blob: 3979b1ebca17a592cea02e5eafc0df67e5799ae9 [file] [log] [blame]
 /* * 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 "Intersection_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) SkDebugf("%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) SkDebugf("(%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) SkDebugf("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) SkDebugf("%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) SkDebugf("%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) SkDebugf("%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) SkDebugf("%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) SkDebugf("%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) { SkDebugf("%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]) { SkDebugf("%s [%d,%d] duplicate index in order: %d,%d,%d", __FUNCTION__, (int)index, (int)inner, order[0], order[1], order[2]); if (cmp == 4) { SkDebugf(",%d", order[3]); } SkDebugf("\n"); goto next; } if (cmpPts & 1 << cmpOrder[pt]) { SkDebugf("%s [%d,%d] duplicate index in order: %d,%d,%d", __FUNCTION__, (int)index, (int)inner, cmpOrder[0], cmpOrder[1], cmpOrder[2]); if (cmp == 4) { SkDebugf(",%d", cmpOrder[3]); } SkDebugf("\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) { SkDebugf("%s [%d,%d] mismatch indices: order=%d,%d,%d", __FUNCTION__, (int)index, (int)inner, order[0], order[1], order[2]); if (cmp == 4) { SkDebugf(",%d", order[3]); } SkDebugf(" cmpOrder=%d,%d,%d", cmpOrder[0], cmpOrder[1], cmpOrder[2]); if (cmp == 4) { SkDebugf(",%d", cmpOrder[3]); } SkDebugf("\n"); continue; } if (cmp == 4) { // check for bow ties int match = 0; while (cmpOrder[match] != order[0]) { ++match; } if (cmpOrder[match ^ 2] != order[2]) { SkDebugf("%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 { SkDebugf("%s connectTo0[idx]=%d", __FUNCTION__, connectTo0[idx]); } if (connectTo3[idx] >= 0 && connectTo3[idx] < 3) { continue; } else { SkDebugf("%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]) { SkDebugf("%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) { SkDebugf("%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]) { SkDebugf("%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]) { SkDebugf("%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]) { SkDebugf("%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) { SkDebugf("%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]) { SkDebugf("%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]) { SkDebugf("%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: ; } }