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 Computer, 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 "platform/geometry/FloatQuad.h"
33
34 #include <algorithm>
35 #include <limits>
36
37 namespace blink {
38
min4(float a,float b,float c,float d)39 static inline float min4(float a, float b, float c, float d)
40 {
41 return std::min(std::min(a, b), std::min(c, d));
42 }
43
max4(float a,float b,float c,float d)44 static inline float max4(float a, float b, float c, float d)
45 {
46 return std::max(std::max(a, b), std::max(c, d));
47 }
48
dot(const FloatSize & a,const FloatSize & b)49 inline float dot(const FloatSize& a, const FloatSize& b)
50 {
51 return a.width() * b.width() + a.height() * b.height();
52 }
53
determinant(const FloatSize & a,const FloatSize & b)54 inline float determinant(const FloatSize& a, const FloatSize& b)
55 {
56 return a.width() * b.height() - a.height() * b.width();
57 }
58
isPointInTriangle(const FloatPoint & p,const FloatPoint & t1,const FloatPoint & t2,const FloatPoint & t3)59 inline bool isPointInTriangle(const FloatPoint& p, const FloatPoint& t1, const FloatPoint& t2, const FloatPoint& t3)
60 {
61 // Compute vectors
62 FloatSize v0 = t3 - t1;
63 FloatSize v1 = t2 - t1;
64 FloatSize v2 = p - t1;
65
66 // Compute dot products
67 float dot00 = dot(v0, v0);
68 float dot01 = dot(v0, v1);
69 float dot02 = dot(v0, v2);
70 float dot11 = dot(v1, v1);
71 float dot12 = dot(v1, v2);
72
73 // Compute barycentric coordinates
74 float invDenom = 1.0f / (dot00 * dot11 - dot01 * dot01);
75 float u = (dot11 * dot02 - dot01 * dot12) * invDenom;
76 float v = (dot00 * dot12 - dot01 * dot02) * invDenom;
77
78 // Check if point is in triangle
79 return (u >= 0) && (v >= 0) && (u + v <= 1);
80 }
81
boundingBox() const82 FloatRect FloatQuad::boundingBox() const
83 {
84 float left = min4(m_p1.x(), m_p2.x(), m_p3.x(), m_p4.x());
85 float top = min4(m_p1.y(), m_p2.y(), m_p3.y(), m_p4.y());
86
87 float right = max4(m_p1.x(), m_p2.x(), m_p3.x(), m_p4.x());
88 float bottom = max4(m_p1.y(), m_p2.y(), m_p3.y(), m_p4.y());
89
90 return FloatRect(left, top, right - left, bottom - top);
91 }
92
withinEpsilon(float a,float b)93 static inline bool withinEpsilon(float a, float b)
94 {
95 return fabs(a - b) < std::numeric_limits<float>::epsilon();
96 }
97
isRectilinear() const98 bool FloatQuad::isRectilinear() const
99 {
100 return (withinEpsilon(m_p1.x(), m_p2.x()) && withinEpsilon(m_p2.y(), m_p3.y()) && withinEpsilon(m_p3.x(), m_p4.x()) && withinEpsilon(m_p4.y(), m_p1.y()))
101 || (withinEpsilon(m_p1.y(), m_p2.y()) && withinEpsilon(m_p2.x(), m_p3.x()) && withinEpsilon(m_p3.y(), m_p4.y()) && withinEpsilon(m_p4.x(), m_p1.x()));
102 }
103
containsPoint(const FloatPoint & p) const104 bool FloatQuad::containsPoint(const FloatPoint& p) const
105 {
106 return isPointInTriangle(p, m_p1, m_p2, m_p3) || isPointInTriangle(p, m_p1, m_p3, m_p4);
107 }
108
109 // Note that we only handle convex quads here.
containsQuad(const FloatQuad & other) const110 bool FloatQuad::containsQuad(const FloatQuad& other) const
111 {
112 return containsPoint(other.p1()) && containsPoint(other.p2()) && containsPoint(other.p3()) && containsPoint(other.p4());
113 }
114
rightMostCornerToVector(const FloatRect & rect,const FloatSize & vector)115 static inline FloatPoint rightMostCornerToVector(const FloatRect& rect, const FloatSize& vector)
116 {
117 // Return the corner of the rectangle that if it is to the left of the vector
118 // would mean all of the rectangle is to the left of the vector.
119 // The vector here represents the side between two points in a clockwise convex polygon.
120 //
121 // Q XXX
122 // QQQ XXX If the lower left corner of X is left of the vector that goes from the top corner of Q to
123 // QQQ the right corner of Q, then all of X is left of the vector, and intersection impossible.
124 // Q
125 //
126 FloatPoint point;
127 if (vector.width() >= 0)
128 point.setY(rect.maxY());
129 else
130 point.setY(rect.y());
131 if (vector.height() >= 0)
132 point.setX(rect.x());
133 else
134 point.setX(rect.maxX());
135 return point;
136 }
137
intersectsRect(const FloatRect & rect) const138 bool FloatQuad::intersectsRect(const FloatRect& rect) const
139 {
140 // For each side of the quad clockwise we check if the rectangle is to the left of it
141 // since only content on the right can onlap with the quad.
142 // This only works if the quad is convex.
143 FloatSize v1, v2, v3, v4;
144
145 // Ensure we use clockwise vectors.
146 if (!isCounterclockwise()) {
147 v1 = m_p2 - m_p1;
148 v2 = m_p3 - m_p2;
149 v3 = m_p4 - m_p3;
150 v4 = m_p1 - m_p4;
151 } else {
152 v1 = m_p4 - m_p1;
153 v2 = m_p1 - m_p2;
154 v3 = m_p2 - m_p3;
155 v4 = m_p3 - m_p4;
156 }
157
158 FloatPoint p = rightMostCornerToVector(rect, v1);
159 if (determinant(v1, p - m_p1) < 0)
160 return false;
161
162 p = rightMostCornerToVector(rect, v2);
163 if (determinant(v2, p - m_p2) < 0)
164 return false;
165
166 p = rightMostCornerToVector(rect, v3);
167 if (determinant(v3, p - m_p3) < 0)
168 return false;
169
170 p = rightMostCornerToVector(rect, v4);
171 if (determinant(v4, p - m_p4) < 0)
172 return false;
173
174 // If not all of the rectangle is outside one of the quad's four sides, then that means at least
175 // a part of the rectangle is overlapping the quad.
176 return true;
177 }
178
179 // Tests whether the line is contained by or intersected with the circle.
lineIntersectsCircle(const FloatPoint & center,float radius,const FloatPoint & p0,const FloatPoint & p1)180 static inline bool lineIntersectsCircle(const FloatPoint& center, float radius, const FloatPoint& p0, const FloatPoint& p1)
181 {
182 float x0 = p0.x() - center.x(), y0 = p0.y() - center.y();
183 float x1 = p1.x() - center.x(), y1 = p1.y() - center.y();
184 float radius2 = radius * radius;
185 if ((x0 * x0 + y0 * y0) <= radius2 || (x1 * x1 + y1 * y1) <= radius2)
186 return true;
187 if (p0 == p1)
188 return false;
189
190 float a = y0 - y1;
191 float b = x1 - x0;
192 float c = x0 * y1 - x1 * y0;
193 float distance2 = c * c / (a * a + b * b);
194 // If distance between the center point and the line > the radius,
195 // the line doesn't cross (or is contained by) the ellipse.
196 if (distance2 > radius2)
197 return false;
198
199 // The nearest point on the line is between p0 and p1?
200 float x = - a * c / (a * a + b * b);
201 float y = - b * c / (a * a + b * b);
202 return (((x0 <= x && x <= x1) || (x0 >= x && x >= x1))
203 && ((y0 <= y && y <= y1) || (y1 <= y && y <= y0)));
204 }
205
intersectsCircle(const FloatPoint & center,float radius) const206 bool FloatQuad::intersectsCircle(const FloatPoint& center, float radius) const
207 {
208 return containsPoint(center) // The circle may be totally contained by the quad.
209 || lineIntersectsCircle(center, radius, m_p1, m_p2)
210 || lineIntersectsCircle(center, radius, m_p2, m_p3)
211 || lineIntersectsCircle(center, radius, m_p3, m_p4)
212 || lineIntersectsCircle(center, radius, m_p4, m_p1);
213 }
214
intersectsEllipse(const FloatPoint & center,const FloatSize & radii) const215 bool FloatQuad::intersectsEllipse(const FloatPoint& center, const FloatSize& radii) const
216 {
217 // Transform the ellipse to an origin-centered circle whose radius is the product of major radius and minor radius.
218 // Here we apply the same transformation to the quad.
219 FloatQuad transformedQuad(*this);
220 transformedQuad.move(-center.x(), -center.y());
221 transformedQuad.scale(radii.height(), radii.width());
222
223 FloatPoint originPoint;
224 return transformedQuad.intersectsCircle(originPoint, radii.height() * radii.width());
225
226 }
227
isCounterclockwise() const228 bool FloatQuad::isCounterclockwise() const
229 {
230 // Return if the two first vectors are turning clockwise. If the quad is convex then all following vectors will turn the same way.
231 return determinant(m_p2 - m_p1, m_p3 - m_p2) < 0;
232 }
233
234 } // namespace blink
235