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
diff --git a/tests/PathOpsCubicReduceOrderTest.cpp b/tests/PathOpsCubicReduceOrderTest.cpp
new file mode 100644
index 0000000..25f6b2a
--- /dev/null
+++ b/tests/PathOpsCubicReduceOrderTest.cpp
@@ -0,0 +1,226 @@
+/*
+ * 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 "PathOpsQuadIntersectionTestData.h"
+#include "SkIntersections.h"
+#include "SkPathOpsRect.h"
+#include "SkReduceOrder.h"
+#include "Test.h"
+
+static bool controls_inside(const SkDCubic& cubic) {
+ return between(cubic[0].fX, cubic[1].fX, cubic[3].fX)
+ && between(cubic[0].fX, cubic[2].fX, cubic[3].fX)
+ && between(cubic[0].fY, cubic[1].fY, cubic[3].fY)
+ && between(cubic[0].fY, cubic[2].fY, cubic[3].fY);
+}
+
+static bool tiny(const SkDCubic& cubic) {
+ int index, minX, maxX, minY, maxY;
+ minX = maxX = minY = maxY = 0;
+ for (index = 1; index < 4; ++index) {
+ if (cubic[minX].fX > cubic[index].fX) {
+ minX = index;
+ }
+ if (cubic[minY].fY > cubic[index].fY) {
+ minY = index;
+ }
+ if (cubic[maxX].fX < cubic[index].fX) {
+ maxX = index;
+ }
+ if (cubic[maxY].fY < cubic[index].fY) {
+ maxY = index;
+ }
+ }
+ return approximately_equal(cubic[maxX].fX, cubic[minX].fX)
+ && approximately_equal(cubic[maxY].fY, cubic[minY].fY);
+}
+
+static void find_tight_bounds(const SkDCubic& cubic, SkDRect& bounds) {
+ SkDCubicPair cubicPair = cubic.chopAt(0.5);
+ if (!tiny(cubicPair.first()) && !controls_inside(cubicPair.first())) {
+ find_tight_bounds(cubicPair.first(), bounds);
+ } else {
+ bounds.add(cubicPair.first()[0]);
+ bounds.add(cubicPair.first()[3]);
+ }
+ if (!tiny(cubicPair.second()) && !controls_inside(cubicPair.second())) {
+ find_tight_bounds(cubicPair.second(), bounds);
+ } else {
+ bounds.add(cubicPair.second()[0]);
+ bounds.add(cubicPair.second()[3]);
+ }
+}
+
+static void CubicReduceOrderTest(skiatest::Reporter* reporter) {
+ size_t index;
+ SkReduceOrder reducer;
+ int order;
+ enum {
+ RunAll,
+ RunPointDegenerates,
+ RunNotPointDegenerates,
+ RunLines,
+ RunNotLines,
+ RunModEpsilonLines,
+ RunLessEpsilonLines,
+ RunNegEpsilonLines,
+ RunQuadraticLines,
+ RunQuadraticPoints,
+ RunQuadraticModLines,
+ RunComputedLines,
+ RunNone
+ } run = RunAll;
+ int firstTestIndex = 0;
+#if 0
+ run = RunComputedLines;
+ firstTestIndex = 18;
+#endif
+ int firstPointDegeneratesTest = run == RunAll ? 0 : run == RunPointDegenerates
+ ? firstTestIndex : SK_MaxS32;
+ int firstNotPointDegeneratesTest = run == RunAll ? 0 : run == RunNotPointDegenerates
+ ? firstTestIndex : SK_MaxS32;
+ int firstLinesTest = run == RunAll ? 0 : run == RunLines ? firstTestIndex : SK_MaxS32;
+ int firstNotLinesTest = run == RunAll ? 0 : run == RunNotLines ? firstTestIndex : SK_MaxS32;
+ int firstModEpsilonTest = run == RunAll ? 0 : run == RunModEpsilonLines
+ ? firstTestIndex : SK_MaxS32;
+ int firstLessEpsilonTest = run == RunAll ? 0 : run == RunLessEpsilonLines
+ ? firstTestIndex : SK_MaxS32;
+ int firstNegEpsilonTest = run == RunAll ? 0 : run == RunNegEpsilonLines
+ ? firstTestIndex : SK_MaxS32;
+ int firstQuadraticPointTest = run == RunAll ? 0 : run == RunQuadraticPoints
+ ? firstTestIndex : SK_MaxS32;
+ int firstQuadraticLineTest = run == RunAll ? 0 : run == RunQuadraticLines
+ ? firstTestIndex : SK_MaxS32;
+ int firstQuadraticModLineTest = run == RunAll ? 0 : run == RunQuadraticModLines
+ ? firstTestIndex : SK_MaxS32;
+ int firstComputedLinesTest = run == RunAll ? 0 : run == RunComputedLines
+ ? firstTestIndex : SK_MaxS32;
+
+ for (index = firstPointDegeneratesTest; index < pointDegenerates_count; ++index) {
+ const SkDCubic& cubic = pointDegenerates[index];
+ order = reducer.reduce(cubic, SkReduceOrder::kAllow_Quadratics, SkReduceOrder::kFill_Style);
+ if (order != 1) {
+ SkDebugf("[%d] pointDegenerates order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ }
+ for (index = firstNotPointDegeneratesTest; index < notPointDegenerates_count; ++index) {
+ const SkDCubic& cubic = notPointDegenerates[index];
+ order = reducer.reduce(cubic, SkReduceOrder::kAllow_Quadratics, SkReduceOrder::kFill_Style);
+ if (order == 1) {
+ SkDebugf("[%d] notPointDegenerates order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ }
+ for (index = firstLinesTest; index < lines_count; ++index) {
+ const SkDCubic& cubic = lines[index];
+ order = reducer.reduce(cubic, SkReduceOrder::kAllow_Quadratics, SkReduceOrder::kFill_Style);
+ if (order != 2) {
+ SkDebugf("[%d] lines order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ }
+ for (index = firstNotLinesTest; index < notLines_count; ++index) {
+ const SkDCubic& cubic = notLines[index];
+ order = reducer.reduce(cubic, SkReduceOrder::kAllow_Quadratics, SkReduceOrder::kFill_Style);
+ if (order == 2) {
+ SkDebugf("[%d] notLines order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ }
+ for (index = firstModEpsilonTest; index < modEpsilonLines_count; ++index) {
+ const SkDCubic& cubic = modEpsilonLines[index];
+ order = reducer.reduce(cubic, SkReduceOrder::kAllow_Quadratics, SkReduceOrder::kFill_Style);
+ if (order == 2) {
+ SkDebugf("[%d] line mod by epsilon order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ }
+ for (index = firstLessEpsilonTest; index < lessEpsilonLines_count; ++index) {
+ const SkDCubic& cubic = lessEpsilonLines[index];
+ order = reducer.reduce(cubic, SkReduceOrder::kAllow_Quadratics, SkReduceOrder::kFill_Style);
+ if (order != 2) {
+ SkDebugf("[%d] line less by epsilon/2 order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ }
+ for (index = firstNegEpsilonTest; index < negEpsilonLines_count; ++index) {
+ const SkDCubic& cubic = negEpsilonLines[index];
+ order = reducer.reduce(cubic, SkReduceOrder::kAllow_Quadratics, SkReduceOrder::kFill_Style);
+ if (order != 2) {
+ SkDebugf("[%d] line neg by epsilon/2 order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ }
+ for (index = firstQuadraticPointTest; index < quadraticPoints_count; ++index) {
+ const SkDQuad& quad = quadraticPoints[index];
+ SkDCubic cubic = quad.toCubic();
+ order = reducer.reduce(cubic, SkReduceOrder::kAllow_Quadratics, SkReduceOrder::kFill_Style);
+ if (order != 1) {
+ SkDebugf("[%d] point quad order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ }
+ for (index = firstQuadraticLineTest; index < quadraticLines_count; ++index) {
+ const SkDQuad& quad = quadraticLines[index];
+ SkDCubic cubic = quad.toCubic();
+ order = reducer.reduce(cubic, SkReduceOrder::kAllow_Quadratics, SkReduceOrder::kFill_Style);
+ if (order != 2) {
+ SkDebugf("[%d] line quad order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ }
+ for (index = firstQuadraticModLineTest; index < quadraticModEpsilonLines_count; ++index) {
+ const SkDQuad& quad = quadraticModEpsilonLines[index];
+ SkDCubic cubic = quad.toCubic();
+ order = reducer.reduce(cubic, SkReduceOrder::kAllow_Quadratics, SkReduceOrder::kFill_Style);
+ if (order != 3) {
+ SkDebugf("[%d] line mod quad order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ }
+
+ // test if computed line end points are valid
+ for (index = firstComputedLinesTest; index < lines_count; ++index) {
+ const SkDCubic& cubic = lines[index];
+ bool controlsInside = controls_inside(cubic);
+ order = reducer.reduce(cubic, SkReduceOrder::kAllow_Quadratics,
+ SkReduceOrder::kStroke_Style);
+ if (order == 2 && reducer.fLine[0] == reducer.fLine[1]) {
+ SkDebugf("[%d] line computed ends match order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ if (controlsInside) {
+ if ( (reducer.fLine[0].fX != cubic[0].fX && reducer.fLine[0].fX != cubic[3].fX)
+ || (reducer.fLine[0].fY != cubic[0].fY && reducer.fLine[0].fY != cubic[3].fY)
+ || (reducer.fLine[1].fX != cubic[0].fX && reducer.fLine[1].fX != cubic[3].fX)
+ || (reducer.fLine[1].fY != cubic[0].fY && reducer.fLine[1].fY != cubic[3].fY)) {
+ SkDebugf("[%d] line computed ends order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ } else {
+ // binary search for extrema, compare against actual results
+ // while a control point is outside of bounding box formed by end points, split
+ SkDRect bounds = {DBL_MAX, DBL_MAX, -DBL_MAX, -DBL_MAX};
+ find_tight_bounds(cubic, bounds);
+ if ( (!AlmostEqualUlps(reducer.fLine[0].fX, bounds.fLeft)
+ && !AlmostEqualUlps(reducer.fLine[0].fX, bounds.fRight))
+ || (!AlmostEqualUlps(reducer.fLine[0].fY, bounds.fTop)
+ && !AlmostEqualUlps(reducer.fLine[0].fY, bounds.fBottom))
+ || (!AlmostEqualUlps(reducer.fLine[1].fX, bounds.fLeft)
+ && !AlmostEqualUlps(reducer.fLine[1].fX, bounds.fRight))
+ || (!AlmostEqualUlps(reducer.fLine[1].fY, bounds.fTop)
+ && !AlmostEqualUlps(reducer.fLine[1].fY, bounds.fBottom))) {
+ SkDebugf("[%d] line computed tight bounds order=%d\n", static_cast<int>(index), order);
+ REPORTER_ASSERT(reporter, 0);
+ }
+ }
+ }
+}
+
+#include "TestClassDef.h"
+DEFINE_TESTCLASS("PathOpsReduceOrderCubic", ReduceOrderCubicTestClass, CubicReduceOrderTest)