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 using namespace std;
38
39 namespace WebCore {
40
min4(float a,float b,float c,float d)41 static inline float min4(float a, float b, float c, float d)
42 {
43 return min(min(a, b), min(c, d));
44 }
45
max4(float a,float b,float c,float d)46 static inline float max4(float a, float b, float c, float d)
47 {
48 return max(max(a, b), max(c, d));
49 }
50
dot(const FloatSize & a,const FloatSize & b)51 inline float dot(const FloatSize& a, const FloatSize& b)
52 {
53 return a.width() * b.width() + a.height() * b.height();
54 }
55
determinant(const FloatSize & a,const FloatSize & b)56 inline float determinant(const FloatSize& a, const FloatSize& b)
57 {
58 return a.width() * b.height() - a.height() * b.width();
59 }
60
isPointInTriangle(const FloatPoint & p,const FloatPoint & t1,const FloatPoint & t2,const FloatPoint & t3)61 inline bool isPointInTriangle(const FloatPoint& p, const FloatPoint& t1, const FloatPoint& t2, const FloatPoint& t3)
62 {
63 // Compute vectors
64 FloatSize v0 = t3 - t1;
65 FloatSize v1 = t2 - t1;
66 FloatSize v2 = p - t1;
67
68 // Compute dot products
69 float dot00 = dot(v0, v0);
70 float dot01 = dot(v0, v1);
71 float dot02 = dot(v0, v2);
72 float dot11 = dot(v1, v1);
73 float dot12 = dot(v1, v2);
74
75 // Compute barycentric coordinates
76 float invDenom = 1.0f / (dot00 * dot11 - dot01 * dot01);
77 float u = (dot11 * dot02 - dot01 * dot12) * invDenom;
78 float v = (dot00 * dot12 - dot01 * dot02) * invDenom;
79
80 // Check if point is in triangle
81 return (u >= 0) && (v >= 0) && (u + v <= 1);
82 }
83
boundingBox() const84 FloatRect FloatQuad::boundingBox() const
85 {
86 float left = min4(m_p1.x(), m_p2.x(), m_p3.x(), m_p4.x());
87 float top = min4(m_p1.y(), m_p2.y(), m_p3.y(), m_p4.y());
88
89 float right = max4(m_p1.x(), m_p2.x(), m_p3.x(), m_p4.x());
90 float bottom = max4(m_p1.y(), m_p2.y(), m_p3.y(), m_p4.y());
91
92 return FloatRect(left, top, right - left, bottom - top);
93 }
94
withinEpsilon(float a,float b)95 static inline bool withinEpsilon(float a, float b)
96 {
97 return fabs(a - b) < numeric_limits<float>::epsilon();
98 }
99
isRectilinear() const100 bool FloatQuad::isRectilinear() const
101 {
102 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()))
103 || (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()));
104 }
105
containsPoint(const FloatPoint & p) const106 bool FloatQuad::containsPoint(const FloatPoint& p) const
107 {
108 return isPointInTriangle(p, m_p1, m_p2, m_p3) || isPointInTriangle(p, m_p1, m_p3, m_p4);
109 }
110
111 // Note that we only handle convex quads here.
containsQuad(const FloatQuad & other) const112 bool FloatQuad::containsQuad(const FloatQuad& other) const
113 {
114 return containsPoint(other.p1()) && containsPoint(other.p2()) && containsPoint(other.p3()) && containsPoint(other.p4());
115 }
116
rightMostCornerToVector(const FloatRect & rect,const FloatSize & vector)117 static inline FloatPoint rightMostCornerToVector(const FloatRect& rect, const FloatSize& vector)
118 {
119 // Return the corner of the rectangle that if it is to the left of the vector
120 // would mean all of the rectangle is to the left of the vector.
121 // The vector here represents the side between two points in a clockwise convex polygon.
122 //
123 // Q XXX
124 // QQQ XXX If the lower left corner of X is left of the vector that goes from the top corner of Q to
125 // QQQ the right corner of Q, then all of X is left of the vector, and intersection impossible.
126 // Q
127 //
128 FloatPoint point;
129 if (vector.width() >= 0)
130 point.setY(rect.maxY());
131 else
132 point.setY(rect.y());
133 if (vector.height() >= 0)
134 point.setX(rect.x());
135 else
136 point.setX(rect.maxX());
137 return point;
138 }
139
intersectsRect(const FloatRect & rect) const140 bool FloatQuad::intersectsRect(const FloatRect& rect) const
141 {
142 // For each side of the quad clockwise we check if the rectangle is to the left of it
143 // since only content on the right can onlap with the quad.
144 // This only works if the quad is convex.
145 FloatSize v1, v2, v3, v4;
146
147 // Ensure we use clockwise vectors.
148 if (!isCounterclockwise()) {
149 v1 = m_p2 - m_p1;
150 v2 = m_p3 - m_p2;
151 v3 = m_p4 - m_p3;
152 v4 = m_p1 - m_p4;
153 } else {
154 v1 = m_p4 - m_p1;
155 v2 = m_p1 - m_p2;
156 v3 = m_p2 - m_p3;
157 v4 = m_p3 - m_p4;
158 }
159
160 FloatPoint p = rightMostCornerToVector(rect, v1);
161 if (determinant(v1, p - m_p1) < 0)
162 return false;
163
164 p = rightMostCornerToVector(rect, v2);
165 if (determinant(v2, p - m_p2) < 0)
166 return false;
167
168 p = rightMostCornerToVector(rect, v3);
169 if (determinant(v3, p - m_p3) < 0)
170 return false;
171
172 p = rightMostCornerToVector(rect, v4);
173 if (determinant(v4, p - m_p4) < 0)
174 return false;
175
176 // If not all of the rectangle is outside one of the quad's four sides, then that means at least
177 // a part of the rectangle is overlapping the quad.
178 return true;
179 }
180
181 // Tests whether the line is contained by or intersected with the circle.
lineIntersectsCircle(const FloatPoint & center,float radius,const FloatPoint & p0,const FloatPoint & p1)182 static inline bool lineIntersectsCircle(const FloatPoint& center, float radius, const FloatPoint& p0, const FloatPoint& p1)
183 {
184 float x0 = p0.x() - center.x(), y0 = p0.y() - center.y();
185 float x1 = p1.x() - center.x(), y1 = p1.y() - center.y();
186 float radius2 = radius * radius;
187 if ((x0 * x0 + y0 * y0) <= radius2 || (x1 * x1 + y1 * y1) <= radius2)
188 return true;
189 if (p0 == p1)
190 return false;
191
192 float a = y0 - y1;
193 float b = x1 - x0;
194 float c = x0 * y1 - x1 * y0;
195 float distance2 = c * c / (a * a + b * b);
196 // If distance between the center point and the line > the radius,
197 // the line doesn't cross (or is contained by) the ellipse.
198 if (distance2 > radius2)
199 return false;
200
201 // The nearest point on the line is between p0 and p1?
202 float x = - a * c / (a * a + b * b);
203 float y = - b * c / (a * a + b * b);
204 return (((x0 <= x && x <= x1) || (x0 >= x && x >= x1))
205 && ((y0 <= y && y <= y1) || (y1 <= y && y <= y0)));
206 }
207
intersectsCircle(const FloatPoint & center,float radius) const208 bool FloatQuad::intersectsCircle(const FloatPoint& center, float radius) const
209 {
210 return containsPoint(center) // The circle may be totally contained by the quad.
211 || lineIntersectsCircle(center, radius, m_p1, m_p2)
212 || lineIntersectsCircle(center, radius, m_p2, m_p3)
213 || lineIntersectsCircle(center, radius, m_p3, m_p4)
214 || lineIntersectsCircle(center, radius, m_p4, m_p1);
215 }
216
intersectsEllipse(const FloatPoint & center,const FloatSize & radii) const217 bool FloatQuad::intersectsEllipse(const FloatPoint& center, const FloatSize& radii) const
218 {
219 // Transform the ellipse to an origin-centered circle whose radius is the product of major radius and minor radius.
220 // Here we apply the same transformation to the quad.
221 FloatQuad transformedQuad(*this);
222 transformedQuad.move(-center.x(), -center.y());
223 transformedQuad.scale(radii.height(), radii.width());
224
225 FloatPoint originPoint;
226 return transformedQuad.intersectsCircle(originPoint, radii.height() * radii.width());
227
228 }
229
isCounterclockwise() const230 bool FloatQuad::isCounterclockwise() const
231 {
232 // Return if the two first vectors are turning clockwise. If the quad is convex then all following vectors will turn the same way.
233 return determinant(m_p2 - m_p1, m_p3 - m_p2) < 0;
234 }
235
236 } // namespace WebCore
237