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/ConvexHull_Test.cpp b/experimental/Intersection/ConvexHull_Test.cpp
new file mode 100644
index 0000000..dffca6d
--- /dev/null
+++ b/experimental/Intersection/ConvexHull_Test.cpp
@@ -0,0 +1,465 @@
+#include "CubicIntersection.h"
+#include "CubicIntersection_Tests.h"
+#include "IntersectionUtilities.h"
+
+const Cubic convex[] = {
+ {{0, 0}, {2, 0}, {2, 1}, {0, 1}},
+ {{1, 0}, {1, 1}, {0, 1}, {0, 0}},
+ {{1, 1}, {0, 1}, {0, 0}, {1, 0}},
+ {{0, 1}, {0, 0}, {1, 0}, {1, 1}},
+ {{0, 0}, {10, 0}, {10, 10}, {5, 6}},
+};
+
+size_t convex_count = sizeof(convex) / sizeof(convex[0]);
+
+const Cubic bowtie[] = {
+ {{0, 0}, {1, 1}, {1, 0}, {0, 1}},
+ {{1, 0}, {0, 1}, {1, 1}, {0, 0}},
+ {{1, 1}, {0, 0}, {0, 1}, {1, 0}},
+ {{0, 1}, {1, 0}, {0, 0}, {1, 1}},
+};
+
+size_t bowtie_count = sizeof(bowtie) / sizeof(bowtie[0]);
+
+const Cubic arrow[] = {
+ {{0, 0}, {10, 0}, {10, 10}, {5, 4}},
+ {{10, 0}, {10, 10}, {5, 4}, {0, 0}},
+ {{10, 10}, {5, 4}, {0, 0}, {10, 0}},
+ {{5, 4}, {0, 0}, {10, 0}, {10, 10}},
+};
+
+size_t arrow_count = sizeof(arrow) / sizeof(arrow[0]);
+
+const Cubic three[] = {
+ {{1, 0}, {1, 0}, {1, 1}, {0, 1}}, // 0 == 1
+ {{0, 0}, {1, 1}, {1, 1}, {0, 1}}, // 1 == 2
+ {{0, 0}, {1, 0}, {0, 1}, {0, 1}}, // 2 == 3
+ {{1, 0}, {1, 1}, {1, 0}, {0, 1}}, // 0 == 2
+ {{1, 0}, {1, 1}, {0, 1}, {1, 0}}, // 0 == 3
+ {{0, 0}, {1, 0}, {1, 1}, {1, 0}}, // 1 == 3
+};
+
+size_t three_count = sizeof(three) / sizeof(three[0]);
+
+const Cubic triangle[] = {
+ {{0, 0}, {1, 0}, {2, 0}, {0, 1}}, // extra point on horz
+ {{1, 0}, {2, 0}, {0, 1}, {0, 0}},
+ {{2, 0}, {0, 1}, {0, 0}, {1, 0}},
+ {{0, 1}, {0, 0}, {1, 0}, {2, 0}},
+
+ {{0, 0}, {0, 1}, {0, 2}, {1, 1}}, // extra point on vert
+ {{0, 1}, {0, 2}, {1, 1}, {0, 0}},
+ {{0, 2}, {1, 1}, {0, 0}, {0, 1}},
+ {{1, 1}, {0, 0}, {0, 1}, {0, 2}},
+
+ {{0, 0}, {1, 1}, {2, 2}, {2, 0}}, // extra point on diag
+ {{1, 1}, {2, 2}, {2, 0}, {0, 0}},
+ {{2, 2}, {2, 0}, {0, 0}, {1, 1}},
+ {{2, 0}, {0, 0}, {1, 1}, {2, 2}},
+
+ {{0, 0}, {2, 0}, {2, 2}, {1, 1}}, // extra point on diag
+ {{2, 0}, {2, 2}, {1, 1}, {0, 0}},
+ {{2, 2}, {1, 1}, {0, 0}, {2, 0}},
+ {{1, 1}, {0, 0}, {2, 0}, {2, 2}},
+};
+
+size_t triangle_count = sizeof(triangle) / sizeof(triangle[0]);
+
+const struct CubicDataSet {
+ const Cubic* data;
+ size_t size;
+} cubicDataSet[] = {
+ { three, three_count },
+ { convex, convex_count },
+ { bowtie, bowtie_count },
+ { arrow, arrow_count },
+ { triangle, triangle_count },
+};
+
+size_t cubicDataSet_count = sizeof(cubicDataSet) / sizeof(cubicDataSet[0]);
+
+typedef double Matrix3x2[3][2];
+
+static bool rotateToAxis(const _Point& a, const _Point& b, Matrix3x2& matrix) {
+ double dx = b.x - a.x;
+ double dy = b.y - a.y;
+ double length = sqrt(dx * dx + dy * dy);
+ if (length == 0) {
+ return false;
+ }
+ double invLength = 1 / length;
+ matrix[0][0] = dx * invLength;
+ matrix[1][0] = dy * invLength;
+ matrix[2][0] = 0;
+ matrix[0][1] = -dy * invLength;
+ matrix[1][1] = dx * invLength;
+ matrix[2][1] = 0;
+ return true;
+}
+
+static void transform(const Cubic& cubic, const Matrix3x2& matrix, Cubic& rotPath) {
+ for (int index = 0; index < 4; ++index) {
+ rotPath[index].x = cubic[index].x * matrix[0][0]
+ + cubic[index].y * matrix[1][0] + matrix[2][0];
+ rotPath[index].y = cubic[index].x * matrix[0][1]
+ + cubic[index].y * matrix[1][1] + matrix[2][1];
+ }
+}
+
+// brute force way to find convex hull:
+// pick two points
+// rotate all four until the two points are horizontal
+// are the remaining two points both above or below the horizontal line?
+// if so, the two points must be an edge of the convex hull
+static int rotate_to_hull(const Cubic& cubic, char order[4], size_t idx, size_t inr) {
+ bool debug_rotate_to_hull = false;
+ int outsidePtSet[4];
+ memset(outsidePtSet, -1, sizeof(outsidePtSet));
+ for (int outer = 0; outer < 3; ++outer) {
+ for (int priorOuter = 0; priorOuter < outer; ++priorOuter) {
+ if (cubic[outer].approximatelyEqual(cubic[priorOuter])) {
+ goto skip;
+ }
+ }
+ for (int inner = outer + 1; inner < 4; ++inner) {
+ for (int priorInner = outer + 1; priorInner < inner; ++priorInner) {
+ if (cubic[inner].approximatelyEqual(cubic[priorInner])) {
+ goto skipInner;
+ }
+ }
+ if (cubic[outer].approximatelyEqual(cubic[inner])) {
+ continue;
+ }
+ Matrix3x2 matrix;
+ if (!rotateToAxis(cubic[outer], cubic[inner], matrix)) {
+ continue;
+ }
+ Cubic rotPath;
+ transform(cubic, matrix, rotPath);
+ int sides[3];
+ int zeroes;
+ zeroes = -1;
+ bzero(sides, sizeof(sides));
+ if (debug_rotate_to_hull) printf("%s [%d,%d] [o=%d,i=%d] src=(%g,%g) rot=", __FUNCTION__,
+ (int)idx, (int)inr, (int)outer, (int)inner,
+ cubic[inner].x, cubic[inner].y);
+ for (int index = 0; index < 4; ++index) {
+ if (debug_rotate_to_hull) printf("(%g,%g) ", rotPath[index].x, rotPath[index].y);
+ sides[side(rotPath[index].y - rotPath[inner].y)]++;
+ if (index != outer && index != inner
+ && side(rotPath[index].y - rotPath[inner].y) == 1)
+ zeroes = index;
+ }
+ if (debug_rotate_to_hull) printf("sides=(%d,%d,%d)\n", sides[0], sides[1], sides[2]);
+ if (sides[0] && sides[2]) {
+ continue;
+ }
+ if (sides[1] == 3 && zeroes >= 0) {
+ // verify that third point is between outer, inner
+ // if either of remaining two equals outer or equal, pick lower
+ if (rotPath[zeroes].approximatelyEqual(rotPath[inner])
+ && zeroes < inner) {
+ if (debug_rotate_to_hull) printf("%s [%d,%d] [o=%d,i=%d] zeroes < inner\n",
+ __FUNCTION__, (int)idx, (int)inr, (int)outer, (int)inner);
+ continue;
+ }
+ if (rotPath[zeroes].approximatelyEqual(rotPath[outer])
+ && zeroes < outer) {
+ if (debug_rotate_to_hull) printf("%s [%d,%d] [o=%d,i=%d] zeroes < outer\n",
+ __FUNCTION__, (int)idx, (int)inr, (int)outer, (int)inner);
+ continue;
+ }
+ if (rotPath[zeroes].x < rotPath[inner].x
+ && rotPath[zeroes].x < rotPath[outer].x) {
+ if (debug_rotate_to_hull) printf("%s [%d,%d] [o=%d,i=%d] zeroes < inner && outer\n",
+ __FUNCTION__, (int)idx, (int)inr, (int)outer, (int)inner);
+ continue;
+ }
+ if (rotPath[zeroes].x > rotPath[inner].x
+ && rotPath[zeroes].x > rotPath[outer].x) {
+ if (debug_rotate_to_hull) printf("%s [%d,%d] [o=%d,i=%d] zeroes > inner && outer\n",
+ __FUNCTION__, (int)idx, (int)inr, (int)outer, (int)inner);
+ continue;
+ }
+ }
+ if (outsidePtSet[outer] < 0) {
+ outsidePtSet[outer] = inner;
+ } else {
+ if (outsidePtSet[inner] > 0) {
+ if (debug_rotate_to_hull) printf("%s [%d,%d] [o=%d,i=%d] too many rays from one point\n",
+ __FUNCTION__, (int)idx, (int)inr, (int)outer, (int)inner);
+ }
+ outsidePtSet[inner] = outer;
+ }
+skipInner:
+ ;
+ }
+skip:
+ ;
+ }
+ int totalSides = 0;
+ int first = 0;
+ for (; first < 4; ++first) {
+ if (outsidePtSet[first] >= 0) {
+ break;
+ }
+ }
+ if (first > 3) {
+ order[0] = 0;
+ return 1;
+ }
+ int next = first;
+ do {
+ order[totalSides++] = next;
+ next = outsidePtSet[next];
+ } while (next != -1 && next != first);
+ return totalSides;
+}
+
+int firstIndex = 0;
+int firstInner = 0;
+
+void ConvexHull_Test() {
+ for (size_t index = firstIndex; index < cubicDataSet_count; ++index) {
+ const CubicDataSet& set = cubicDataSet[index];
+ for (size_t inner = firstInner; inner < set.size; ++inner) {
+ const Cubic& cubic = set.data[inner];
+ char order[4], cmpOrder[4];
+ int cmp = rotate_to_hull(cubic, cmpOrder, index, inner);
+ if (cmp < 3) {
+ continue;
+ }
+ int result = convex_hull(cubic, order);
+ if (cmp != result) {
+ printf("%s [%d,%d] result=%d cmp=%d\n", __FUNCTION__,
+ (int)index, (int)inner, result, cmp);
+ continue;
+ }
+ // check for same indices
+ char pts = 0;
+ char cmpPts = 0;
+ int pt, bit;
+ for (pt = 0; pt < cmp; ++pt) {
+ if (pts & 1 << order[pt]) {
+ printf("%s [%d,%d] duplicate index in order: %d,%d,%d",
+ __FUNCTION__, (int)index, (int)inner,
+ order[0], order[1], order[2]);
+ if (cmp == 4) {
+ printf(",%d", order[3]);
+ }
+ printf("\n");
+ goto next;
+ }
+ if (cmpPts & 1 << cmpOrder[pt]) {
+ printf("%s [%d,%d] duplicate index in order: %d,%d,%d",
+ __FUNCTION__, (int)index, (int)inner,
+ cmpOrder[0], cmpOrder[1], cmpOrder[2]);
+ if (cmp == 4) {
+ printf(",%d", cmpOrder[3]);
+ }
+ printf("\n");
+ goto next;
+ }
+ pts |= 1 << order[pt];
+ cmpPts |= 1 << cmpOrder[pt];
+ }
+ for (bit = 0; bit < 4; ++bit) {
+ if (pts & 1 << bit) {
+ continue;
+ }
+ for (pt = 0; pt < cmp; ++pt) {
+ if (order[pt] == bit) {
+ continue;
+ }
+ if (cubic[order[pt]] == cubic[bit]) {
+ pts |= 1 << bit;
+ }
+ }
+ }
+ for (bit = 0; bit < 4; ++bit) {
+ if (cmpPts & 1 << bit) {
+ continue;
+ }
+ for (pt = 0; pt < cmp; ++pt) {
+ if (cmpOrder[pt] == bit) {
+ continue;
+ }
+ if (cubic[cmpOrder[pt]] == cubic[bit]) {
+ cmpPts |= 1 << bit;
+ }
+ }
+ }
+ if (pts != cmpPts) {
+ printf("%s [%d,%d] mismatch indices: order=%d,%d,%d",
+ __FUNCTION__, (int)index, (int)inner,
+ order[0], order[1], order[2]);
+ if (cmp == 4) {
+ printf(",%d", order[3]);
+ }
+ printf(" cmpOrder=%d,%d,%d", cmpOrder[0], cmpOrder[1], cmpOrder[2]);
+ if (cmp == 4) {
+ printf(",%d", cmpOrder[3]);
+ }
+ printf("\n");
+ continue;
+ }
+ if (cmp == 4) { // check for bow ties
+ int match = 0;
+ while (cmpOrder[match] != order[0]) {
+ ++match;
+ }
+ if (cmpOrder[match ^ 2] != order[2]) {
+ printf("%s [%d,%d] bowtie mismatch: order=%d,%d,%d,%d"
+ " cmpOrder=%d,%d,%d,%d\n",
+ __FUNCTION__, (int)index, (int)inner,
+ order[0], order[1], order[2], order[3],
+ cmpOrder[0], cmpOrder[1], cmpOrder[2], cmpOrder[3]);
+ }
+ }
+ next:
+ ;
+ }
+ }
+}
+
+const double a = 1.0/3;
+const double b = 2.0/3;
+
+const Cubic x_cubic[] = {
+ {{0, 0}, {a, 0}, {b, 0}, {1, 0}}, // 0
+ {{0, 0}, {a, 0}, {b, 0}, {1, 1}}, // 1
+ {{0, 0}, {a, 0}, {b, 1}, {1, 0}}, // 2
+ {{0, 0}, {a, 0}, {b, 1}, {1, 1}}, // 3
+ {{0, 0}, {a, 1}, {b, 0}, {1, 0}}, // 4
+ {{0, 0}, {a, 1}, {b, 0}, {1, 1}}, // 5
+ {{0, 0}, {a, 1}, {b, 1}, {1, 0}}, // 6
+ {{0, 0}, {a, 1}, {b, 1}, {1, 1}}, // 7
+ {{0, 1}, {a, 0}, {b, 0}, {1, 0}}, // 8
+ {{0, 1}, {a, 0}, {b, 0}, {1, 1}}, // 9
+ {{0, 1}, {a, 0}, {b, 1}, {1, 0}}, // 10
+ {{0, 1}, {a, 0}, {b, 1}, {1, 1}}, // 11
+ {{0, 1}, {a, 1}, {b, 0}, {1, 0}}, // 12
+ {{0, 1}, {a, 1}, {b, 0}, {1, 1}}, // 13
+ {{0, 1}, {a, 1}, {b, 1}, {1, 0}}, // 14
+ {{0, 1}, {a, 1}, {b, 1}, {1, 1}}, // 15
+};
+
+size_t x_cubic_count = sizeof(x_cubic) / sizeof(x_cubic[0]);
+
+static int first_x_test = 0;
+
+void ConvexHull_X_Test() {
+ for (size_t index = first_x_test; index < x_cubic_count; ++index) {
+ const Cubic& cubic = x_cubic[index];
+ char connectTo0[2] = {-1, -1};
+ char connectTo3[2] = {-1, -1};
+ convex_x_hull(cubic, connectTo0, connectTo3);
+ int idx, cmp;
+ for (idx = 0; idx < 2; ++idx) {
+ if (connectTo0[idx] >= 1 && connectTo0[idx] < 4) {
+ continue;
+ } else {
+ printf("%s connectTo0[idx]=%d", __FUNCTION__, connectTo0[idx]);
+ }
+ if (connectTo3[idx] >= 0 && connectTo3[idx] < 3) {
+ continue;
+ } else {
+ printf("%s connectTo3[idx]=%d", __FUNCTION__, connectTo3[idx]);
+ }
+ goto nextTest;
+ }
+ char rOrder[4];
+ char cmpOrder[4];
+ cmp = rotate_to_hull(cubic, cmpOrder, index, 0);
+ if (index == 0 || index == 15) {
+ // FIXME: make rotate_to_hull work for degenerate 2 edge hull cases
+ cmpOrder[0] = 0;
+ cmpOrder[1] = 3;
+ cmp = 2;
+ }
+ if (cmp < 3) {
+ // FIXME: make rotate_to_hull work for index == 3 etc
+ continue;
+ }
+ for (idx = 0; idx < cmp; ++idx) {
+ if (cmpOrder[idx] == 0) {
+ rOrder[0] = cmpOrder[(idx + 1) % cmp];
+ rOrder[1] = cmpOrder[(idx + cmp - 1) % cmp];
+ } else if (cmpOrder[idx] == 3) {
+ rOrder[2] = cmpOrder[(idx + 1) % cmp];
+ rOrder[3] = cmpOrder[(idx + cmp - 1) % cmp];
+ }
+ }
+ if (connectTo0[0] != connectTo0[1]) {
+ if (rOrder[0] == rOrder[1]) {
+ printf("%s [%d] (1) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
+ __FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
+ connectTo3[0], connectTo3[1],
+ rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
+ continue;
+ }
+ int unused = 6 - connectTo0[0] - connectTo0[1];
+ int rUnused = 6 - rOrder[0] - rOrder[1];
+ if (unused != rUnused) {
+ printf("%s [%d] (2) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
+ __FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
+ connectTo3[0], connectTo3[1],
+ rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
+ continue;
+ }
+ } else {
+ if (rOrder[0] != rOrder[1]) {
+ printf("%s [%d] (3) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
+ __FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
+ connectTo3[0], connectTo3[1],
+ rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
+ continue;
+ }
+ if (connectTo0[0] != rOrder[0]) {
+ printf("%s [%d] (4) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
+ __FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
+ connectTo3[0], connectTo3[1],
+ rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
+ continue;
+ }
+ }
+ if (connectTo3[0] != connectTo3[1]) {
+ if (rOrder[2] == rOrder[3]) {
+ printf("%s [%d] (5) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
+ __FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
+ connectTo3[0], connectTo3[1],
+ rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
+ continue;
+ }
+ int unused = 6 - connectTo3[0] - connectTo3[1];
+ int rUnused = 6 - rOrder[2] - rOrder[3];
+ if (unused != rUnused) {
+ printf("%s [%d] (6) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
+ __FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
+ connectTo3[0], connectTo3[1],
+ rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
+ continue;
+ }
+ } else {
+ if (rOrder[2] != rOrder[3]) {
+ printf("%s [%d] (7) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
+ __FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
+ connectTo3[0], connectTo3[1],
+ rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
+ continue;
+ }
+ if (connectTo3[1] != rOrder[3]) {
+ printf("%s [%d] (8) order=(%d,%d,%d,%d) r_order=(%d,%d,%d,%d)\n",
+ __FUNCTION__, (int)index, connectTo0[0], connectTo0[1],
+ connectTo3[0], connectTo3[1],
+ rOrder[0], rOrder[1], rOrder[2], rOrder[3]);
+ continue;
+ }
+ }
+nextTest:
+ ;
+ }
+}
+
+
+