235f56a92f
add quartic solution for intersecting quadratics git-svn-id: http://skia.googlecode.com/svn/trunk@5541 2bbb7eff-a529-9590-31e7-b0007b416f81
84 lines
2.6 KiB
C++
84 lines
2.6 KiB
C++
/*
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* Copyright 2012 Google Inc.
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*
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* Use of this source code is governed by a BSD-style license that can be
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* found in the LICENSE file.
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*/
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#include "CurveIntersection.h"
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#include "CurveUtilities.h"
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#include "LineParameters.h"
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#include <algorithm> // used for std::swap
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#define DEBUG_BEZIER_CLIP 1
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// return false if unable to clip (e.g., unable to create implicit line)
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// caller should subdivide, or create degenerate if the values are too small
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bool bezier_clip(const Quadratic& q1, const Quadratic& q2, double& minT, double& maxT) {
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minT = 1;
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maxT = 0;
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// determine normalized implicit line equation for pt[0] to pt[3]
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// of the form ax + by + c = 0, where a*a + b*b == 1
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// find the implicit line equation parameters
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LineParameters endLine;
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endLine.quadEndPoints(q1);
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if (!endLine.normalize()) {
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printf("line cannot be normalized: need more code here\n");
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assert(0);
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return false;
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}
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double distance = endLine.controlPtDistance(q1);
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// find fat line
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double top = 0;
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double bottom = distance / 2; // http://students.cs.byu.edu/~tom/557/text/cic.pdf (7.6)
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if (top > bottom) {
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std::swap(top, bottom);
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}
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// compute intersecting candidate distance
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Quadratic distance2y; // points with X of (0, 1/2, 1)
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endLine.quadDistanceY(q2, distance2y);
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int flags = 0;
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if (approximately_lesser(distance2y[0].y, top)) {
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flags |= kFindTopMin;
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} else if (approximately_greater(distance2y[0].y, bottom)) {
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flags |= kFindBottomMin;
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} else {
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minT = 0;
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}
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if (approximately_lesser(distance2y[2].y, top)) {
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flags |= kFindTopMax;
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} else if (approximately_greater(distance2y[2].y, bottom)) {
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flags |= kFindBottomMax;
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} else {
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maxT = 1;
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}
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// Find the intersection of distance convex hull and fat line.
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int idx = 0;
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do {
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int next = idx + 1;
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if (next == 3) {
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next = 0;
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}
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x_at(distance2y[idx], distance2y[next], top, bottom, flags, minT, maxT);
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idx = next;
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} while (idx);
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#if DEBUG_BEZIER_CLIP
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_Rect r1, r2;
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r1.setBounds(q1);
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r2.setBounds(q2);
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_Point testPt = {0.487, 0.337};
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if (r1.contains(testPt) && r2.contains(testPt)) {
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printf("%s q1=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g)"
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" q2=(%1.9g,%1.9g %1.9g,%1.9g %1.9g,%1.9g) minT=%1.9g maxT=%1.9g\n",
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__FUNCTION__, q1[0].x, q1[0].y, q1[1].x, q1[1].y, q1[2].x, q1[2].y,
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q2[0].x, q2[0].y, q2[1].x, q2[1].y, q2[2].x, q2[2].y, minT, maxT);
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}
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#endif
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return minT < maxT; // returns false if distance shows no intersection
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}
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