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/*
* Copyright 2012 Google Inc.
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "CurveIntersection.h"
#include "CurveUtilities.h"
#include "LineParameters.h"
// return false if unable to clip (e.g., unable to create implicit line)
// caller should subdivide, or create degenerate if the values are too small
bool bezier_clip(const Cubic& cubic1, const Cubic& cubic2, double& minT, double& maxT) {
minT = 1;
maxT = 0;
// determine normalized implicit line equation for pt[0] to pt[3]
// of the form ax + by + c = 0, where a*a + b*b == 1
// find the implicit line equation parameters
LineParameters endLine;
endLine.cubicEndPoints(cubic1);
if (!endLine.normalize()) {
printf("line cannot be normalized: need more code here\n");
return false;
}
double distance[2];
distance[0] = endLine.controlPtDistance(cubic1, 1);
distance[1] = endLine.controlPtDistance(cubic1, 2);
// find fat line
double top = distance[0];
double bottom = distance[1];
if (top > bottom) {
SkTSwap(top, bottom);
}
if (top * bottom >= 0) {
const double scale = 3/4.0; // http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf (13)
if (top < 0) {
top *= scale;
bottom = 0;
} else {
top = 0;
bottom *= scale;
}
} else {
const double scale = 4/9.0; // http://cagd.cs.byu.edu/~tom/papers/bezclip.pdf (15)
top *= scale;
bottom *= scale;
}
// compute intersecting candidate distance
Cubic distance2y; // points with X of (0, 1/3, 2/3, 1)
endLine.cubicDistanceY(cubic2, distance2y);
int flags = 0;
if (approximately_lesser_or_equal(distance2y[0].y, top)) {
flags |= kFindTopMin;
} else if (approximately_greater_or_equal(distance2y[0].y, bottom)) {
flags |= kFindBottomMin;
} else {
minT = 0;
}
if (approximately_lesser_or_equal(distance2y[3].y, top)) {
flags |= kFindTopMax;
} else if (approximately_greater_or_equal(distance2y[3].y, bottom)) {
flags |= kFindBottomMax;
} else {
maxT = 1;
}
// Find the intersection of distance convex hull and fat line.
char to_0[2];
char to_3[2];
bool do_1_2_edge = convex_x_hull(distance2y, to_0, to_3);
x_at(distance2y[0], distance2y[to_0[0]], top, bottom, flags, minT, maxT);
if (to_0[0] != to_0[1]) {
x_at(distance2y[0], distance2y[to_0[1]], top, bottom, flags, minT, maxT);
}
x_at(distance2y[to_3[0]], distance2y[3], top, bottom, flags, minT, maxT);
if (to_3[0] != to_3[1]) {
x_at(distance2y[to_3[1]], distance2y[3], top, bottom, flags, minT, maxT);
}
if (do_1_2_edge) {
x_at(distance2y[1], distance2y[2], top, bottom, flags, minT, maxT);
}
return minT < maxT; // returns false if distance shows no intersection
}
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