mirror of
https://github.com/scratchfoundation/paper.js.git
synced 2025-01-07 13:22:07 -05:00
436 lines
16 KiB
JavaScript
436 lines
16 KiB
JavaScript
new function() {
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var MAX_RECURSION = 20;
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var MAX_ITERATION = 20;
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/**
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* This method is analogous to paperjs#PathItem.getIntersections, but calls
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* Curve.getIntersections2 instead.
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*/
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PathItem.prototype.getIntersections2 = function(path) {
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// First check the bounds of the two paths. If they don't intersect,
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// we don't need to iterate through their curves.
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if (!this.getBounds().touches(path.getBounds()))
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return [];
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var locations = [],
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curves1 = this.getCurves(),
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curves2 = path.getCurves(),
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length2 = curves2.length,
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values2 = [];
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for (var i = 0; i < length2; i++)
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values2[i] = curves2[i].getValues();
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for (var i = 0, l = curves1.length; i < l; i++) {
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var curve1 = curves1[i],
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values1 = curve1.getValues();
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for (var j = 0; j < length2; j++)
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Curve.getIntersections2(values1, values2[j], curve1, curves2[j],
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locations);
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}
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return locations;
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};
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/**
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* This method is analogous to paperjs#Curve.getIntersections
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*/
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Curve.getIntersections2 = function(v1, v2, curve1, curve2, locations) {
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var linear1 = Curve.isLinear(v1),
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linear2 = Curve.isLinear(v2);
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// Determine the correct intersection method based on values of linear1 & 2:
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(linear1 && linear2
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? getLineLineIntersection
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: linear1 || linear2
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? getCurveLineIntersections
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: getCurveIntersections)(v1, v2, curve1, curve2, locations);
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return locations;
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};
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function addLocation(locations, curve1, parameter, point, curve2) {
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// Avoid duplicates when hitting segments (closed paths too)
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var first = locations[0],
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last = locations[locations.length - 1];
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if ((!first || !point.equals(first._point))
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&& (!last || !point.equals(last._point)))
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locations.push(new CurveLocation(curve1, parameter, point, curve2));
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}
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function getCurveIntersections(v1, v2, curve1, curve2, locations, v1t, v2t,
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recursion) {
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// NOTE: v1t and v1t are only used for recusion
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recursion = (recursion || 0) + 1;
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// Avoid endless recursion.
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// Perhaps we should fall back to a more expensive method after this, but
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// so far endless recursion happens only when there is no real intersection
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// and the infinite fatline continue to intersect with the other curve
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// outside its bounds!
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if (recursion > MAX_RECURSION)
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return;
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// Set up the parameter ranges.
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v1t = v1t || [ 0, 1 ];
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v2t = v2t || [ 0, 1 ];
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// Get the clipped parts from the original curve, to avoid cumulative errors
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var p1 = Curve.getPart(v1, v1t[0], v1t[1]);
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var p2 = Curve.getPart(v2, v2t[0], v2t[1]);
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// markCurve(p1, '#f0f', true);
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// markCurve(p2, '#0ff', false);
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var iteration = 0;
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// Loop until both parameter range converge. We have to handle the
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// degenerate case seperately, where fat-line clipping can become
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// numerically unstable when one of the curves has converged to a point and
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// the other hasn't.
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while (iteration++ < MAX_ITERATION
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&& (Math.abs(v1t[1] - v1t[0]) > /*#=*/ Numerical.TOLERANCE
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|| Math.abs(v2t[1] - v2t[0]) > /*#=*/ Numerical.TOLERANCE)) {
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// First we clip v2 with v1's fat-line
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var range = v2t.slice();
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var intersects1 = clipFatLine(p1, p2, range),
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intersects2 = 0;
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// Stop if there are no possible intersections
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if (intersects1 === 0)
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break;
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if (intersects1 > 0) {
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// Get the clipped parts from the original v2, to avoid cumulative
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// errors ...and reuse some objects.
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v2t = range;
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p2 = Curve.getPart(v2, v2t[0], v2t[1]);
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// markCurve(p2, '#0ff', false);
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// Next we clip v1 with nuv2's fat-line
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intersects2 = clipFatLine(p2, p1, range = v1t.slice());
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// Stop if there are no possible intersections
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if (intersects2 === 0)
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break;
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if (intersects1 > 0) {
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// Get the clipped parts from the original v2, to avoid
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// cumulative errors
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v1t = range;
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p1 = Curve.getPart(v1, v1t[0], v1t[1]);
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}
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// markCurve(p1, '#f0f', true);
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}
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// Get the clipped parts from the original v1
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// Check if there could be multiple intersections
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if (intersects1 < 0 || intersects2 < 0) {
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// Subdivide the curve which has converged the least from the
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// original range [0,1], which would be the curve with the largest
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// parameter range after clipping
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if (v1t[1] - v1t[0] > v2t[1] - v2t[0]) {
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// subdivide v1 and recurse
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var t = (v1t[0] + v1t[1]) / 2;
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getCurveIntersections(v1, v2, curve1, curve2, locations,
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[ v1t[0], t ], v2t, recursion);
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getCurveIntersections(v1, v2, curve1, curve2, locations,
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[ t, v1t[1] ], v2t, recursion);
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break;
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} else {
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// subdivide v2 and recurse
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var t = (v2t[0] + v2t[1]) / 2;
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getCurveIntersections(v1, v2, curve1, curve2, locations, v1t,
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[ v2t[0], t ], recursion);
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getCurveIntersections(v1, v2, curve1, curve2, locations, v1t,
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[ t, v2t[1] ], recursion);
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break;
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}
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}
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// We need to bailout of clipping and try a numerically stable method if
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// any of the following are true.
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// 1. One of the parameter ranges is converged to a point.
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// 2. Both of the parameter ranges have converged reasonably well
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// (according to Numerical.TOLERANCE).
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// 3. One of the parameter range is converged enough so that it is
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// *flat enough* to calculate line curve intersection implicitly.
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//
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// Check if one of the parameter range has converged completely to a
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// point. Now things could get only worse if we iterate more for the
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// other curve to converge if it hasn't yet happened so.
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var converged1 = (Math.abs(v1t[1] - v1t[0]) < /*#=*/ Numerical.EPSILON),
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converged2 = (Math.abs(v2t[1] - v2t[0]) < /*#=*/ Numerical.EPSILON);
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if (converged1 || converged2) {
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addLocation(locations, curve1, null, converged1
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? curve1.getPointAt(v1t[0], true)
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: curve2.getPointAt(v2t[0], true), curve2);
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break;
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}
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if (Math.abs(v1t[1] - v1t[0]) <= /*#=*/ Numerical.TOLERANCE
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&& Math.abs(v2t[1] - v2t[0]) <= /*#=*/ Numerical.TOLERANCE) {
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// Both parameter ranges have converged.
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addLocation(locations, curve1, v1t[0],
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curve1.getPointAt(v1t[0], true), curve2);
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break;
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}
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// see if either or both of the curves are flat enough to be treated
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// as lines.
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var flat1 = Curve.isFlatEnough(p1, /*#=*/ Numerical.TOLERANCE),
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flat2 = Curve.isFlatEnough(p2, /*#=*/ Numerical.TOLERANCE);
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if (flat1 && flat2) {
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getLineLineIntersection(p1, p2, curve1, curve2, locations);
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break;
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}
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if (flat1 || flat2) {
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// Use curve line intersection method while specifying which
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// curve to be treated as line
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getCurveLineIntersections(p1, p2, curve1, curve2, locations, flat1);
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break;
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}
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}
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}
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/**
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* Clip curve V2 with fat-line of v1
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* @param {Array} v1 section of the first curve, for which we will make a
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* fat-line
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* @param {Array} v2 section of the second curve; we will clip this curve with
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* the fat-line of v1
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* @param {Object} v2t the parameter range of v2
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* @return {Number} 0: no Intersection, 1: one intersection, -1: more than one
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* ntersection
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*/
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function clipFatLine(v1, v2, v2t) {
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// first curve, P
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var p0x = v1[0], p0y = v1[1], p1x = v1[2], p1y = v1[3],
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p2x = v1[4], p2y = v1[5], p3x = v1[6], p3y = v1[7],
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// second curve, Q
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q0x = v2[0], q0y = v2[1], q1x = v2[2], q1y = v2[3],
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q2x = v2[4], q2y = v2[5], q3x = v2[6], q3y = v2[7],
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// Calculate the fat-line L for P is the baseline l and two
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// offsets which completely encloses the curve P.
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d1 = getSignedDistance(p0x, p0y, p3x, p3y, p1x, p1y) || 0,
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d2 = getSignedDistance(p0x, p0y, p3x, p3y, p2x, p2y) || 0,
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factor = d1 * d2 > 0 ? 3 / 4 : 4 / 9,
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dmin = factor * Math.min(0, d1, d2),
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dmax = factor * Math.max(0, d1, d2),
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// Calculate non-parametric bezier curve D(ti, di(t)) - di(t) is the
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// distance of Q from the baseline l of the fat-line, ti is equally
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// spaced in [0, 1]
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dq0 = getSignedDistance(p0x, p0y, p3x, p3y, q0x, q0y),
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dq1 = getSignedDistance(p0x, p0y, p3x, p3y, q1x, q1y),
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dq2 = getSignedDistance(p0x, p0y, p3x, p3y, q2x, q2y),
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dq3 = getSignedDistance(p0x, p0y, p3x, p3y, q3x, q3y),
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// Find the minimum and maximum distances from l, this is useful for
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// checking whether the curves intersect with each other or not.
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mindist = Math.min(dq0, dq1, dq2, dq3),
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maxdist = Math.max(dq0, dq1, dq2, dq3);
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// If the fatlines don't overlap, we have no intersections!
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if (dmin > maxdist || dmax < mindist)
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return 0;
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var tmp;
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if (dq3 < dq0) {
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tmp = dmin;
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dmin = dmax;
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dmax = tmp;
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}
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var Dt = getConvexHull(dq0, dq1, dq2, dq3);
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// Calculate the convex hull for non-parametric bezier curve D(ti, di(t))
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// Now we clip the convex hulls for D(ti, di(t)) with dmin and dmax
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// for the coorresponding t values (tmin, tmax): Portions of curve v2 before
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// tmin and after tmax can safely be clipped away
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var tmaxdmin = -Infinity, ixd, ixdx, i, len, inv_m;
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var tmin = Infinity, tmax = -Infinity, Dtl, dtlx1, dtly1, dtlx2, dtly2;
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for (i = 0, len = Dt.length; i < len; i++) {
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Dtl = Dt[i];
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dtlx1 = Dtl[0];
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dtly1 = Dtl[1];
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dtlx2 = Dtl[2];
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dtly2 = Dtl[3];
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if (dtly2 < dtly1) {
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tmp = dtly2;
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dtly2 = dtly1;
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dtly1 = tmp;
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tmp = dtlx2;
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dtlx2 = dtlx1;
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dtlx1 = tmp;
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}
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// we know that (dtlx2 - dtlx1) is never 0
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inv_m = (dtly2 - dtly1) / (dtlx2 - dtlx1);
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if (dmin >= dtly1 && dmin <= dtly2) {
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ixdx = dtlx1 + (dmin - dtly1) / inv_m;
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if (ixdx < tmin) tmin = ixdx;
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if (ixdx > tmaxdmin) tmaxdmin = ixdx;
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}
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if (dmax >= dtly1 && dmax <= dtly2) {
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ixdx = dtlx1 + (dmax - dtly1) / inv_m;
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if (ixdx > tmax) tmax = ixdx;
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if (ixdx < tmin) tmin = 0;
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}
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}
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// Return the parameter values for v2 for which we can be sure that the
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// intersection with v1 lies within.
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if (tmin !== Infinity && tmax !== -Infinity) {
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var mindmin = Math.min(dmin, dmax);
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var mindmax = Math.max(dmin, dmax);
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if (dq3 > mindmin && dq3 < mindmax)
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tmax = 1;
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if (dq0 > mindmin && dq0 < mindmax)
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tmin = 0;
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if (tmaxdmin > tmax)
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tmax = 1;
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// tmin and tmax are within the range (0, 1). We need to project it to
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// the original parameter range for v2.
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var v2tmin = v2t[0];
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var tdiff = (v2t[1] - v2tmin);
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v2t[0] = v2tmin + tmin * tdiff;
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v2t[1] = v2tmin + tmax * tdiff;
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// If the new parameter range fails to converge by atleast 20% of the
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// original range, possibly we have multiple intersections. We need to
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// subdivide one of the curves.
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if ((tdiff - (v2t[1] - v2t[0])) / tdiff >= 0.2)
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return 1;
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}
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// TODO: Try checking with a perpendicular fatline to see if the curves
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// overlap if it is any faster than this
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if (Curve.getBounds(v1).touches(Curve.getBounds(v2)))
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return -1;
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return 0;
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}
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/**
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* Calculate the convex hull for the non-paramertic bezier curve D(ti, di(t)).
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* The ti is equally spaced across [0..1] — [0, 1/3, 2/3, 1] for
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* di(t), [dq0, dq1, dq2, dq3] respectively. In other words our CVs for the
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* curve are already sorted in the X axis in the increasing order. Calculating
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* convex-hull is much easier than a set of arbitrary points.
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*/
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function getConvexHull(dq0, dq1, dq2, dq3) {
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var distq1 = getSignedDistance(0, dq0, 1, dq3, 1 / 3, dq1);
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var distq2 = getSignedDistance(0, dq0, 1, dq3, 2 / 3, dq2);
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var hull;
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// Check if [1/3, dq1] and [2/3, dq2] are on the same side of line
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// [0,dq0, 1,dq3]
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if (distq1 * distq2 < 0) {
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// dq1 and dq2 lie on different sides on [0, q0, 1, q3]
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// Convexhull is a quadrilateral and line [0, q0, 1, q3] is NOT part of
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// the convexhull so we are pretty much done here.
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hull = [
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[ 0, dq0, 1 / 3, dq1 ],
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[ 1 / 3, dq1, 1, dq3 ],
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[ 2 / 3, dq2, 0, dq0 ],
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[ 1, dq3, 2 / 3, dq2 ]
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];
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} else {
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// dq1 and dq2 lie on the same sides on [0, q0, 1, q3]. c-hull can be a
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// triangle or a quadrilateral and line [0, q0, 1, q3] is part of the
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// c-hull. Check if the hull is a triangle or a quadrilateral
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var dqmin, dqmax, dqapex1, dqapex2;
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distq1 = Math.abs(distq1);
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distq2 = Math.abs(distq2);
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var vqa1a2x, vqa1a2y, vqa1Maxx, vqa1Maxy, vqa1Minx, vqa1Miny;
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if (distq1 > distq2) {
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dqmin = [ 2 / 3, dq2 ];
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dqmax = [ 1 / 3, dq1 ];
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// apex is dq3 and the other apex point is dq0 vector
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// dqapex->dqapex2 or base vector which is already part of c-hull
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vqa1a2x = 1;
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vqa1a2y = dq3 - dq0;
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// vector dqapex->dqmax
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vqa1Maxx = 2 / 3;
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vqa1Maxy = dq3 - dq1;
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// vector dqapex->dqmin
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vqa1Minx = 1 / 3;
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vqa1Miny = dq3 - dq2;
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} else {
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dqmin = [ 1 / 3, dq1 ];
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dqmax = [ 2 / 3, dq2 ];
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// apex is dq0 in this case, and the other apex point is dq3 vector
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// dqapex->dqapex2 or base vector which is already part of c-hull
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vqa1a2x = -1;
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vqa1a2y = dq0 - dq3;
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// vector dqapex->dqmax
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vqa1Maxx = -2 / 3;
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vqa1Maxy = dq0 - dq2;
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// vector dqapex->dqmin
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vqa1Minx = -1 / 3;
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vqa1Miny = dq0 - dq1;
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}
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// Compare cross products of these vectors to determine, if
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// point is in triangles [ dq3, dqMax, dq0 ] or [ dq0, dqMax, dq3 ]
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var vcrossa1a2_a1Min = vqa1a2x * vqa1Miny - vqa1a2y * vqa1Minx;
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var vcrossa1Max_a1Min = vqa1Maxx * vqa1Miny - vqa1Maxy * vqa1Minx;
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if (vcrossa1Max_a1Min * vcrossa1a2_a1Min < 0) {
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// Point [2/3, dq2] is inside the triangle and c-hull is a triangle
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hull = [
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[ 0, dq0, dqmax[0], dqmax[1] ],
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[ dqmax[0], dqmax[1], 1, dq3 ],
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[ 1, dq3, 0, dq0 ]
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];
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} else {
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// Convexhull is a quadrilateral and we need all lines in the
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// correct order where line [0, q0, 1, q3] is part of the c-hull
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hull = [
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[ 0, dq0, 1 / 3, dq1 ],
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[ 1 / 3, dq1, 2 / 3, dq2 ],
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[ 2 / 3, dq2, 1, dq3 ],
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[ 1, dq3, 0, dq0 ]
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];
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}
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}
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return hull;
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}
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// This is basically an "unrolled" version of #Line.getDistance() with sign
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// May be a static method could be better!
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function getSignedDistance(a1x, a1y, a2x, a2y, bx, by) {
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var m = (a2y - a1y) / (a2x - a1x),
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b = a1y - (m * a1x);
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return (by - (m * bx) - b) / Math.sqrt(m * m + 1);
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}
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/**
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* Intersections between curve and line becomes rather simple here mostly
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* because of Numerical class. We can rotate the curve and line so that the line
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* is on X axis, and solve the implicit equations for X axis and the curve
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*/
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function getCurveLineIntersections(v1, v2, curve1, curve2, locations, flip) {
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if (flip === undefined)
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flip = Curve.isLinear(v1);
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var vc = flip ? v2 : v1,
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vl = flip ? v1 : v2,
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l1x = vl[0], l1y = vl[1],
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l2x = vl[6], l2y = vl[7],
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// Rotate both the curve and line around l1 so that line is on x axis
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lvx = l2x - l1x,
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lvy = l2y - l1y,
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// Angle with x axis (1, 0)
|
|
angle = Math.atan2(-lvy, lvx),
|
|
sin = Math.sin(angle),
|
|
cos = Math.cos(angle),
|
|
// (rl1x, rl1y) = (0, 0)
|
|
rl2x = lvx * cos - lvy * sin,
|
|
rl2y = lvy * cos + lvx * sin,
|
|
vcr = [];
|
|
|
|
for(var i = 0; i < 8; i += 2) {
|
|
var x = vc[i] - l1x,
|
|
y = vc[i + 1] - l1y;
|
|
vcr.push(
|
|
x * cos - y * sin,
|
|
y * cos + x * sin);
|
|
}
|
|
var roots = [],
|
|
count = Curve.solveCubic(vcr, 1, 0, roots);
|
|
// NOTE: count could theoretically be -1 for inifnite solutions, although
|
|
// that should only happen with lines, in which case we should not be here.
|
|
for (var i = 0; i < count; i++) {
|
|
var t = roots[i];
|
|
if (t >= 0 && t <= 1) {
|
|
var point = Curve.evaluate(vcr, t, true, 0);
|
|
// We do have a point on the infinite line. Check if it falls on the
|
|
// line *segment*.
|
|
if (point.x >= 0 && point.x <= rl2x)
|
|
addLocation(locations,
|
|
flip ? curve2 : curve1,
|
|
// The actual intersection point
|
|
t, Curve.evaluate(vc, t, true, 0),
|
|
flip ? curve1 : curve2);
|
|
}
|
|
}
|
|
}
|
|
|
|
function getLineLineIntersection(v1, v2, curve1, curve2, locations) {
|
|
var point = Line.intersect(
|
|
v1[0], v1[1], v1[6], v1[7],
|
|
v2[0], v2[1], v2[6], v2[7], false);
|
|
// Passing null for parameter leads to lazy determination of parameter
|
|
// values in CurveLocation#getParameter() only once they are requested.
|
|
if (point)
|
|
addLocation(locations, curve1, null, point, curve2);
|
|
}
|
|
|
|
};
|