subPath, [basePoint[0], data[0]]);
+            break;
+        case 'Q':
+            addPoint(subPath, data.slice(0, 2));
+            prevCtrlPoint = [data[2] - data[0], data[3] - data[1]]; // Save control point for shorthand
+            break;
+        case 'T':
+            if (prev.instruction == 'Q' && prev.instruction == 'T') {
+                ctrlPoint = [basePoint[0] + prevCtrlPoint[0], basePoint[1] + prevCtrlPoint[1]];
+                addPoint(subPath, ctrlPoint);
+                prevCtrlPoint = [data[0] - ctrlPoint[0], data[1] - ctrlPoint[1]];
+            }
+            break;
+        case 'C':
+            // Approximate quibic Bezier curve with middle points between control points
+            addPoint(subPath, [.5 * (basePoint[0] + data[0]), .5 * (basePoint[1] + data[1])]);
+            addPoint(subPath, [.5 * (data[0] + data[2]), .5 * (data[1] + data[3])]);
+            addPoint(subPath, [.5 * (data[2] + data[4]), .5 * (data[3] + data[5])]);
+            prevCtrlPoint = [data[4] - data[2], data[5] - data[3]]; // Save control point for shorthand
+            break;
+        case 'S':
+            if (prev.instruction == 'C' && prev.instruction == 'S') {
+                addPoint(subPath, [basePoint[0] + .5 * prevCtrlPoint[0], basePoint[1] + .5 * prevCtrlPoint[1]]);
+                ctrlPoint = [basePoint[0] + prevCtrlPoint[0], basePoint[1] + prevCtrlPoint[1]];
+            }
+            addPoint(subPath, [.5 * (ctrlPoint[0] + data[0]), .5 * (ctrlPoint[1]+ data[1])]);
+            addPoint(subPath, [.5 * (data[0] + data[2]), .5 * (data[1] + data[3])]);
+            prevCtrlPoint = [data[2] - data[0], data[3] - data[1]];
+            break;
+        case 'A':
+            // Convert the arc to bezier curves and use the same approximation
+            var curves = a2c.apply(0, basePoint.concat(data));
+            for (var cData; (cData = curves.splice(0,6).map(toAbsolute)).length;) {
+                addPoint(subPath, [.5 * (basePoint[0] + cData[0]), .5 * (basePoint[1] + cData[1])]);
+                addPoint(subPath, [.5 * (cData[0] + cData[2]), .5 * (cData[1] + cData[3])]);
+                addPoint(subPath, [.5 * (cData[2] + cData[4]), .5 * (cData[3] + cData[5])]);
+                if (curves.length) addPoint(subPath, basePoint = cData.slice(-2));
+            }
+            break;
+    }
+    // Save final command coordinates
+    if (data && data.length >= 2) addPoint(subPath, data.slice(-2));
+    return points;
+
+    function toAbsolute(n, i) { return n + basePoint[i % 2] }
+
+    // Writes data about the extreme points on each axle
+    function addPoint(path, point) {
+        if (!path.length || point[1] > path[path.maxY][1]) {
+            path.maxY = path.length;
+            points.maxY = points.length ? Math.max(point[1], points.maxY) : point[1];
+        }
+        if (!path.length || point[0] > path[path.maxX][0]) {
+            path.maxX = path.length;
+            points.maxX = points.length ? Math.max(point[0], points.maxX) : point[0];
+        }
+        if (!path.length || point[1] < path[path.minY][1]) {
+            path.minY = path.length;
+            points.minY = points.length ? Math.min(point[1], points.minY) : point[1];
+        }
+        if (!path.length || point[0] < path[path.minX][0]) {
+            path.minX = path.length;
+            points.minX = points.length ? Math.min(point[0], points.minX) : point[0];
+        }
+        path.push(point);
+    }
+}
+
+/**
+ * Forms a convex hull from set of points of every subpath using monotone chain convex hull algorithm.
+ * http://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain
+ *
+ * @param points An array of [X, Y] coordinates
+ */
+function convexHull(points) {
+    points.sort(function(a, b) {
+        return a[0] == b[0] ? a[1] - b[1] : a[0] - b[0];
+    });
+
+    var lower = [],
+        minY = 0;
+    for (var i = 0; i < points.length; i++) {
+        while (lower.length >= 2 && cross(lower[lower.length - 2], lower[lower.length - 1], points[i]) <= 0) {
+            lower.pop();
+        }
+        if (points[i][1] < points[minY][1]) {
+            minY = lower.length;
+        }
+        lower.push(points[i]);
+    }
+
+    var upper = [],
+        maxY = points.length - 1;
+    for (var i = points.length ; i--;) {
+        while (upper.length >= 2 && cross(upper[upper.length - 2], upper[upper.length - 1], points[i]) <= 0) {
+            upper.pop();
+        }
+        if (points[i][1] > points[maxY][1]) {
+            maxY = upper.length;
+        }
+        upper.push(points[i]);
+    }
+
+    // last points are equal to starting points of the other part
+    upper.pop();
+    lower.pop();
+
+    var hull = lower.concat(upper);
+
+    hull.minX = 0; // by sorting
+    hull.maxX = lower.length;
+    hull.minY = minY;
+    hull.maxY = (lower.length + maxY) % hull.length;
+
+    return hull;
+}
+
+function cross(o, a, b) {
+    return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0])
+}
+
 /* Based on code from Snap.svg (Apache 2 license). http://snapsvg.io/
  * Thanks to Dmitry Baranovskiy for his great work!
  */

plugins/mergePaths.js

@@ -11,7 +11,8 @@ exports.params = {
 };
 
 var path2js = require('./_path.js').path2js,
-    js2path = require('./_path.js').js2path;
+    js2path = require('./_path.js').js2path,
+    interesects = require('./_path.js').interesects;
 
 /**
  * Merge multiple Paths into one.
@@ -51,7 +52,7 @@ exports.fn = function(item, params) {
                 prevPathJS = path2js(prevContentItem),
                 curPathJS = path2js(contentItem);
 
-            if (equalData) {
+            if (equalData && !interesects(prevPathJS, curPathJS)) {
                 js2path(prevContentItem, prevPathJS.concat(curPathJS), params);
                 return false;
             }