1/*
2 * Copyright (C) 2010 Google Inc. All rights reserved.
3 *
4 * Redistribution and use in source and binary forms, with or without
5 * modification, are permitted provided that the following conditions
6 * are met:
7 *
8 * 1.  Redistributions of source code must retain the above copyright
9 *     notice, this list of conditions and the following disclaimer.
10 * 2.  Redistributions in binary form must reproduce the above copyright
11 *     notice, this list of conditions and the following disclaimer in the
12 *     documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY APPLE AND ITS CONTRIBUTORS "AS IS" AND ANY
15 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
16 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
17 * DISCLAIMED. IN NO EVENT SHALL APPLE OR ITS CONTRIBUTORS BE LIABLE FOR ANY
18 * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
19 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
20 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
21 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
22 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
23 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
24 */
25
26#ifndef LoopBlinnMathUtils_h
27#define LoopBlinnMathUtils_h
28
29#include "FloatPoint.h"
30#include "FloatPoint3D.h"
31#include <math.h>
32
33namespace WebCore {
34
35// Use a namespace for these so we can easily import them.
36namespace LoopBlinnMathUtils {
37
38float roundToZero(float val);
39bool approxEqual(const FloatPoint& v0, const FloatPoint& v1);
40bool approxEqual(const FloatPoint3D& v0, const FloatPoint3D& v1);
41bool approxEqual(float f0, float f1);
42
43// Determines whether the line segment between (p1, q1) intersects
44// that between (p2, q2).
45bool linesIntersect(const FloatPoint& p1,
46                    const FloatPoint& q1,
47                    const FloatPoint& p2,
48                    const FloatPoint& q2);
49
50// Determines whether "point" is inside the 2D triangle defined by
51// vertices a, b, and c. This test defines that points exactly on an
52// edge are not considered to be inside the triangle.
53bool pointInTriangle(const FloatPoint& point,
54                     const FloatPoint& a,
55                     const FloatPoint& b,
56                     const FloatPoint& c);
57
58// Determines whether the triangles defined by the points (a1, b1, c1)
59// and (a2, b2, c2) overlap. The definition of this function is that
60// if the two triangles only share an adjacent edge or vertex, they
61// are not considered to overlap.
62bool trianglesOverlap(const FloatPoint& a1,
63                      const FloatPoint& b1,
64                      const FloatPoint& c1,
65                      const FloatPoint& a2,
66                      const FloatPoint& b2,
67                      const FloatPoint& c2);
68
69// Given a src cubic bezier, chops it at the specified t value,
70// where 0 < t < 1, and returns the two new cubics in dst[0..3]
71// and dst[3..6].
72void chopCubicAt(const FloatPoint src[4], FloatPoint dst[7], float t);
73
74// "X-Ray" queries. An XRay is a half-line originating at the given
75// point and extending to x=+infinity.
76typedef FloatPoint XRay;
77
78// Given an arbitrary cubic bezier, return the number of times an XRay
79// crosses the cubic. Valid return values are [0..3].
80//
81// By definition the cubic is open at the starting point; in other
82// words, if pt.fY is equivalent to cubic[0].fY, and pt.fX is to the
83// left of the curve, the line is not considered to cross the curve,
84// but if it is equal to cubic[3].fY then it is considered to
85// cross.
86//
87// Outgoing "ambiguous" argument indicates whether the answer is ambiguous
88// because the query occurred exactly at one of the endpoints' y
89// coordinates or at a tangent point, indicating that another query y
90// coordinate is preferred for robustness.
91int numXRayCrossingsForCubic(const XRay& xRay,
92                             const FloatPoint cubic[4],
93                             bool& ambiguous);
94
95// Given a line segment from lineEndpoints[0] to lineEndpoints[1], and an
96// XRay, returns true if they intersect. Outgoing "ambiguous" argument
97// indicates whether the answer is ambiguous because the query occurred
98// exactly at one of the endpoints' y coordinates, indicating that another
99// query y coordinate is preferred for robustness.
100bool xRayCrossesLine(const XRay& xRay,
101                     const FloatPoint lineEndpoints[2],
102                     bool& ambiguous);
103
104
105bool isConvex(const FloatPoint* vertices, int nVertices);
106
107} // namespace LoopBlinnMathUtils
108
109} // namespace WebCore
110
111#endif // LoopBlinnMathUtils_h
112