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, 80 insertions, 0 deletions

diff --git a/tests/PathOpsLineParametetersTest.cpp b/tests/PathOpsLineParametetersTest.cpp
new file mode 100644
index 0000000000..2dad1b2e2c
--- /dev/null
+++ b/tests/PathOpsLineParametetersTest.cpp
@@ -0,0 +1,80 @@
+/*
+ * 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 "SkLineParameters.h"
+#include "Test.h"
+
+// tests to verify that distance calculations are coded correctly
+static const SkDCubic tests[] = {
+    {{{0, 0}, {1, 1}, {2, 2}, {0, 3}}},
+    {{{0, 0}, {1, 1}, {2, 2}, {3, 0}}},
+    {{{0, 0}, {5, 0}, {-2, 4}, {3, 4}}},
+    {{{0, 2}, {1, 0}, {2, 0}, {3, 0}}},
+    {{{0, .2}, {1, 0}, {2, 0}, {3, 0}}},
+    {{{0, .02}, {1, 0}, {2, 0}, {3, 0}}},
+    {{{0, .002}, {1, 0}, {2, 0}, {3, 0}}},
+    {{{0, .0002}, {1, 0}, {2, 0}, {3, 0}}},
+    {{{0, .00002}, {1, 0}, {2, 0}, {3, 0}}},
+    {{{0, FLT_EPSILON * 2}, {1, 0}, {2, 0}, {3, 0}}},
+};
+
+static const double answers[][2] = {
+    {1, 2},
+    {1, 2},
+    {4, 4},
+    {1.1094003924, 0.5547001962},
+    {0.133038021, 0.06651901052},
+    {0.0133330370, 0.006666518523},
+    {0.001333333037, 0.0006666665185},
+    {0.000133333333, 6.666666652e-05},
+    {1.333333333e-05, 6.666666667e-06},
+    {1.5894571940104115e-07, 7.9472859700520577e-08},
+};
+
+static const size_t tests_count = sizeof(tests) / sizeof(tests[0]);
+
+static void LineParameterTest(skiatest::Reporter* reporter) {
+    for (size_t index = 0; index < tests_count; ++index) {
+        SkLineParameters lineParameters;
+        const SkDCubic& cubic = tests[index];
+        lineParameters.cubicEndPoints(cubic);
+        double denormalizedDistance[2];
+        denormalizedDistance[0] = lineParameters.controlPtDistance(cubic, 1);
+        denormalizedDistance[1] = lineParameters.controlPtDistance(cubic, 2);
+        double normalSquared = lineParameters.normalSquared();
+        size_t inner;
+        for (inner = 0; inner < 2; ++inner) {
+            double distSq = denormalizedDistance[inner];
+            distSq *= distSq;
+            double answersSq = answers[index][inner];
+            answersSq *= answersSq;
+            if (AlmostEqualUlps(distSq, normalSquared * answersSq)) {
+                continue;
+            }
+            SkDebugf("%s [%d,%d] denormalizedDistance:%g != answer:%g"
+                    " distSq:%g answerSq:%g normalSquared:%g\n",
+                    __FUNCTION__, static_cast<int>(index), (int)inner,
+                    denormalizedDistance[inner], answers[index][inner],
+                    distSq, answersSq, normalSquared);
+        }
+        lineParameters.normalize();
+        double normalizedDistance[2];
+        normalizedDistance[0] = lineParameters.controlPtDistance(cubic, 1);
+        normalizedDistance[1] = lineParameters.controlPtDistance(cubic, 2);
+        for (inner = 0; inner < 2; ++inner) {
+            if (AlmostEqualUlps(fabs(normalizedDistance[inner]), answers[index][inner])) {
+                continue;
+            }
+            SkDebugf("%s [%d,%d] normalizedDistance:%1.10g != answer:%g\n",
+                    __FUNCTION__, static_cast<int>(index), (int)inner,
+                    normalizedDistance[inner], answers[index][inner]);
+            REPORTER_ASSERT(reporter, 0);
+        }
+    }
+}
+
+#include "TestClassDef.h"
+DEFINE_TESTCLASS("PathOpsLineParameters", PathOpsLineParametersClass, LineParameterTest)