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, 132 insertions, 0 deletions

diff --git a/tests/PathOpsQuadLineIntersectionTest.cpp b/tests/PathOpsQuadLineIntersectionTest.cpp
new file mode 100644
index 0000000000..09c28c1cea
--- /dev/null
+++ b/tests/PathOpsQuadLineIntersectionTest.cpp
@@ -0,0 +1,132 @@
+/*
+ * 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 "PathOpsExtendedTest.h"
+#include "SkIntersections.h"
+#include "SkPathOpsLine.h"
+#include "SkPathOpsQuad.h"
+#include "SkReduceOrder.h"
+#include "Test.h"
+
+static struct lineQuad {
+    SkDQuad quad;
+    SkDLine line;
+    int result;
+    SkDPoint expected[2];
+} lineQuadTests[] = {
+    //        quad                    line                  results
+    {{{{1, 1}, {2, 1}, {0, 2}}}, {{{0, 0}, {1, 1}}},  1,  {{1, 1}, {0, 0}} },
+    {{{{0, 0}, {1, 1}, {3, 1}}}, {{{0, 0}, {3, 1}}},  2,  {{0, 0}, {3, 1}} },
+    {{{{2, 0}, {1, 1}, {2, 2}}}, {{{0, 0}, {0, 2}}},  0,  {{0, 0}, {0, 0}} },
+    {{{{4, 0}, {0, 1}, {4, 2}}}, {{{3, 1}, {4, 1}}},  0,  {{0, 0}, {0, 0}} },
+    {{{{0, 0}, {0, 1}, {1, 1}}}, {{{0, 1}, {1, 0}}},  1,  {{.25, .75}, {0, 0}} },
+};
+
+static size_t lineQuadTests_count = sizeof(lineQuadTests) / sizeof(lineQuadTests[0]);
+
+static int doIntersect(SkIntersections& intersections, const SkDQuad& quad, const SkDLine& line,
+                       bool& flipped) {
+    int result;
+    flipped = false;
+    if (line[0].fX == line[1].fX) {
+        double top = line[0].fY;
+        double bottom = line[1].fY;
+        flipped = top > bottom;
+        if (flipped) {
+            SkTSwap<double>(top, bottom);
+        }
+        result = intersections.vertical(quad, top, bottom, line[0].fX, flipped);
+    } else if (line[0].fY == line[1].fY) {
+        double left = line[0].fX;
+        double right = line[1].fX;
+        flipped = left > right;
+        if (flipped) {
+            SkTSwap<double>(left, right);
+        }
+        result = intersections.horizontal(quad, left, right, line[0].fY, flipped);
+    } else {
+        intersections.intersect(quad, line);
+        result = intersections.used();
+    }
+    return result;
+}
+
+static struct oneLineQuad {
+    SkDQuad quad;
+    SkDLine line;
+} oneOffs[] = {
+    {{{{369.848602, 145.680267}, {382.360413, 121.298294}, {406.207703, 121.298294}}},
+        {{{406.207703, 121.298294}, {348.781738, 123.864815}}}}
+    };
+
+static size_t oneOffs_count = sizeof(oneOffs) / sizeof(oneOffs[0]);
+
+static void testOneOffs(skiatest::Reporter* reporter) {
+    SkIntersections intersections;
+    bool flipped = false;
+    for (size_t index = 0; index < oneOffs_count; ++index) {
+        const SkDQuad& quad = oneOffs[index].quad;
+        const SkDLine& line = oneOffs[index].line;
+        int result = doIntersect(intersections, quad, line, flipped);
+        for (int inner = 0; inner < result; ++inner) {
+            double quadT = intersections[0][inner];
+            SkDPoint quadXY = quad.xyAtT(quadT);
+            double lineT = intersections[1][inner];
+            SkDPoint lineXY = line.xyAtT(lineT);
+            REPORTER_ASSERT(reporter, quadXY.approximatelyEqual(lineXY));
+        }
+    }
+}
+
+static void TestQuadLineIntersection(skiatest::Reporter* reporter) {
+    testOneOffs(reporter);
+    for (size_t index = 0; index < lineQuadTests_count; ++index) {
+        int iIndex = static_cast<int>(index);
+        const SkDQuad& quad = lineQuadTests[index].quad;
+        const SkDLine& line = lineQuadTests[index].line;
+        SkReduceOrder reducer1, reducer2;
+        int order1 = reducer1.reduce(quad, SkReduceOrder::kFill_Style);
+        int order2 = reducer2.reduce(line);
+        if (order1 < 3) {
+            SkDebugf("%s [%d] quad order=%d\n", __FUNCTION__, iIndex, order1);
+            REPORTER_ASSERT(reporter, 0);
+        }
+        if (order2 < 2) {
+            SkDebugf("%s [%d] line order=%d\n", __FUNCTION__, iIndex, order2);
+            REPORTER_ASSERT(reporter, 0);
+        }
+        SkIntersections intersections;
+        bool flipped = false;
+        int result = doIntersect(intersections, quad, line, flipped);
+        REPORTER_ASSERT(reporter, result == lineQuadTests[index].result);
+        if (intersections.used() <= 0) {
+            continue;
+        }
+        for (int pt = 0; pt < result; ++pt) {
+            double tt1 = intersections[0][pt];
+            REPORTER_ASSERT(reporter, tt1 >= 0 && tt1 <= 1);
+            SkDPoint t1 = quad.xyAtT(tt1);
+            double tt2 = intersections[1][pt];
+            REPORTER_ASSERT(reporter, tt2 >= 0 && tt2 <= 1);
+            SkDPoint t2 = line.xyAtT(tt2);
+            if (!t1.approximatelyEqual(t2)) {
+                SkDebugf("%s [%d,%d] x!= t1=%1.9g (%1.9g,%1.9g) t2=%1.9g (%1.9g,%1.9g)\n",
+                    __FUNCTION__, iIndex, pt, tt1, t1.fX, t1.fY, tt2, t2.fX, t2.fY);
+                REPORTER_ASSERT(reporter, 0);
+            }
+            if (!t1.approximatelyEqual(lineQuadTests[index].expected[0])
+                    && (lineQuadTests[index].result == 1
+                    || !t1.approximatelyEqual(lineQuadTests[index].expected[1]))) {
+                SkDebugf("%s t1=(%1.9g,%1.9g)\n", __FUNCTION__, t1.fX, t1.fY);
+                REPORTER_ASSERT(reporter, 0);
+            }
+        }
+    }
+}
+
+#include "TestClassDef.h"
+DEFINE_TESTCLASS("PathOpsQuadLineIntersection", QuadLineIntersectionTestClass, \
+        TestQuadLineIntersection)