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Fix for #773

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Indroduced more reliable method for finding self intersection on curves.
This commit is contained in:
Jan 2015-09-30 12:19:09 +02:00
parent ea3cc63e2e
commit ec70fa1806
2 changed files with 116 additions and 85 deletions
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161
src/path/Curve.js
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@ -417,13 +417,16 @@ var Curve = Base.extend(/** @lends Curve# */{
* Returns all intersections between two {@link Curve} objects as an array * Returns all intersections between two {@link Curve} objects as an array
* of {@link CurveLocation} objects. * of {@link CurveLocation} objects.
* *
* If the parameter curve is null, the self intersection of the curve is
* returned, if it exists.
*
* @param {Curve} curve the other curve to find the intersections with * @param {Curve} curve the other curve to find the intersections with
* @return {CurveLocation[]} the locations of all intersection between the * @return {CurveLocation[]} the locations of all intersection between the
* curves * curves
*/ */
getIntersections: function(curve) { getIntersections: function(curve) {
return Curve.getIntersections(this.getValues(), curve.getValues(), return Curve.getIntersections(this.getValues(), curve ? curve.getValues() : null,
this, curve, [], {}); this, curve ? curve : this, [], {});
}, },
// TODO: adjustThroughPoint // TODO: adjustThroughPoint
@ -1757,25 +1760,74 @@ new function() { // Scope for intersection using bezier fat-line clipping
// #getIntersections() calls as it is required to create the resulting // #getIntersections() calls as it is required to create the resulting
// CurveLocation objects. // CurveLocation objects.
getIntersections: function(v1, v2, c1, c2, locations, param) { getIntersections: function(v1, v2, c1, c2, locations, param) {
// Avoid checking curves if completely out of control bounds. if (!v2) { // if v2 is null or undefined, search for self intersection
// As a little optimization, we can scale the handles with 0.75 // get side of both handles
// before calculating the control bounds and still be sure that the var h1Side = Line.getSide(v1[0], v1[1], v1[6], v1[7], v1[2], v1[3], false);
// curve is fully contained. var h2Side = Line.getSide(v1[0], v1[1], v1[6], v1[7], v1[4], v1[5], false);
var c1p1x = v1[0], c1p1y = v1[1], if (h1Side == h2Side) {
c1p2x = v1[6], c1p2y = v1[7], var edgeSum = (v1[0] - v1[4]) * (v1[3] - v1[7]) + (v1[2] - v1[6]) * (v1[5] - v1[1]);
c2p1x = v2[0], c2p1y = v2[1], // if both handles are on the same side, the curve can only have a self intersection if
c2p2x = v2[6], c2p2y = v2[7], // the edge sum and the handles's side have different signs. If the handles are on the
c1h1x = (3 * v1[2] + c1p1x) / 4, // left side, the edge sum must be negative for a self intersection (and vice versa)
c1h1y = (3 * v1[3] + c1p1y) / 4, if (Math.sign(edgeSum) == h1Side) return locations;
c1h2x = (3 * v1[4] + c1p2x) / 4, }
c1h2y = (3 * v1[5] + c1p2y) / 4, // As a second condition we check if the curve has an inflection point. If an inflection point
c2h1x = (3 * v2[2] + c2p1x) / 4, // exists, the curve cannot have a self intersection.
c2h1y = (3 * v2[3] + c2p1y) / 4, var ax = v1[6] - 3 * v1[4] + 3 * v1[2] - v1[0];
c2h2x = (3 * v2[4] + c2p2x) / 4, var bx = v1[4] - 2 * v1[2] + v1[0];
c2h2y = (3 * v2[5] + c2p2y) / 4, var cx = v1[2] - v1[0];
min = Math.min, var ay = v1[7] - 3 * v1[5] + 3 * v1[3] - v1[1];
max = Math.max; var by = v1[5] - 2 * v1[3] + v1[1];
if (!( var cy = v1[3] - v1[1];
var hasInflectionPoint = (Math.pow(ay * cx - ax * cy, 2) - 4 * (ay * bx - ax * by) * (by * cx - bx * cy) >= 0);
if (!hasInflectionPoint) {
// the curve may have a self intersection, find parameter to split curve. We search for the
// parameter where the velocity has an extremum by finding the roots of the cross product
// between the bezier curve's first and second derivative
var roots = [],
rootCount = Numerical.solveCubic(ax * ax + ay * ay, 3 * (ax * bx + ay * by),
(2 * (bx * bx + by * by) + ax * cx + ay * cy), (bx * cx + by * cy), roots, 0, 1);
// Select extremum with smallest curvature. This is always on the loop in case of a self intersection
var tSplit, maxCurvature;
for (var i = 0; i < rootCount; i++) {
var curvature = Math.abs(c1.getCurvatureAt(roots[i], true));
if (!maxCurvature || curvature > maxCurvature) {
maxCurvature = curvature;
tSplit = roots[i];
}
}
// Divide the curve in two and then apply the normal curve intersection code.
var parts = Curve.subdivide(v1, tSplit);
if (!param) param = {};
// After splitting, the end is always connected:
param.endConnected = true;
// Since the curve was split above, we need to
// adjust the parameters for both locations.
param.renormalize = function(t1, t2) {
return [t1 * tSplit, t2 * (1 - tSplit) + tSplit];
};
Curve.getIntersections(parts[0], parts[1], c1, c1, locations, param);
}
} else {
// Avoid checking curves if completely out of control bounds.
// As a little optimization, we can scale the handles with 0.75
// before calculating the control bounds and still be sure that the
// curve is fully contained.
var c1p1x = v1[0], c1p1y = v1[1],
c1p2x = v1[6], c1p2y = v1[7],
c2p1x = v2[0], c2p1y = v2[1],
c2p2x = v2[6], c2p2y = v2[7],
c1h1x = (3 * v1[2] + c1p1x) / 4,
c1h1y = (3 * v1[3] + c1p1y) / 4,
c1h2x = (3 * v1[4] + c1p2x) / 4,
c1h2y = (3 * v1[5] + c1p2y) / 4,
c2h1x = (3 * v2[2] + c2p1x) / 4,
c2h1y = (3 * v2[3] + c2p1y) / 4,
c2h2x = (3 * v2[4] + c2p2x) / 4,
c2h2y = (3 * v2[5] + c2p2y) / 4,
min = Math.min,
max = Math.max;
if (!(
max(c1p1x, c1h1x, c1h2x, c1p2x) >= max(c1p1x, c1h1x, c1h2x, c1p2x) >=
min(c2p1x, c2h1x, c2h2x, c2p2x) && min(c2p1x, c2h1x, c2h2x, c2p2x) &&
min(c1p1x, c1h1x, c1h2x, c1p2x) <= min(c1p1x, c1h1x, c1h2x, c1p2x) <=
@ -1784,44 +1836,45 @@ new function() { // Scope for intersection using bezier fat-line clipping
min(c2p1y, c2h1y, c2h2y, c2p2y) && min(c2p1y, c2h1y, c2h2y, c2p2y) &&
min(c1p1y, c1h1y, c1h2y, c1p2y) <= min(c1p1y, c1h1y, c1h2y, c1p2y) <=
max(c2p1y, c2h1y, c2h2y, c2p2y) max(c2p1y, c2h1y, c2h2y, c2p2y)
) )
// Also detect and handle overlaps: // Also detect and handle overlaps:
|| !param.startConnected && !param.endConnected || !param.startConnected && !param.endConnected
&& addOverlap(v1, v2, c1, c2, locations, param)) && addOverlap(v1, v2, c1, c2, locations, param))
return locations; return locations;
var straight1 = Curve.isStraight(v1), var straight1 = Curve.isStraight(v1),
straight2 = Curve.isStraight(v2), straight2 = Curve.isStraight(v2),
c1p1 = new Point(c1p1x, c1p1y), c1p1 = new Point(c1p1x, c1p1y),
c1p2 = new Point(c1p2x, c1p2y), c1p2 = new Point(c1p2x, c1p2y),
c2p1 = new Point(c2p1x, c2p1y), c2p1 = new Point(c2p1x, c2p1y),
c2p2 = new Point(c2p2x, c2p2y), c2p2 = new Point(c2p2x, c2p2y),
// NOTE: Use smaller Numerical.EPSILON to compare beginnings and // NOTE: Use smaller Numerical.EPSILON to compare beginnings and
// end points to avoid matching them on almost collinear lines. // end points to avoid matching them on almost collinear lines.
epsilon = /*#=*/Numerical.EPSILON; epsilon = /*#=*/Numerical.EPSILON;
// Handle the special case where the first curve's stat-point // Handle the special case where the first curve's stat-point
// overlaps with the second curve's start- or end-points. // overlaps with the second curve's start- or end-points.
if (c1p1.isClose(c2p1, epsilon)) if (c1p1.isClose(c2p1, epsilon))
addLocation(locations, param, v1, c1, 0, c1p1, v2, c2, 0, c2p1); addLocation(locations, param, v1, c1, 0, c1p1, v2, c2, 0, c2p1);
if (!param.startConnected && c1p1.isClose(c2p2, epsilon)) if (!param.startConnected && c1p1.isClose(c2p2, epsilon))
addLocation(locations, param, v1, c1, 0, c1p1, v2, c2, 1, c2p2); addLocation(locations, param, v1, c1, 0, c1p1, v2, c2, 1, c2p2);
// Determine the correct intersection method based on whether one or // Determine the correct intersection method based on whether one or
// curves are straight lines: // curves are straight lines:
(straight1 && straight2 (straight1 && straight2
? addLineIntersection ? addLineIntersection
: straight1 || straight2 : straight1 || straight2
? addCurveLineIntersections ? addCurveLineIntersections
: addCurveIntersections)( : addCurveIntersections)(
v1, v2, c1, c2, locations, param, v1, v2, c1, c2, locations, param,
// Define the defaults for these parameters of // Define the defaults for these parameters of
// addCurveIntersections(): // addCurveIntersections():
// tMin, tMax, uMin, uMax, oldTDiff, reverse, recursion // tMin, tMax, uMin, uMax, oldTDiff, reverse, recursion
0, 1, 0, 1, 0, false, 0); 0, 1, 0, 1, 0, false, 0);
// Handle the special case where the first curve's end-point // Handle the special case where the first curve's end-point
// overlaps with the second curve's start- or end-points. // overlaps with the second curve's start- or end-points.
if (!param.endConnected && c1p2.isClose(c2p1, epsilon)) if (!param.endConnected && c1p2.isClose(c2p1, epsilon))
addLocation(locations, param, v1, c1, 1, c1p2, v2, c2, 0, c2p1); addLocation(locations, param, v1, c1, 1, c1p2, v2, c2, 0, c2p1);
if (c1p2.isClose(c2p2, epsilon)) if (c1p2.isClose(c2p2, epsilon))
addLocation(locations, param, v1, c1, 1, c1p2, v2, c2, 1, c2p2); addLocation(locations, param, v1, c1, 1, c1p2, v2, c2, 1, c2p2);
}
return locations; return locations;
} }
}}; }};

40
src/path/PathItem.js
View file

@ -88,37 +88,15 @@ var PathItem = Item.extend(/** @lends PathItem# */{
values1 = self ? values2[i] : curve1.getValues(matrix1); values1 = self ? values2[i] : curve1.getValues(matrix1);
if (self) { if (self) {
// First check for self-intersections within the same curve // First check for self-intersections within the same curve
var seg1 = curve1.getSegment1(), var p1 = curve1.getSegment1()._point,
seg2 = curve1.getSegment2(), p2 = curve1.getSegment2()._point;
p1 = seg1._point, Curve.getIntersections(values1, null, curve1, curve1,
p2 = seg2._point, locations, {
h1 = seg1._handleOut, include: include,
h2 = seg2._handleIn, // Only possible if there is only one closed curve:
l1 = new Line(p1.subtract(h1), p1.add(h1)), startConnected: length1 === 1 && p1.equals(p2)
l2 = new Line(p2.subtract(h2), p1.add(h2)); }
// Check if extended handles of endpoints of this curve );
// intersects each other. We cannot have a self intersection
// within this curve if they don't intersect due to convex-hull
// property.
if (l1.intersect(l2, false)) {
// Self intersecting is found by dividing the curve in two
// and and then applying the normal curve intersection code.
var parts = Curve.subdivide(values1, 0.5);
Curve.getIntersections(parts[0], parts[1], curve1, curve1,
locations, {
include: include,
// Only possible if there is only one closed curve:
startConnected: length1 === 1 && p1.equals(p2),
// After splitting, the end is always connected:
endConnected: true,
renormalize: function(t1, t2) {
// Since the curve was split above, we need to
// adjust the parameters for both locations.
return [t1 / 2, (1 + t2) / 2];
}
}
);
}
} }
// Check for intersections with other curves. For self intersection, // Check for intersections with other curves. For self intersection,
// we can start at i + 1 instead of 0 // we can start at i + 1 instead of 0