Add intersections for path ops

This CL depends on 
https://codereview.chromium.org/12827020/
"Add base types for path ops"

The intersection of a line, quadratic, or cubic
with another curve (or with itself) is found by
solving the implicit equation for the curve pair.

The curves are first reduced to find the simplest
form that will describe the original, and to detect
degenerate or special-case data like horizontal and
vertical lines.

For cubic self-intersection, and for a pair of cubics,
the intersection is found by recursively
approximating the cubic with a series of quadratics.

The implicit solutions depend on the root finding
contained in the DCubic and DQuad structs, and
the quartic root finder included here.
Review URL: https://codereview.chromium.org/12880016

git-svn-id: http://skia.googlecode.com/svn/trunk@8552 2bbb7eff-a529-9590-31e7-b0007b416f81

1 files changed, 300 insertions, 0 deletions

diff --git a/tests/PathOpsCubicIntersectionTestData.cpp b/tests/PathOpsCubicIntersectionTestData.cpp
new file mode 100644
index 0000000000..04c46d5267
--- /dev/null
+++ b/tests/PathOpsCubicIntersectionTestData.cpp
@@ -0,0 +1,300 @@
+/*
+ * 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 "PathOpsCubicIntersectionTestData.h"
+#include <limits>
+
+static const double D = FLT_EPSILON / 2;
+static const double G = FLT_EPSILON / 3;
+static const double N = -FLT_EPSILON / 2;
+static const double M = -FLT_EPSILON / 3;
+
+const SkDCubic pointDegenerates[] = {
+    {{{0, 0}, {0, 0}, {0, 0}, {0, 0}}},
+    {{{1, 1}, {1, 1}, {1, 1}, {1, 1}}},
+    {{{1 + FLT_EPSILON_HALF, 1}, {1, 1 + FLT_EPSILON_HALF}, {1, 1}, {1, 1}}},
+    {{{1 + D, 1}, {1 - D, 1}, {1, 1}, {1, 1}}},
+    {{{0, 0}, {0, 0}, {1, 0}, {0, 0}}},
+    {{{0, 0}, {1, 0}, {0, 0}, {0, 0}}},
+    {{{0, 0}, {0, 0}, {0, 1}, {0, 0}}},
+    {{{0, 0}, {0, 1}, {0, 0}, {0, 0}}},
+    {{{0, 0}, {0, 0}, {1, 1}, {0, 0}}},
+    {{{0, 0}, {1, 1}, {0, 0}, {0, 0}}},
+    {{{0, 0}, {1, 1}, {2, 2}, {0, 0}}},
+    {{{1, 1}, {2, 2}, {2, 2}, {1, 1}}},
+    {{{0, 0}, {0, D}, {1, 0}, {0, 0}}},
+    {{{0, 0}, {1, 0}, {0, D}, {0, 0}}},
+    {{{0, 0}, {D, 0}, {0, 1}, {0, 0}}},
+    {{{0, 0}, {0, 1}, {D, 0}, {0, 0}}},
+    {{{1, 1}, {2, 2}, {2, 2+D}, {1, 1}}},
+    {{{0, 0}, {0, N}, {1, 0}, {0, 0}}},
+    {{{0, 0}, {1, 0}, {0, N}, {0, 0}}},
+    {{{0, 0}, {N, 0}, {0, 1}, {0, 0}}},
+    {{{0, 0}, {0, 1}, {N, 0}, {0, 0}}},
+    {{{0, 0}, {1, 1}, {N, 0}, {0, 0}}},
+    {{{0, 0}, {D, 0}, {1, 1}, {0, 0}}},
+    {{{0, 0}, {1, 1}, {D, 0}, {0, 0}}},
+    {{{0, 0}, {N, 0}, {1, 1}, {0, 0}}},
+    {{{1, 1}, {2, 2}, {2, 2+N}, {1, 1}}},
+};
+
+const size_t pointDegenerates_count = sizeof(pointDegenerates) / sizeof(pointDegenerates[0]);
+
+const SkDCubic notPointDegenerates[] = {
+    {{{1 + FLT_EPSILON * 2, 1}, {1, FLT_EPSILON * 2}, {1, 1}, {1, 1}}},
+    {{{1 + FLT_EPSILON * 2, 1}, {1 - FLT_EPSILON * 2, 1}, {1, 1}, {1, 1}}}
+};
+
+const size_t notPointDegenerates_count =
+        sizeof(notPointDegenerates) / sizeof(notPointDegenerates[0]);
+
+// from http://www.truetex.com/bezint.htm
+const SkDCubic tests[][2] = {
+    {  // intersects in one place (data gives bezier clip fits
+     {{{0, 45},
+      {6.0094158284751593, 51.610357411322688},
+      {12.741093228940867, 55.981703949474607},
+      {20.021417396476362, 58.652245509710262}}},
+     {{{2.2070737699246674, 52.703494107327209},
+      {31.591482272629477, 23.811002295222025},
+      {76.824588616426425, 44.049473790502674},
+      {119.25488947221436, 55.599248272955073}}}
+    }, {  // intersects in three places
+        {{{0, 45}, {50, 100}, {150,   0}, {200, 55}}},
+        {{{0, 55}, {50,   0}, {150, 100}, {200, 45}}}
+    }, {  // intersects in one place, cross over is nearly parallel
+        {{{0,   0}, {0, 100}, {200,   0}, {200, 100}}},
+        {{{0, 100}, {0,   0}, {200, 100}, {200,   0}}}
+    }, {  // intersects in two places
+        {{{0,   0}, {0, 100}, {200, 100}, {200,   0}}},
+        {{{0, 100}, {0,   0}, {200,   0}, {200, 100}}}
+    }, {
+        {{{150, 100}, {150 + 0.1, 150}, {150, 200}, {150, 250}}},
+        {{{250, 150}, {200, 150 + 0.1}, {150, 150}, {100, 150}}}
+    }, {  // single intersection around 168,185
+        {{{200, 100}, {150, 100}, {150, 150}, {200, 150}}},
+        {{{250, 150}, {250, 100}, {100, 100}, {100, 150}}}
+    }, {
+        {{{1.0, 1.5}, {15.5, 0.5}, {-8.0, 3.5}, {5.0, 1.5}}},
+        {{{4.0, 0.5}, {5.0, 15.0}, {2.0, -8.5}, {4.0, 4.5}}}
+    }, {
+        {{{664.00168, 0},       {726.11545, 124.22757}, {736.89069, 267.89743},
+                {694.0017, 400.0002}}},
+        {{{850.66843, 115.55563}, {728.515, 115.55563}, {725.21347, 275.15309},
+                {694.0017, 400.0002}}}
+    }, {
+        {{{1, 1},   {12.5, 6.5}, {-4, 6.5}, {7.5, 1}}},
+        {{{1, 6.5}, {12.5, 1},   {-4, 1},   {.5, 6}}}
+    }, {
+        {{{315.748, 312.84}, {312.644, 318.134}, {305.836, 319.909}, {300.542, 316.804}}},
+        {{{317.122, 309.05}, {316.112, 315.102}, {310.385, 319.19},  {304.332, 318.179}}}
+    }, {
+        {{{1046.604051, 172.937967},  {1046.604051, 178.9763059}, {1041.76745,  183.9279165}, {1035.703842, 184.0432409}}},
+        {{{1046.452235, 174.7640504}, {1045.544872, 180.1973817}, {1040.837966, 184.0469882}, {1035.505925, 184.0469882}}}
+    }, {
+        {{{125.79356, 199.57382}, {51.16556, 128.93575}, {87.494,  16.67848}, {167.29361, 16.67848}}},
+        {{{167.29361, 55.81876}, {100.36128, 55.81876}, {68.64099, 145.4755}, {125.7942, 199.57309}}}
+    }
+};
+
+const size_t tests_count = sizeof(tests) / sizeof(tests[0]);
+
+SkDCubic hexTests[][2] = {
+    {
+        // placeholder for hex converted below
+        {{{0, 0}, {0, 0}, {0, 0}, {0, 0}}}, {{{0, 0}, {0, 0}, {0, 0}, {0, 0}}}
+    }
+};
+
+const size_t hexTests_count = sizeof(hexTests) / sizeof(hexTests[0]);
+
+static const uint64_t testx[2][8] = {
+    {
+        0xf0d0d1ca63075a40LLU, 0x9408ce996a237740LLU, 0x6d5675460fbe5e40LLU, 0x6ef501e1b7487940LLU,
+        0x9a71d2f8143d6540LLU, 0x6bc18bbe02907a40LLU, 0x5b94d92093aa6b40LLU, 0x6ac18bbe02907a40LLU
+    },
+    {
+        0x92c56ed7b6145d40LLU, 0xede4f1255edb7740LLU, 0x1138c1101af75940LLU, 0x42e4f1255edb7740LLU,
+        0x408e51603ad95640LLU, 0x1e2e8fe9dd927740LLU, 0x1cb4777cd3a75440LLU, 0x212e1390de017740LLU
+    }
+};
+
+void convert_testx() {
+    const uint64_t* inPtr = testx[0];
+    double* outPtr = &hexTests[sizeof(tests) / sizeof(tests[0]) - 1][0][0].fX;
+    for (unsigned index = 0; index < sizeof(testx) / sizeof(testx[0][0]); ++index) {
+        uint64_t input = *inPtr++;
+        unsigned char* output = (unsigned char*) outPtr++;
+        for (unsigned byte = 0; byte < sizeof(input); ++byte) {
+            output[byte] = input >> (7 - byte) * 8;
+        }
+    }
+}
+
+const SkDCubic lines[] = {
+    {{{0, 0}, {0, 0}, {0, 0}, {1, 0}}},  // 0: horizontal
+    {{{1, 0}, {0, 0}, {0, 0}, {0, 0}}},
+    {{{1, 0}, {2, 0}, {3, 0}, {4, 0}}},
+    {{{0, 0}, {0, 0}, {0, 0}, {0, 1}}},  // 5: vertical
+    {{{0, 1}, {0, 0}, {0, 0}, {0, 0}}},
+    {{{0, 1}, {0, 2}, {0, 3}, {0, 4}}},
+    {{{0, 0}, {0, 0}, {0, 0}, {1, 1}}},  // 10: 3 coincident
+    {{{1, 1}, {0, 0}, {0, 0}, {0, 0}}},
+    {{{0, 0}, {0, 0}, {1, 1}, {2, 2}}},  // 14: 2 coincident
+    {{{0, 0}, {1, 1}, {0, 0}, {2, 2}}},
+    {{{1, 1}, {0, 0}, {0, 0}, {2, 2}}},  // 17:
+    {{{1, 1}, {0, 0}, {2, 2}, {0, 0}}},
+    {{{1, 1}, {2, 2}, {0, 0}, {0, 0}}},
+    {{{1, 1}, {2, 2}, {3, 3}, {2, 2}}},  // middle-last coincident
+    {{{1, 1}, {2, 2}, {3, 3}, {3, 3}}},  // middle-last coincident
+    {{{1, 1}, {1, 1}, {2, 2}, {2, 2}}},  // 2 pairs coincident
+    {{{1, 1}, {2, 2}, {1, 1}, {2, 2}}},
+    {{{1, 1}, {1, 1}, {3, 3}, {3, 3}}},  // first-middle middle-last coincident
+    {{{1, 1}, {2, 2}, {3, 3}, {4, 4}}},  // no coincident
+    {{{1, 1}, {3, 3}, {2, 2}, {4, 4}}},
+    {{{1, 1}, {2, 2}, {4, 4}, {3, 3}}},
+    {{{1, 1}, {3, 3}, {4, 4}, {2, 2}}},
+    {{{1, 1}, {4, 4}, {2, 2}, {3, 3}}},
+    {{{1, 1}, {4, 4}, {3, 3}, {2, 2}}},
+    {{{2, 2}, {1, 1}, {3, 3}, {4, 4}}},
+    {{{2, 2}, {1, 1}, {4, 4}, {3, 3}}},
+    {{{2, 2}, {3, 3}, {1, 1}, {4, 4}}},
+    {{{2, 2}, {3, 3}, {4, 4}, {1, 1}}},
+    {{{2, 2}, {4, 4}, {1, 1}, {3, 3}}},
+    {{{2, 2}, {4, 4}, {3, 3}, {1, 1}}},
+};
+
+const size_t lines_count = sizeof(lines) / sizeof(lines[0]);
+
+// 'not a line' tries to fool the line detection code
+const SkDCubic notLines[] = {
+    {{{0, 0}, {0, 0}, {0, 1}, {1, 0}}},
+    {{{0, 0}, {0, 1}, {0, 0}, {1, 0}}},
+    {{{0, 0}, {0, 1}, {1, 0}, {0, 0}}},
+    {{{0, 1}, {0, 0}, {0, 0}, {1, 0}}},
+    {{{0, 1}, {0, 0}, {1, 0}, {0, 0}}},
+    {{{0, 1}, {1, 0}, {0, 0}, {0, 0}}},
+};
+
+const size_t notLines_count = sizeof(notLines) / sizeof(notLines[0]);
+
+static const double E = FLT_EPSILON * 2;
+static const double F = FLT_EPSILON * 3;
+
+const SkDCubic modEpsilonLines[] = {
+    {{{0, E}, {0, 0}, {0, 0}, {1, 0}}},  // horizontal
+    {{{0, 0}, {0, E}, {1, 0}, {0, 0}}},
+    {{{0, 0}, {1, 0}, {0, E}, {0, 0}}},
+    {{{1, 0}, {0, 0}, {0, 0}, {0, E}}},
+    {{{1, E}, {2, 0}, {3, 0}, {4, 0}}},
+    {{{E, 0}, {0, 0}, {0, 0}, {0, 1}}},  // vertical
+    {{{0, 0}, {E, 0}, {0, 1}, {0, 0}}},
+    {{{0, 0}, {0, 1}, {E, 0}, {0, 0}}},
+    {{{0, 1}, {0, 0}, {0, 0}, {E, 0}}},
+    {{{E, 1}, {0, 2}, {0, 3}, {0, 4}}},
+    {{{E, 0}, {0, 0}, {0, 0}, {1, 1}}},  // 3 coincident
+    {{{0, 0}, {E, 0}, {1, 1}, {0, 0}}},
+    {{{0, 0}, {1, 1}, {E, 0}, {0, 0}}},
+    {{{1, 1}, {0, 0}, {0, 0}, {E, 0}}},
+    {{{0, E}, {0, 0}, {1, 1}, {2, 2}}},  // 2 coincident
+    {{{0, 0}, {1, 1}, {0, E}, {2, 2}}},
+    {{{0, 0}, {1, 1}, {2, 2}, {0, E}}},
+    {{{1, 1}, {0, E}, {0, 0}, {2, 2}}},
+    {{{1, 1}, {0, E}, {2, 2}, {0, 0}}},
+    {{{1, 1}, {2, 2}, {E, 0}, {0, 0}}},
+    {{{1, 1}, {2, 2+E}, {3, 3}, {2, 2}}},  // middle-last coincident
+    {{{1, 1}, {2+E, 2}, {3, 3}, {3, 3}}},  // middle-last coincident
+    {{{1, 1}, {1, 1}, {2, 2}, {2+E, 2}}},  // 2 pairs coincident
+    {{{1, 1}, {2, 2}, {1, 1}, {2+E, 2}}},
+    {{{1, 1}, {2, 2}, {2, 2+E}, {1, 1}}},
+    {{{1, 1}, {1, 1+E}, {3, 3}, {3, 3}}},  // first-middle middle-last coincident
+    {{{1, 1}, {2+E, 2}, {3, 3}, {4, 4}}},  // no coincident
+    {{{1, 1}, {3, 3}, {2, 2}, {4, 4+F}}},  // INVESTIGATE: why the epsilon is bigger
+    {{{1, 1+F}, {2, 2}, {4, 4}, {3, 3}}},  // INVESTIGATE: why the epsilon is bigger
+    {{{1, 1}, {3, 3}, {4, 4+E}, {2, 2}}},
+    {{{1, 1}, {4, 4}, {2, 2}, {3, 3+E}}},
+    {{{1, 1}, {4, 4}, {3, 3}, {2+E, 2}}},
+    {{{2, 2}, {1, 1}, {3+E, 3}, {4, 4}}},
+    {{{2, 2}, {1+E, 1}, {4, 4}, {3, 3}}},
+    {{{2, 2+E}, {3, 3}, {1, 1}, {4, 4}}},
+    {{{2+E, 2}, {3, 3}, {4, 4}, {1, 1}}},
+    {{{2, 2}, {4+E, 4}, {1, 1}, {3, 3}}},
+    {{{2, 2}, {4, 4}, {3, 3}, {1, 1+E}}},
+};
+
+const size_t modEpsilonLines_count = sizeof(modEpsilonLines) / sizeof(modEpsilonLines[0]);
+
+const SkDCubic lessEpsilonLines[] = {
+    {{{0, D}, {0, 0}, {0, 0}, {1, 0}}},  // horizontal
+    {{{1, 0}, {0, 0}, {0, 0}, {0, D}}},
+    {{{1, D}, {2, 0}, {3, 0}, {4, 0}}},
+    {{{D, 0}, {0, 0}, {0, 0}, {0, 1}}},  // vertical
+    {{{0, 1}, {0, 0}, {0, 0}, {D, 0}}},
+    {{{D, 1}, {0, 2}, {0, 3}, {0, 4}}},
+    {{{D, 0}, {0, 0}, {0, 0}, {1, 1}}},  // 3 coincident
+    {{{1, 1}, {0, 0}, {0, 0}, {D, 0}}},
+    {{{0, D}, {0, 0}, {1, 1}, {2, 2}}},  // 2 coincident
+    {{{0, 0}, {1, 1}, {0, D}, {2, 2}}},
+    {{{0, 0}, {1, 1}, {2, 2}, {0, D}}},
+    {{{1, 1}, {0, D}, {0, 0}, {2, 2}}},
+    {{{1, 1}, {0, D}, {2, 2}, {0, 0}}},
+    {{{1, 1}, {2, 2}, {D, 0}, {0, 0}}},
+    {{{1, 1}, {2, 2+D}, {3, 3}, {2, 2}}},  // middle-last coincident
+    {{{1, 1}, {2+D, 2}, {3, 3}, {3, 3}}},  // middle-last coincident
+    {{{1, 1}, {1, 1}, {2, 2}, {2+D, 2}}},  // 2 pairs coincident
+    {{{1, 1}, {2, 2}, {1, 1}, {2+D, 2}}},
+    {{{1, 1}, {1, 1+D}, {3, 3}, {3, 3}}},  // first-middle middle-last coincident
+    {{{1, 1}, {2+D/2, 2}, {3, 3}, {4, 4}}},  // no coincident (FIXME: N as opposed to N/2 failed)
+    {{{1, 1}, {3, 3}, {2, 2}, {4, 4+D}}},
+    {{{1, 1+D}, {2, 2}, {4, 4}, {3, 3}}},
+    {{{1, 1}, {3, 3}, {4, 4+D}, {2, 2}}},
+    {{{1, 1}, {4, 4}, {2, 2}, {3, 3+D}}},
+    {{{1, 1}, {4, 4}, {3, 3}, {2+G, 2}}},  // INVESTIGATE: why the epsilon is smaller
+    {{{2, 2}, {1, 1}, {3+D, 3}, {4, 4}}},
+    {{{2, 2}, {1+D, 1}, {4, 4}, {3, 3}}},
+    {{{2, 2+D}, {3, 3}, {1, 1}, {4, 4}}},
+    {{{2+G, 2}, {3, 3}, {4, 4}, {1, 1}}},  // INVESTIGATE: why the epsilon is smaller
+    {{{2, 2}, {4+D, 4}, {1, 1}, {3, 3}}},
+    {{{2, 2}, {4, 4}, {3, 3}, {1, 1+D}}},
+};
+
+const size_t lessEpsilonLines_count = sizeof(lessEpsilonLines) / sizeof(lessEpsilonLines[0]);
+
+const SkDCubic negEpsilonLines[] = {
+    {{{0, N}, {0, 0}, {0, 0}, {1, 0}}},  // horizontal
+    {{{1, 0}, {0, 0}, {0, 0}, {0, N}}},
+    {{{1, N}, {2, 0}, {3, 0}, {4, 0}}},
+    {{{N, 0}, {0, 0}, {0, 0}, {0, 1}}},  // vertical
+    {{{0, 1}, {0, 0}, {0, 0}, {N, 0}}},
+    {{{N, 1}, {0, 2}, {0, 3}, {0, 4}}},
+    {{{N, 0}, {0, 0}, {0, 0}, {1, 1}}},  // 3 coincident
+    {{{1, 1}, {0, 0}, {0, 0}, {N, 0}}},
+    {{{0, N}, {0, 0}, {1, 1}, {2, 2}}},  // 2 coincident
+    {{{0, 0}, {1, 1}, {0, N}, {2, 2}}},
+    {{{0, 0}, {1, 1}, {2, 2}, {0, N}}},
+    {{{1, 1}, {0, N}, {0, 0}, {2, 2}}},
+    {{{1, 1}, {0, N}, {2, 2}, {0, 0}}},
+    {{{1, 1}, {2, 2}, {N, 0}, {0, 0}}},
+    {{{1, 1}, {2, 2+N}, {3, 3}, {2, 2}}},  // middle-last coincident
+    {{{1, 1}, {2+N, 2}, {3, 3}, {3, 3}}},  // middle-last coincident
+    {{{1, 1}, {1, 1}, {2, 2}, {2+N, 2}}},  // 2 pairs coincident
+    {{{1, 1}, {2, 2}, {1, 1}, {2+N, 2}}},
+    {{{1, 1}, {1, 1+N}, {3, 3}, {3, 3}}},  // first-middle middle-last coincident
+    {{{1, 1}, {2+N/2, 2}, {3, 3}, {4, 4}}},  // no coincident (FIXME: N as opposed to N/2 failed)
+    {{{1, 1}, {3, 3}, {2, 2}, {4, 4+N}}},
+    {{{1, 1+N}, {2, 2}, {4, 4}, {3, 3}}},
+    {{{1, 1}, {3, 3}, {4, 4+N}, {2, 2}}},
+    {{{1, 1}, {4, 4}, {2, 2}, {3, 3+N}}},
+    {{{1, 1}, {4, 4}, {3, 3}, {2+M, 2}}},  // INVESTIGATE: why the epsilon is smaller
+    {{{2, 2}, {1, 1}, {3+N, 3}, {4, 4}}},
+    {{{2, 2}, {1+N, 1}, {4, 4}, {3, 3}}},
+    {{{2, 2+N}, {3, 3}, {1, 1}, {4, 4}}},
+    {{{2+M, 2}, {3, 3}, {4, 4}, {1, 1}}},  // INVESTIGATE: why the epsilon is smaller
+    {{{2, 2}, {4+N, 4}, {1, 1}, {3, 3}}},
+    {{{2, 2}, {4, 4}, {3, 3}, {1, 1+N}}},
+};
+
+const size_t negEpsilonLines_count = sizeof(negEpsilonLines) / sizeof(negEpsilonLines[0]);