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