From 9166dcb3a0e8784bea83d76ae01aa338c049ae05 Mon Sep 17 00:00:00 2001
From: "caryclark@google.com"
 <caryclark@google.com@2bbb7eff-a529-9590-31e7-b0007b416f81>
Date: Mon, 8 Apr 2013 11:50:00 +0000
Subject: 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
---
 tests/PathOpsQuadIntersectionTestData.cpp | 104 ++++++++++++++++++++++++++++++
 1 file changed, 104 insertions(+)
 create mode 100644 tests/PathOpsQuadIntersectionTestData.cpp

(limited to 'tests/PathOpsQuadIntersectionTestData.cpp')

diff --git a/tests/PathOpsQuadIntersectionTestData.cpp b/tests/PathOpsQuadIntersectionTestData.cpp
new file mode 100644
index 0000000000..3c3bcdf468
--- /dev/null
+++ b/tests/PathOpsQuadIntersectionTestData.cpp
@@ -0,0 +1,104 @@
+/*
+ * 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 "PathOpsQuadIntersectionTestData.h"
+
+const SkDQuad quadraticPoints[] = {
+    {{{0, 0}, {1, 0}, {0, 0}}},
+    {{{0, 0}, {0, 1}, {0, 0}}},
+    {{{0, 0}, {1, 1}, {0, 0}}},
+    {{{1, 1}, {2, 2}, {1, 1}}},
+};
+
+const size_t quadraticPoints_count = sizeof(quadraticPoints) / sizeof(quadraticPoints[0]);
+
+const SkDQuad quadraticLines[] = {
+    {{{0, 0}, {0, 0}, {1, 0}}},
+    {{{1, 0}, {0, 0}, {0, 0}}},
+    {{{1, 0}, {2, 0}, {3, 0}}},
+    {{{0, 0}, {0, 0}, {0, 1}}},
+    {{{0, 1}, {0, 0}, {0, 0}}},
+    {{{0, 1}, {0, 2}, {0, 3}}},
+    {{{0, 0}, {0, 0}, {1, 1}}},
+    {{{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}, {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]);
+
+static const double F = FLT_EPSILON * 3;
+static const double H = FLT_EPSILON * 4;
+static const double J = FLT_EPSILON * 5;
+static const double K = FLT_EPSILON * 8;  // INVESTIGATE: why are larger multiples necessary?
+
+const SkDQuad 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]);
+
+const SkDQuad quadraticTests[][2] = {
+    {  // one intersection
+     {{{0, 0},
+      {0, 1},
+      {1, 1}}},
+     {{{0, 1},
+      {0, 0},
+      {1, 0}}}
+    },
+    {  // four intersections
+     {{{1, 0},
+      {2, 6},
+      {3, 0}}},
+     {{{0, 1},
+      {6, 2},
+      {0, 3}}}
+    }
+};
+
+const size_t quadraticTests_count = sizeof(quadraticTests) / sizeof(quadraticTests[0]);
-- 
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