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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