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 namespace blink { 38 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 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 49 inline float dot(const FloatSize& a, const FloatSize& b) 50 { 51 return a.width() * b.width() + a.height() * b.height(); 52 } 53 54 inline float determinant(const FloatSize& a, const FloatSize& b) 55 { 56 return a.width() * b.height() - a.height() * b.width(); 57 } 58 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 82 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 93 static inline bool withinEpsilon(float a, float b) 94 { 95 return fabs(a - b) < std::numeric_limits<float>::epsilon(); 96 } 97 98 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 } 103 104 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. 110 bool FloatQuad::containsQuad(const FloatQuad& other) const 111 { 112 return containsPoint(other.p1()) && containsPoint(other.p2()) && containsPoint(other.p3()) && containsPoint(other.p4()); 113 } 114 115 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 } 137 138 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. 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 } 205 206 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 } 214 215 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 } 227 228 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
