work in progress for shape operations
A experimental/Intersection
A experimental/Intersection/Intersections.h
A experimental/Intersection/DataTypes.cpp
A experimental/Intersection/QuadraticReduceOrder.cpp
A experimental/Intersection/IntersectionUtilities.cpp
A experimental/Intersection/CubicIntersection_Tests.h
A experimental/Intersection/LineParameteters_Test.cpp
A experimental/Intersection/ReduceOrder.cpp
A experimental/Intersection/QuadraticIntersection.cpp
A experimental/Intersection/Extrema.h
A experimental/Intersection/CubicIntersection_TestData.h
A experimental/Intersection/QuadraticParameterization_Test.cpp
A experimental/Intersection/TestUtilities.cpp
A experimental/Intersection/CubicRoots.cpp
A experimental/Intersection/QuadraticParameterization.cpp
A experimental/Intersection/QuadraticSubDivide.cpp
A experimental/Intersection/LineIntersection_Test.cpp
A experimental/Intersection/LineIntersection.cpp
A experimental/Intersection/CubicParameterizationCode.cpp
A experimental/Intersection/LineParameters.h
A experimental/Intersection/CubicIntersection.h
A experimental/Intersection/CubeRoot.cpp
A experimental/Intersection/SkAntiEdge.h
A experimental/Intersection/ConvexHull_Test.cpp
A experimental/Intersection/CubicBezierClip_Test.cpp
A experimental/Intersection/CubicIntersection_Tests.cpp
A experimental/Intersection/CubicBezierClip.cpp
A experimental/Intersection/CubicIntersectionT.cpp
A experimental/Intersection/Inline_Tests.cpp
A experimental/Intersection/ReduceOrder_Test.cpp
A experimental/Intersection/QuadraticIntersection_TestData.h
A experimental/Intersection/DataTypes.h
A experimental/Intersection/Extrema.cpp
A experimental/Intersection/EdgeApp.cpp
A experimental/Intersection/CubicIntersection_TestData.cpp
A experimental/Intersection/IntersectionUtilities.h
A experimental/Intersection/CubicReduceOrder.cpp
A experimental/Intersection/CubicCoincidence.cpp
A experimental/Intersection/CubicIntersection_Test.cpp
A experimental/Intersection/CubicIntersection.cpp
A experimental/Intersection/QuadraticUtilities.h
A experimental/Intersection/SkAntiEdge.cpp
A experimental/Intersection/TestUtilities.h
A experimental/Intersection/CubicParameterization_Test.cpp
A experimental/Intersection/LineIntersection.h
A experimental/Intersection/CubicSubDivide.cpp
A experimental/Intersection/CubicParameterization.cpp
A experimental/Intersection/QuadraticBezierClip_Test.cpp
A experimental/Intersection/QuadraticBezierClip.cpp
A experimental/Intersection/BezierClip_Test.cpp
A experimental/Intersection/ConvexHull.cpp
A experimental/Intersection/BezierClip.cpp
A experimental/Intersection/QuadraticIntersection_TestData.cpp
git-svn-id: http://skia.googlecode.com/svn/trunk@3005 2bbb7eff-a529-9590-31e7-b0007b416f81
diff --git a/experimental/Intersection/QuadraticReduceOrder.cpp b/experimental/Intersection/QuadraticReduceOrder.cpp
new file mode 100644
index 0000000..02d1956
--- /dev/null
+++ b/experimental/Intersection/QuadraticReduceOrder.cpp
@@ -0,0 +1,164 @@
+#include "CubicIntersection.h"
+#include "Extrema.h"
+#include "IntersectionUtilities.h"
+#include "LineParameters.h"
+
+static double interp_quad_coords(double a, double b, double c, double t)
+{
+ double ab = interp(a, b, t);
+ double bc = interp(b, c, t);
+ return interp(ab, bc, t);
+}
+
+static int coincident_line(const Quadratic& quad, Quadratic& reduction) {
+ reduction[0] = reduction[1] = quad[0];
+ return 1;
+}
+
+static int vertical_line(const Quadratic& quad, Quadratic& reduction) {
+ double tValue;
+ reduction[0] = quad[0];
+ reduction[1] = quad[2];
+ int smaller = reduction[1].y > reduction[0].y;
+ int larger = smaller ^ 1;
+ if (SkFindQuadExtrema(quad[0].y, quad[1].y, quad[2].y, &tValue)) {
+ double yExtrema = interp_quad_coords(quad[0].y, quad[1].y, quad[2].y, tValue);
+ if (reduction[smaller].y > yExtrema) {
+ reduction[smaller].y = yExtrema;
+ } else if (reduction[larger].y < yExtrema) {
+ reduction[larger].y = yExtrema;
+ }
+ }
+ return 2;
+}
+
+static int horizontal_line(const Quadratic& quad, Quadratic& reduction) {
+ double tValue;
+ reduction[0] = quad[0];
+ reduction[1] = quad[2];
+ int smaller = reduction[1].x > reduction[0].x;
+ int larger = smaller ^ 1;
+ if (SkFindQuadExtrema(quad[0].x, quad[1].x, quad[2].x, &tValue)) {
+ double xExtrema = interp_quad_coords(quad[0].x, quad[1].x, quad[2].x, tValue);
+ if (reduction[smaller].x > xExtrema) {
+ reduction[smaller].x = xExtrema;
+ } else if (reduction[larger].x < xExtrema) {
+ reduction[larger].x = xExtrema;
+ }
+ }
+ return 2;
+}
+
+static int check_linear(const Quadratic& quad, Quadratic& reduction,
+ int minX, int maxX, int minY, int maxY) {
+ int startIndex = 0;
+ int endIndex = 2;
+ while (quad[startIndex].approximatelyEqual(quad[endIndex])) {
+ --endIndex;
+ if (endIndex == 0) {
+ printf("%s shouldn't get here if all four points are about equal", __FUNCTION__);
+ assert(0);
+ }
+ }
+ LineParameters lineParameters;
+ lineParameters.quadEndPoints(quad, startIndex, endIndex);
+ double normalSquared = lineParameters.normalSquared();
+ double distance = lineParameters.controlPtDistance(quad); // not normalized
+ double limit = normalSquared * SquaredEpsilon;
+ double distSq = distance * distance;
+ if (distSq > limit) {
+ return 0;
+ }
+ // four are colinear: return line formed by outside
+ reduction[0] = quad[0];
+ reduction[1] = quad[2];
+ int sameSide;
+ bool useX = quad[maxX].x - quad[minX].x >= quad[maxY].y - quad[minY].y;
+ if (useX) {
+ sameSide = sign(quad[0].x - quad[1].x) + sign(quad[2].x - quad[1].x);
+ } else {
+ sameSide = sign(quad[0].y - quad[1].y) + sign(quad[2].y - quad[1].y);
+ }
+ if ((sameSide & 3) != 2) {
+ return 2;
+ }
+ double tValue;
+ int root;
+ if (useX) {
+ root = SkFindQuadExtrema(quad[0].x, quad[1].x, quad[2].x, &tValue);
+ } else {
+ root = SkFindQuadExtrema(quad[0].y, quad[1].y, quad[2].y, &tValue);
+ }
+ if (root) {
+ _Point extrema;
+ extrema.x = interp_quad_coords(quad[0].x, quad[1].x, quad[2].x, tValue);
+ extrema.y = interp_quad_coords(quad[0].x, quad[1].x, quad[2].x, tValue);
+ // sameSide > 0 means mid is smaller than either [0] or [2], so replace smaller
+ int replace;
+ if (useX) {
+ if (extrema.x < quad[0].x ^ extrema.x < quad[2].x) {
+ return 2;
+ }
+ replace = (extrema.x < quad[0].x | extrema.x < quad[2].x)
+ ^ quad[0].x < quad[2].x;
+ } else {
+ if (extrema.y < quad[0].y ^ extrema.y < quad[2].y) {
+ return 2;
+ }
+ replace = (extrema.y < quad[0].y | extrema.y < quad[2].y)
+ ^ quad[0].y < quad[2].y;
+ }
+ reduction[replace] = extrema;
+ }
+ return 2;
+}
+
+// reduce to a quadratic or smaller
+// look for identical points
+// look for all four points in a line
+ // note that three points in a line doesn't simplify a cubic
+// look for approximation with single quadratic
+ // save approximation with multiple quadratics for later
+int reduceOrder(const Quadratic& quad, Quadratic& reduction) {
+ int index, minX, maxX, minY, maxY;
+ int minXSet, minYSet;
+ minX = maxX = minY = maxY = 0;
+ minXSet = minYSet = 0;
+ for (index = 1; index < 3; ++index) {
+ if (quad[minX].x > quad[index].x) {
+ minX = index;
+ }
+ if (quad[minY].y > quad[index].y) {
+ minY = index;
+ }
+ if (quad[maxX].x < quad[index].x) {
+ maxX = index;
+ }
+ if (quad[maxY].y < quad[index].y) {
+ maxY = index;
+ }
+ }
+ for (index = 0; index < 3; ++index) {
+ if (approximately_equal(quad[index].x, quad[minX].x)) {
+ minXSet |= 1 << index;
+ }
+ if (approximately_equal(quad[index].y, quad[minY].y)) {
+ minYSet |= 1 << index;
+ }
+ }
+ if (minXSet == 0xF) { // test for vertical line
+ if (minYSet == 0xF) { // return 1 if all four are coincident
+ return coincident_line(quad, reduction);
+ }
+ return vertical_line(quad, reduction);
+ }
+ if (minYSet == 0xF) { // test for horizontal line
+ return horizontal_line(quad, reduction);
+ }
+ int result = check_linear(quad, reduction, minX, maxX, minY, maxY);
+ if (result) {
+ return result;
+ }
+ memcpy(reduction, quad, sizeof(Quadratic));
+ return 3;
+}