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/CubicIntersection_TestData.cpp b/experimental/Intersection/CubicIntersection_TestData.cpp
new file mode 100644
index 0000000..95d44d7
--- /dev/null
+++ b/experimental/Intersection/CubicIntersection_TestData.cpp
@@ -0,0 +1,373 @@
+#include "CubicIntersection_TestData.h"
+#include <limits>
+
+const Cubic pointDegenerates[] = {
+ {{0, 0}, {0, 0}, {0, 0}, {0, 0}},
+ {{1, 1}, {1, 1}, {1, 1}, {1, 1}},
+ {{1 + PointEpsilon - std::numeric_limits<double>::epsilon(), 1},
+ {1, 1 + PointEpsilon - std::numeric_limits<double>::epsilon()}, {1, 1}, {1, 1}},
+ {{1 + PointEpsilon/2 - std::numeric_limits<double>::epsilon(), 1},
+ {1 - (PointEpsilon/2 - std::numeric_limits<double>::epsilon()), 1}, {1, 1}, {1, 1}}
+};
+
+const size_t pointDegenerates_count = sizeof(pointDegenerates) / sizeof(pointDegenerates[0]);
+
+const Cubic notPointDegenerates[] = {
+ {{1 + PointEpsilon + std::numeric_limits<double>::epsilon(), 1}, {1, 1 + PointEpsilon}, {1, 1}, {1, 1}},
+ {{1 + PointEpsilon/2 + std::numeric_limits<double>::epsilon(), 1}, {1 - PointEpsilon/2, 1}, {1, 1}, {1, 1}}
+};
+
+const size_t notPointDegenerates_count = sizeof(notPointDegenerates) / sizeof(notPointDegenerates[0]);
+
+// from http://www.truetex.com/bezint.htm
+const Cubic 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]);
+
+Cubic hexTests[][2] = {
+ {
+ {{0}} // placeholder for hex converted below
+ }
+};
+
+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].x;
+ 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 Cubic lines[] = {
+ {{0, 0}, {0, 0}, {0, 0}, {1, 0}}, // 0: horizontal
+ {{0, 0}, {0, 0}, {1, 0}, {0, 0}},
+ {{0, 0}, {1, 0}, {0, 0}, {0, 0}},
+ {{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, 0}, {0, 0}, {0, 1}, {0, 0}},
+ {{0, 0}, {0, 1}, {0, 0}, {0, 0}},
+ {{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
+ {{0, 0}, {0, 0}, {1, 1}, {0, 0}},
+ {{0, 0}, {1, 1}, {0, 0}, {0, 0}},
+ {{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}},
+ {{0, 0}, {1, 1}, {2, 2}, {0, 0}},
+ {{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}, {2, 2}, {2, 2}, {1, 1}},
+ {{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 Cubic 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 = PointEpsilon * 2;
+static const double F = PointEpsilon * 3;
+static const double H = PointEpsilon * 4;
+static const double J = PointEpsilon * 5;
+static const double K = PointEpsilon * 8; // INVESTIGATE: why are larger multiples necessary?
+
+const Cubic 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]);
+
+static const double D = PointEpsilon / 2;
+static const double G = PointEpsilon / 3;
+
+const Cubic lessEpsilonLines[] = {
+ {{0, D}, {0, 0}, {0, 0}, {1, 0}}, // horizontal
+ {{0, 0}, {0, D}, {1, 0}, {0, 0}},
+ {{0, 0}, {1, 0}, {0, D}, {0, 0}},
+ {{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, 0}, {D, 0}, {0, 1}, {0, 0}},
+ {{0, 0}, {0, 1}, {D, 0}, {0, 0}},
+ {{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
+ {{0, 0}, {D, 0}, {1, 1}, {0, 0}},
+ {{0, 0}, {1, 1}, {D, 0}, {0, 0}},
+ {{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}, {2, 2}, {2, 2+D}, {1, 1}},
+ {{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]);
+
+static const double N = -PointEpsilon / 2;
+static const double M = -PointEpsilon / 3;
+
+const Cubic negEpsilonLines[] = {
+ {{0, N}, {0, 0}, {0, 0}, {1, 0}}, // horizontal
+ {{0, 0}, {0, N}, {1, 0}, {0, 0}},
+ {{0, 0}, {1, 0}, {0, N}, {0, 0}},
+ {{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, 0}, {N, 0}, {0, 1}, {0, 0}},
+ {{0, 0}, {0, 1}, {N, 0}, {0, 0}},
+ {{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
+ {{0, 0}, {N, 0}, {1, 1}, {0, 0}},
+ {{0, 0}, {1, 1}, {N, 0}, {0, 0}},
+ {{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}, {2, 2}, {2, 2+N}, {1, 1}},
+ {{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]);
+
+const Quadratic quadraticLines[] = {
+ {{0, 0}, {0, 0}, {1, 0}},
+ {{0, 0}, {1, 0}, {0, 0}},
+ {{1, 0}, {0, 0}, {0, 0}},
+ {{1, 0}, {2, 0}, {3, 0}},
+ {{0, 0}, {0, 0}, {0, 1}},
+ {{0, 0}, {0, 1}, {0, 0}},
+ {{0, 1}, {0, 0}, {0, 0}},
+ {{0, 1}, {0, 2}, {0, 3}},
+ {{0, 0}, {0, 0}, {1, 1}},
+ {{0, 0}, {1, 1}, {0, 0}},
+ {{1, 1}, {0, 0}, {0, 0}},
+ {{1, 1}, {2, 2}, {3, 3}},
+ {{1, 1}, {3, 3}, {3, 3}},
+ {{1, 1}, {1, 1}, {2, 2}},
+ {{1, 1}, {2, 2}, {1, 1}},
+ {{1, 1}, {1, 1}, {3, 3}},
+ {{1, 1}, {2, 2}, {4, 4}}, // no coincident
+ {{1, 1}, {3, 3}, {4, 4}},
+ {{1, 1}, {3, 3}, {2, 2}},
+ {{1, 1}, {4, 4}, {2, 2}},
+ {{1, 1}, {4, 4}, {3, 3}},
+ {{2, 2}, {1, 1}, {3, 3}},
+ {{2, 2}, {1, 1}, {4, 4}},
+ {{2, 2}, {3, 3}, {1, 1}},
+ {{2, 2}, {3, 3}, {4, 4}},
+ {{2, 2}, {4, 4}, {1, 1}},
+ {{2, 2}, {4, 4}, {3, 3}},
+};
+
+const size_t quadraticLines_count = sizeof(quadraticLines) / sizeof(quadraticLines[0]);
+
+const Quadratic quadraticModEpsilonLines[] = {
+ {{0, F}, {0, 0}, {1, 0}},
+ {{0, 0}, {1, 0}, {0, F}},
+ {{1, 0}, {0, F}, {0, 0}},
+ {{1, H}, {2, 0}, {3, 0}},
+ {{F, 0}, {0, 0}, {0, 1}},
+ {{0, 0}, {0, 1}, {F, 0}},
+ {{0, 1}, {F, 0}, {0, 0}},
+ {{H, 1}, {0, 2}, {0, 3}},
+ {{0, F}, {0, 0}, {1, 1}},
+ {{0, 0}, {1, 1}, {F, 0}},
+ {{1, 1}, {F, 0}, {0, 0}},
+ {{1, 1+J}, {2, 2}, {3, 3}},
+ {{1, 1}, {3, 3}, {3+F, 3}},
+ {{1, 1}, {1+F, 1}, {2, 2}},
+ {{1, 1}, {2, 2}, {1, 1+F}},
+ {{1, 1}, {1, 1+F}, {3, 3}},
+ {{1+H, 1}, {2, 2}, {4, 4}}, // no coincident
+ {{1, 1+K}, {3, 3}, {4, 4}},
+ {{1, 1}, {3+F, 3}, {2, 2}},
+ {{1, 1}, {4, 4+F}, {2, 2}},
+ {{1, 1}, {4, 4}, {3+F, 3}},
+ {{2, 2}, {1, 1}, {3, 3+F}},
+ {{2+F, 2}, {1, 1}, {4, 4}},
+ {{2, 2+F}, {3, 3}, {1, 1}},
+ {{2, 2}, {3+F, 3}, {4, 4}},
+ {{2, 2}, {4, 4+F}, {1, 1}},
+ {{2, 2}, {4, 4}, {3+F, 3}},
+};
+
+const size_t quadraticModEpsilonLines_count = sizeof(quadraticModEpsilonLines) / sizeof(quadraticModEpsilonLines[0]);
+
+