8dcf114db9
M Intersection/DataTypes.cpp M Intersection/QuadraticIntersection_Test.cpp M Intersection/EdgeWalker.cpp M Intersection/LineQuadraticIntersection_Test.cpp M Intersection/LineIntersection_Test.cpp M Intersection/LineIntersection.cpp D Intersection/edge.xcodeproj M Intersection/SimplifyFindTop_Test.cpp M Intersection/DataTypes.h A Intersection/SimplifyRect4x4_Test.cpp M Intersection/CubicIntersection_Test.cpp M Intersection/QuadraticUtilities.h M Intersection/LineCubicIntersection_Test.cpp A Intersection/CurveUtilities.h M Intersection/QuadraticBezierClip.cpp M Intersection/QuadraticBounds.cpp M Intersection/LineUtilities.h M Intersection/Intersection_Tests.cpp M Intersection/Simplify.cpp M Intersection/EdgeWalker_TestUtility.cpp M Intersection/QuadraticUtilities.cpp M Intersection/thingsToDo.txt M Intersection/LineUtilities.cpp M Intersection/CubicUtilities.h M Intersection/SimplifyFindNext_Test.cpp M Intersection/Intersection_Tests.h M Intersection/CubicBezierClip.cpp M Intersection/ActiveEdge_Test.cpp M Intersection/CubicBounds.cpp M Intersection/Simplify.h M Intersection/SimplifyNew_Test.cpp M Intersection/EdgeWalker_Test.h M Intersection/CubicUtilities.cpp M Intersection/op.htm M Intersection/ConvexHull.cpp D Intersection/RectUtilities.cpp M Intersection/SimplifyAddIntersectingTs_Test.cpp git-svn-id: http://skia.googlecode.com/svn/trunk@4429 2bbb7eff-a529-9590-31e7-b0007b416f81
320 lines
12 KiB
C++
320 lines
12 KiB
C++
#include "CurveIntersection.h"
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#include "Intersections.h"
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#include "LineIntersection.h"
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#include <algorithm> // used for std::swap
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/*
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Determine the intersection point of two line segments
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Return FALSE if the lines don't intersect
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from: http://paulbourke.net/geometry/lineline2d/
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*/
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int intersect(const _Line& a, const _Line& b, double aRange[2], double bRange[2]) {
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double axLen = a[1].x - a[0].x;
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double ayLen = a[1].y - a[0].y;
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double bxLen = b[1].x - b[0].x;
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double byLen = b[1].y - b[0].y;
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/* Slopes match when denom goes to zero:
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axLen / ayLen == bxLen / byLen
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(ayLen * byLen) * axLen / ayLen == (ayLen * byLen) * bxLen / byLen
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byLen * axLen == ayLen * bxLen
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byLen * axLen - ayLen * bxLen == 0 ( == denom )
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*/
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double denom = byLen * axLen - ayLen * bxLen;
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if (approximately_zero_squared(denom)) {
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/* See if the axis intercepts match:
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ay - ax * ayLen / axLen == by - bx * ayLen / axLen
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axLen * (ay - ax * ayLen / axLen) == axLen * (by - bx * ayLen / axLen)
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axLen * ay - ax * ayLen == axLen * by - bx * ayLen
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*/
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if (approximately_equal_squared(axLen * a[0].y - ayLen * a[0].x,
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axLen * b[0].y - ayLen * b[0].x)) {
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const double* aPtr;
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const double* bPtr;
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if (fabs(axLen) > fabs(ayLen) || fabs(bxLen) > fabs(byLen)) {
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aPtr = &a[0].x;
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bPtr = &b[0].x;
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} else {
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aPtr = &a[0].y;
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bPtr = &b[0].y;
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}
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#if 0 // sorting edges fails to preserve original direction
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double aMin = aPtr[0];
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double aMax = aPtr[2];
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double bMin = bPtr[0];
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double bMax = bPtr[2];
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if (aMin > aMax) {
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std::swap(aMin, aMax);
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}
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if (bMin > bMax) {
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std::swap(bMin, bMax);
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}
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if (aMax < bMin || bMax < aMin) {
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return 0;
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}
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if (aRange) {
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aRange[0] = bMin <= aMin ? 0 : (bMin - aMin) / (aMax - aMin);
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aRange[1] = bMax >= aMax ? 1 : (bMax - aMin) / (aMax - aMin);
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}
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int bIn = (aPtr[0] - aPtr[2]) * (bPtr[0] - bPtr[2]) < 0;
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if (bRange) {
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bRange[bIn] = aMin <= bMin ? 0 : (aMin - bMin) / (bMax - bMin);
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bRange[!bIn] = aMax >= bMax ? 1 : (aMax - bMin) / (bMax - bMin);
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}
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return 1 + ((aRange[0] != aRange[1]) || (bRange[0] != bRange[1]));
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#else
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assert(aRange);
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assert(bRange);
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double a0 = aPtr[0];
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double a1 = aPtr[2];
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double b0 = bPtr[0];
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double b1 = bPtr[2];
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double at0 = (a0 - b0) / (a0 - a1);
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double at1 = (a0 - b1) / (a0 - a1);
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if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
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return 0;
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}
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aRange[0] = std::max(std::min(at0, 1.0), 0.0);
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aRange[1] = std::max(std::min(at1, 1.0), 0.0);
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int bIn = (a0 - a1) * (b0 - b1) < 0;
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bRange[bIn] = std::max(std::min((b0 - a0) / (b0 - b1), 1.0), 0.0);
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bRange[!bIn] = std::max(std::min((b0 - a1) / (b0 - b1), 1.0), 0.0);
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bool second = fabs(aRange[0] - aRange[1]) > FLT_EPSILON;
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assert((fabs(bRange[0] - bRange[1]) <= FLT_EPSILON) ^ second);
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return 1 + second;
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#endif
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}
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}
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double ab0y = a[0].y - b[0].y;
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double ab0x = a[0].x - b[0].x;
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double numerA = ab0y * bxLen - byLen * ab0x;
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if (numerA < 0 && denom > numerA || numerA > 0 && denom < numerA) {
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return 0;
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}
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double numerB = ab0y * axLen - ayLen * ab0x;
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if (numerB < 0 && denom > numerB || numerB > 0 && denom < numerB) {
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return 0;
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}
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/* Is the intersection along the the segments */
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if (aRange) {
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aRange[0] = numerA / denom;
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}
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if (bRange) {
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bRange[0] = numerB / denom;
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}
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return 1;
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}
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int horizontalIntersect(const _Line& line, double y, double tRange[2]) {
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double min = line[0].y;
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double max = line[1].y;
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if (min > max) {
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std::swap(min, max);
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}
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if (min > y || max < y) {
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return 0;
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}
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if (approximately_equal(min, max)) {
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tRange[0] = 0;
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tRange[1] = 1;
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return 2;
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}
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tRange[0] = (y - line[0].y) / (line[1].y - line[0].y);
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return 1;
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}
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// OPTIMIZATION Given: dy = line[1].y - line[0].y
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// and: xIntercept / (y - line[0].y) == (line[1].x - line[0].x) / dy
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// then: xIntercept * dy == (line[1].x - line[0].x) * (y - line[0].y)
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// Assuming that dy is always > 0, the line segment intercepts if:
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// left * dy <= xIntercept * dy <= right * dy
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// thus: left * dy <= (line[1].x - line[0].x) * (y - line[0].y) <= right * dy
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// (clever as this is, it does not give us the t value, so may be useful only
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// as a quick reject -- and maybe not then; it takes 3 muls, 3 adds, 2 cmps)
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int horizontalLineIntersect(const _Line& line, double left, double right,
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double y, double tRange[2]) {
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int result = horizontalIntersect(line, y, tRange);
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if (result != 1) {
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// FIXME: this is incorrect if result == 2
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return result;
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}
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double xIntercept = line[0].x + tRange[0] * (line[1].x - line[0].x);
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if (xIntercept > right || xIntercept < left) {
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return 0;
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}
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return result;
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}
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int horizontalIntersect(const _Line& line, double left, double right,
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double y, bool flipped, Intersections& intersections) {
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int result = horizontalIntersect(line, y, intersections.fT[0]);
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switch (result) {
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case 0:
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break;
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case 1: {
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double xIntercept = line[0].x + intersections.fT[0][0]
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* (line[1].x - line[0].x);
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if (xIntercept > right || xIntercept < left) {
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return 0;
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}
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intersections.fT[1][0] = (xIntercept - left) / (right - left);
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break;
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}
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case 2:
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#if 0 // sorting edges fails to preserve original direction
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double lineL = line[0].x;
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double lineR = line[1].x;
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if (lineL > lineR) {
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std::swap(lineL, lineR);
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}
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double overlapL = std::max(left, lineL);
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double overlapR = std::min(right, lineR);
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if (overlapL > overlapR) {
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return 0;
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}
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if (overlapL == overlapR) {
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result = 1;
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}
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intersections.fT[0][0] = (overlapL - line[0].x) / (line[1].x - line[0].x);
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intersections.fT[1][0] = (overlapL - left) / (right - left);
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if (result > 1) {
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intersections.fT[0][1] = (overlapR - line[0].x) / (line[1].x - line[0].x);
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intersections.fT[1][1] = (overlapR - left) / (right - left);
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}
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#else
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double a0 = line[0].x;
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double a1 = line[1].x;
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double b0 = flipped ? right : left;
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double b1 = flipped ? left : right;
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// FIXME: share common code below
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double at0 = (a0 - b0) / (a0 - a1);
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double at1 = (a0 - b1) / (a0 - a1);
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if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
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return 0;
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}
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intersections.fT[0][0] = std::max(std::min(at0, 1.0), 0.0);
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intersections.fT[0][1] = std::max(std::min(at1, 1.0), 0.0);
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int bIn = (a0 - a1) * (b0 - b1) < 0;
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intersections.fT[1][bIn] = std::max(std::min((b0 - a0) / (b0 - b1),
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1.0), 0.0);
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intersections.fT[1][!bIn] = std::max(std::min((b0 - a1) / (b0 - b1),
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1.0), 0.0);
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bool second = fabs(intersections.fT[0][0] - intersections.fT[0][1])
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> FLT_EPSILON;
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assert((fabs(intersections.fT[1][0] - intersections.fT[1][1])
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<= FLT_EPSILON) ^ second);
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return 1 + second;
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#endif
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break;
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}
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if (flipped) {
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// OPTIMIZATION: instead of swapping, pass original line, use [1].x - [0].x
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for (int index = 0; index < result; ++index) {
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intersections.fT[1][index] = 1 - intersections.fT[1][index];
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}
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}
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return result;
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}
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static int verticalIntersect(const _Line& line, double x, double tRange[2]) {
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double min = line[0].x;
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double max = line[1].x;
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if (min > max) {
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std::swap(min, max);
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}
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if (min > x || max < x) {
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return 0;
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}
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if (approximately_equal(min, max)) {
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tRange[0] = 0;
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tRange[1] = 1;
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return 2;
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}
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tRange[0] = (x - line[0].x) / (line[1].x - line[0].x);
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return 1;
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}
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int verticalIntersect(const _Line& line, double top, double bottom,
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double x, bool flipped, Intersections& intersections) {
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int result = verticalIntersect(line, x, intersections.fT[0]);
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switch (result) {
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case 0:
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break;
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case 1: {
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double yIntercept = line[0].y + intersections.fT[0][0]
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* (line[1].y - line[0].y);
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if (yIntercept > bottom || yIntercept < top) {
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return 0;
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}
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intersections.fT[1][0] = (yIntercept - top) / (bottom - top);
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break;
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}
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case 2:
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#if 0 // sorting edges fails to preserve original direction
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double lineT = line[0].y;
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double lineB = line[1].y;
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if (lineT > lineB) {
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std::swap(lineT, lineB);
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}
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double overlapT = std::max(top, lineT);
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double overlapB = std::min(bottom, lineB);
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if (overlapT > overlapB) {
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return 0;
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}
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if (overlapT == overlapB) {
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result = 1;
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}
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intersections.fT[0][0] = (overlapT - line[0].y) / (line[1].y - line[0].y);
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intersections.fT[1][0] = (overlapT - top) / (bottom - top);
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if (result > 1) {
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intersections.fT[0][1] = (overlapB - line[0].y) / (line[1].y - line[0].y);
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intersections.fT[1][1] = (overlapB - top) / (bottom - top);
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}
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#else
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double a0 = line[0].y;
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double a1 = line[1].y;
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double b0 = flipped ? bottom : top;
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double b1 = flipped ? top : bottom;
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// FIXME: share common code above
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double at0 = (a0 - b0) / (a0 - a1);
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double at1 = (a0 - b1) / (a0 - a1);
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if ((at0 < 0 && at1 < 0) || (at0 > 1 && at1 > 1)) {
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return 0;
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}
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intersections.fT[0][0] = std::max(std::min(at0, 1.0), 0.0);
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intersections.fT[0][1] = std::max(std::min(at1, 1.0), 0.0);
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int bIn = (a0 - a1) * (b0 - b1) < 0;
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intersections.fT[1][bIn] = std::max(std::min((b0 - a0) / (b0 - b1),
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1.0), 0.0);
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intersections.fT[1][!bIn] = std::max(std::min((b0 - a1) / (b0 - b1),
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1.0), 0.0);
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bool second = fabs(intersections.fT[0][0] - intersections.fT[0][1])
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> FLT_EPSILON;
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assert((fabs(intersections.fT[1][0] - intersections.fT[1][1])
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<= FLT_EPSILON) ^ second);
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return 1 + second;
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#endif
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break;
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}
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if (flipped) {
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// OPTIMIZATION: instead of swapping, pass original line, use [1].y - [0].y
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for (int index = 0; index < result; ++index) {
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intersections.fT[1][index] = 1 - intersections.fT[1][index];
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}
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}
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return result;
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}
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// from http://www.bryceboe.com/wordpress/wp-content/uploads/2006/10/intersect.py
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// 4 subs, 2 muls, 1 cmp
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static bool ccw(const _Point& A, const _Point& B, const _Point& C) {
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return (C.y - A.y) * (B.x - A.x) > (B.y - A.y) * (C.x - A.x);
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}
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// 16 subs, 8 muls, 6 cmps
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bool testIntersect(const _Line& a, const _Line& b) {
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return ccw(a[0], b[0], b[1]) != ccw(a[1], b[0], b[1])
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&& ccw(a[0], a[1], b[0]) != ccw(a[0], a[1], b[1]);
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}
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