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 (at) 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 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 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 51 inline float dot(const FloatSize& a, const FloatSize& b) 52 { 53 return a.width() * b.width() + a.height() * b.height(); 54 } 55 56 inline float determinant(const FloatSize& a, const FloatSize& b) 57 { 58 return a.width() * b.height() - a.height() * b.width(); 59 } 60 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 84 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 95 static inline bool withinEpsilon(float a, float b) 96 { 97 return fabs(a - b) < numeric_limits<float>::epsilon(); 98 } 99 100 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 } 105 106 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. 112 bool FloatQuad::containsQuad(const FloatQuad& other) const 113 { 114 return containsPoint(other.p1()) && containsPoint(other.p2()) && containsPoint(other.p3()) && containsPoint(other.p4()); 115 } 116 117 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 } 139 140 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. 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 } 207 208 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 } 216 217 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 } 229 230 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
