1/*
2 * Copyright (C) 2008 Apple Inc. All rights reserved.
3 * Copyright (C) 2012 Nokia Corporation and/or its subsidiary(-ies)
4 * Copyright (C) 2013 Xidorn Quan (quanxunzhen@gmail.com)
5 *
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
8 * are met:
9 *
10 * 1. Redistributions of source code must retain the above copyright
11 * notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
15 * 3. Neither the name of Apple Inc. ("Apple") nor the names of
16 * its contributors may be used to endorse or promote products derived
17 * from this software without specific prior written permission.
18 *
19 * THIS SOFTWARE IS PROVIDED BY APPLE AND ITS CONTRIBUTORS "AS IS" AND ANY
20 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
21 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
22 * DISCLAIMED. IN NO EVENT SHALL APPLE OR ITS CONTRIBUTORS BE LIABLE FOR ANY
23 * DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
24 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
25 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
26 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
27 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
28 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
29 */
30
31#include "config.h"
32#include "FloatQuad.h"
33
34#include <algorithm>
35#include <limits>
36#include <wtf/MathExtras.h>
37
38namespace WebCore {
39
40static inline float min4(float a, float b, float c, float d)
41{
42 return std::min(std::min(a, b), std::min(c, d));
43}
44
45static inline float max4(float a, float b, float c, float d)
46{
47 return std::max(std::max(a, b), std::max(c, d));
48}
49
50inline float dot(const FloatSize& a, const FloatSize& b)
51{
52 return a.width() * b.width() + a.height() * b.height();
53}
54
55inline float determinant(const FloatSize& a, const FloatSize& b)
56{
57 return a.width() * b.height() - a.height() * b.width();
58}
59
60inline bool isPointInTriangle(const FloatPoint& p, const FloatPoint& t1, const FloatPoint& t2, const FloatPoint& t3)
61{
62 // Compute vectors
63 FloatSize v0 = t3 - t1;
64 FloatSize v1 = t2 - t1;
65 FloatSize v2 = p - t1;
66
67 // Compute dot products
68 float dot00 = dot(v0, v0);
69 float dot01 = dot(v0, v1);
70 float dot02 = dot(v0, v2);
71 float dot11 = dot(v1, v1);
72 float dot12 = dot(v1, v2);
73
74 // Compute barycentric coordinates
75 float invDenom = 1.0f / (dot00 * dot11 - dot01 * dot01);
76 float u = (dot11 * dot02 - dot01 * dot12) * invDenom;
77 float v = (dot00 * dot12 - dot01 * dot02) * invDenom;
78
79 // Check if point is in triangle
80 return (u >= 0) && (v >= 0) && (u + v <= 1);
81}
82
83FloatRect FloatQuad::boundingBox() const
84{
85 float left = min4(m_p1.x(), m_p2.x(), m_p3.x(), m_p4.x());
86 float top = min4(m_p1.y(), m_p2.y(), m_p3.y(), m_p4.y());
87
88 float right = max4(m_p1.x(), m_p2.x(), m_p3.x(), m_p4.x());
89 float bottom = max4(m_p1.y(), m_p2.y(), m_p3.y(), m_p4.y());
90
91 return FloatRect(left, top, right - left, bottom - top);
92}
93
94bool FloatQuad::isRectilinear() const
95{
96 return (WTF::areEssentiallyEqual(m_p1.x(), m_p2.x()) && WTF::areEssentiallyEqual(m_p2.y(), m_p3.y()) && WTF::areEssentiallyEqual(m_p3.x(), m_p4.x()) && WTF::areEssentiallyEqual(m_p4.y(), m_p1.y()))
97 || (WTF::areEssentiallyEqual(m_p1.y(), m_p2.y()) && WTF::areEssentiallyEqual(m_p2.x(), m_p3.x()) && WTF::areEssentiallyEqual(m_p3.y(), m_p4.y()) && WTF::areEssentiallyEqual(m_p4.x(), m_p1.x()));
98}
99
100bool FloatQuad::containsPoint(const FloatPoint& p) const
101{
102 return isPointInTriangle(p, m_p1, m_p2, m_p3) || isPointInTriangle(p, m_p1, m_p3, m_p4);
103}
104
105// Note that we only handle convex quads here.
106bool FloatQuad::containsQuad(const FloatQuad& other) const
107{
108 return containsPoint(other.p1()) && containsPoint(other.p2()) && containsPoint(other.p3()) && containsPoint(other.p4());
109}
110
111static inline FloatPoint rightMostCornerToVector(const FloatRect& rect, const FloatSize& vector)
112{
113 // Return the corner of the rectangle that if it is to the left of the vector
114 // would mean all of the rectangle is to the left of the vector.
115 // The vector here represents the side between two points in a clockwise convex polygon.
116 //
117 // Q XXX
118 // QQQ XXX If the lower left corner of X is left of the vector that goes from the top corner of Q to
119 // QQQ the right corner of Q, then all of X is left of the vector, and intersection impossible.
120 // Q
121 //
122 FloatPoint point;
123 if (vector.width() >= 0)
124 point.setY(rect.maxY());
125 else
126 point.setY(rect.y());
127 if (vector.height() >= 0)
128 point.setX(rect.x());
129 else
130 point.setX(rect.maxX());
131 return point;
132}
133
134bool FloatQuad::intersectsRect(const FloatRect& rect) const
135{
136 // For each side of the quad clockwise we check if the rectangle is to the left of it
137 // since only content on the right can onlap with the quad.
138 // This only works if the quad is convex.
139 FloatSize v1, v2, v3, v4;
140
141 // Ensure we use clockwise vectors.
142 if (!isCounterclockwise()) {
143 v1 = m_p2 - m_p1;
144 v2 = m_p3 - m_p2;
145 v3 = m_p4 - m_p3;
146 v4 = m_p1 - m_p4;
147 } else {
148 v1 = m_p4 - m_p1;
149 v2 = m_p1 - m_p2;
150 v3 = m_p2 - m_p3;
151 v4 = m_p3 - m_p4;
152 }
153
154 FloatPoint p = rightMostCornerToVector(rect, v1);
155 if (determinant(v1, p - m_p1) < 0)
156 return false;
157
158 p = rightMostCornerToVector(rect, v2);
159 if (determinant(v2, p - m_p2) < 0)
160 return false;
161
162 p = rightMostCornerToVector(rect, v3);
163 if (determinant(v3, p - m_p3) < 0)
164 return false;
165
166 p = rightMostCornerToVector(rect, v4);
167 if (determinant(v4, p - m_p4) < 0)
168 return false;
169
170 // If not all of the rectangle is outside one of the quad's four sides, then that means at least
171 // a part of the rectangle is overlapping the quad.
172 return true;
173}
174
175// Tests whether the line is contained by or intersected with the circle.
176static inline bool lineIntersectsCircle(const FloatPoint& center, float radius, const FloatPoint& p0, const FloatPoint& p1)
177{
178 float x0 = p0.x() - center.x(), y0 = p0.y() - center.y();
179 float x1 = p1.x() - center.x(), y1 = p1.y() - center.y();
180 float radius2 = radius * radius;
181 if ((x0 * x0 + y0 * y0) <= radius2 || (x1 * x1 + y1 * y1) <= radius2)
182 return true;
183 if (p0 == p1)
184 return false;
185
186 float a = y0 - y1;
187 float b = x1 - x0;
188 float c = x0 * y1 - x1 * y0;
189 float distance2 = c * c / (a * a + b * b);
190 // If distance between the center point and the line > the radius,
191 // the line doesn't cross (or is contained by) the ellipse.
192 if (distance2 > radius2)
193 return false;
194
195 // The nearest point on the line is between p0 and p1?
196 float x = - a * c / (a * a + b * b);
197 float y = - b * c / (a * a + b * b);
198 return (((x0 <= x && x <= x1) || (x0 >= x && x >= x1))
199 && ((y0 <= y && y <= y1) || (y1 <= y && y <= y0)));
200}
201
202bool FloatQuad::intersectsCircle(const FloatPoint& center, float radius) const
203{
204 return containsPoint(center) // The circle may be totally contained by the quad.
205 || lineIntersectsCircle(center, radius, m_p1, m_p2)
206 || lineIntersectsCircle(center, radius, m_p2, m_p3)
207 || lineIntersectsCircle(center, radius, m_p3, m_p4)
208 || lineIntersectsCircle(center, radius, m_p4, m_p1);
209}
210
211bool FloatQuad::intersectsEllipse(const FloatPoint& center, const FloatSize& radii) const
212{
213 // Transform the ellipse to an origin-centered circle whose radius is the product of major radius and minor radius.
214 // Here we apply the same transformation to the quad.
215 FloatQuad transformedQuad(*this);
216 transformedQuad.move(-center.x(), -center.y());
217 transformedQuad.scale(radii.height(), radii.width());
218
219 FloatPoint originPoint;
220 return transformedQuad.intersectsCircle(originPoint, radii.height() * radii.width());
221
222}
223
224bool FloatQuad::isCounterclockwise() const
225{
226 // Return if the two first vectors are turning clockwise. If the quad is convex then all following vectors will turn the same way.
227 return determinant(m_p2 - m_p1, m_p3 - m_p2) < 0;
228}
229
230} // namespace WebCore
231