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skia2/tests/PathOpsCubicIntersectionTestData.cpp
caryclark 54359294a7 cumulative pathops patch 
Replace the implicit curve intersection with a geometric curve intersection. The implicit intersection proved mathematically unstable and took a long time to zero in on an answer.

Use pointers instead of indices to refer to parts of curves. Indices required awkward renumbering.

Unify t and point values so that small intervals can be eliminated in one pass.

Break cubics up front to eliminate loops and cusps.

Make the Simplify and Op code more regular and eliminate arbitrary differences.

Add a builder that takes an array of paths and operators.

Delete unused code.

BUG=skia:3588
R=reed@google.com

Review URL: https://codereview.chromium.org/1037573004
2015-03-26 07:52:43 -07:00

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/*
* 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 = SK_ARRAY_COUNT(pointDegenerates);
const SkDCubic notPointDegenerates[] = {
{{{1 + FLT_EPSILON * 8, 1}, {1, FLT_EPSILON * 8}, {1, 1}, {1, 1}}},
{{{1 + FLT_EPSILON * 8, 1}, {1 - FLT_EPSILON * 8, 1}, {1, 1}, {1, 1}}}
};
const size_t notPointDegenerates_count =
SK_ARRAY_COUNT(notPointDegenerates);
// 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}}}
}, {
{{{104.11546583642826, 370.21352558595504}, {122.96968232592344, 404.54489231839295},
{169.90881005384728, 425.00067000000007}, {221.33045999999999, 425.00067000000001}}},
{{{116.32365976159625, 381.71048540582598}, {103.86096590870899, 381.71048540581626},
{91.394188003200725, 377.17917781762833}, {82.622283093355179, 368.11683661930334}}}
}
};
const size_t tests_count = SK_ARRAY_COUNT(tests);
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 = SK_ARRAY_COUNT(lines);
// '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 = SK_ARRAY_COUNT(notLines);
static const double E = FLT_EPSILON * 8;
static const double F = FLT_EPSILON * 8;
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+F}}}, // INVESTIGATE: why the epsilon is bigger
{{{1, 1+F+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 = SK_ARRAY_COUNT(modEpsilonLines);
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}, {1, 1+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 = SK_ARRAY_COUNT(lessEpsilonLines);
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}, {1, 1+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 = SK_ARRAY_COUNT(negEpsilonLines);
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