1/*
2 * Copyright (C) 2014 Apple Inc. All rights reserved.
3 *
4 * Redistribution and use in source and binary forms, with or without
5 * modification, are permitted provided that the following conditions
6 * are met:
7 * 1. Redistributions of source code must retain the above copyright
8 * notice, this list of conditions and the following disclaimer.
9 * 2. Redistributions in binary form must reproduce the above copyright
10 * notice, this list of conditions and the following disclaimer in the
11 * documentation and/or other materials provided with the distribution.
12 *
13 * THIS SOFTWARE IS PROVIDED BY APPLE INC. AND ITS CONTRIBUTORS ``AS IS''
14 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
15 * THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
16 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR ITS CONTRIBUTORS
17 * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
18 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
19 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
20 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
21 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
22 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
23 * THE POSSIBILITY OF SUCH DAMAGE.
24 */
25
26#include "config.h"
27#include "GeometryUtilities.h"
28#include <wtf/Vector.h>
29
30namespace WebCore {
31
32float euclidianDistance(const FloatPoint& p1, const FloatPoint& p2)
33{
34 FloatSize delta = p1 - p2;
35 return sqrt(delta.width() * delta.width() + delta.height() * delta.height());
36}
37
38float findSlope(const FloatPoint& p1, const FloatPoint& p2, float& c)
39{
40 if (p2.x() == p1.x())
41 return std::numeric_limits<float>::infinity();
42
43 // y = mx + c
44 float slope = (p2.y() - p1.y()) / (p2.x() - p1.x());
45 c = p1.y() - slope * p1.x();
46 return slope;
47}
48
49bool findIntersection(const FloatPoint& p1, const FloatPoint& p2, const FloatPoint& d1, const FloatPoint& d2, FloatPoint& intersection)
50{
51 float pOffset = 0;
52 float pSlope = findSlope(p1, p2, pOffset);
53
54 float dOffset = 0;
55 float dSlope = findSlope(d1, d2, dOffset);
56
57 if (dSlope == pSlope)
58 return false;
59
60 if (pSlope == std::numeric_limits<float>::infinity()) {
61 intersection.setX(p1.x());
62 intersection.setY(dSlope * intersection.x() + dOffset);
63 return true;
64 }
65 if (dSlope == std::numeric_limits<float>::infinity()) {
66 intersection.setX(d1.x());
67 intersection.setY(pSlope * intersection.x() + pOffset);
68 return true;
69 }
70
71 // Find x at intersection, where ys overlap; x = (c' - c) / (m - m')
72 intersection.setX((dOffset - pOffset) / (pSlope - dSlope));
73 intersection.setY(pSlope * intersection.x() + pOffset);
74 return true;
75}
76
77IntRect unionRect(const Vector<IntRect>& rects)
78{
79 IntRect result;
80
81 size_t count = rects.size();
82 for (size_t i = 0; i < count; ++i)
83 result.unite(rects[i]);
84
85 return result;
86}
87
88FloatRect unionRect(const Vector<FloatRect>& rects)
89{
90 FloatRect result;
91
92 size_t count = rects.size();
93 for (size_t i = 0; i < count; ++i)
94 result.unite(rects[i]);
95
96 return result;
97}
98
99FloatPoint mapPoint(FloatPoint p, const FloatRect& srcRect, const FloatRect& destRect)
100{
101 if (!srcRect.width() || !srcRect.height())
102 return p;
103
104 float widthScale = destRect.width() / srcRect.width();
105 float heightScale = destRect.height() / srcRect.height();
106
107 return {
108 destRect.x() + (p.x() - srcRect.x()) * widthScale,
109 destRect.y() + (p.y() - srcRect.y()) * heightScale
110 };
111}
112
113FloatRect mapRect(const FloatRect& r, const FloatRect& srcRect, const FloatRect& destRect)
114{
115 if (!srcRect.width() || !srcRect.height())
116 return FloatRect();
117
118 float widthScale = destRect.width() / srcRect.width();
119 float heightScale = destRect.height() / srcRect.height();
120 return {
121 destRect.x() + (r.x() - srcRect.x()) * widthScale,
122 destRect.y() + (r.y() - srcRect.y()) * heightScale,
123 r.width() * widthScale,
124 r.height() * heightScale
125 };
126}
127
128FloatRect largestRectWithAspectRatioInsideRect(float aspectRatio, const FloatRect& srcRect)
129{
130 FloatRect destRect = srcRect;
131
132 if (aspectRatio > srcRect.size().aspectRatio()) {
133 float dy = destRect.width() / aspectRatio - destRect.height();
134 destRect.inflateY(dy / 2);
135 } else {
136 float dx = destRect.height() * aspectRatio - destRect.width();
137 destRect.inflateX(dx / 2);
138 }
139 return destRect;
140}
141
142FloatRect boundsOfRotatingRect(const FloatRect& r)
143{
144 // Compute the furthest corner from the origin.
145 float maxCornerDistance = euclidianDistance(FloatPoint(), r.minXMinYCorner());
146 maxCornerDistance = std::max(maxCornerDistance, euclidianDistance(FloatPoint(), r.maxXMinYCorner()));
147 maxCornerDistance = std::max(maxCornerDistance, euclidianDistance(FloatPoint(), r.minXMaxYCorner()));
148 maxCornerDistance = std::max(maxCornerDistance, euclidianDistance(FloatPoint(), r.maxXMaxYCorner()));
149
150 return FloatRect(-maxCornerDistance, -maxCornerDistance, 2 * maxCornerDistance, 2 * maxCornerDistance);
151}
152
153FloatRect smallestRectWithAspectRatioAroundRect(float aspectRatio, const FloatRect& srcRect)
154{
155 FloatRect destRect = srcRect;
156
157 if (aspectRatio < srcRect.size().aspectRatio()) {
158 float dy = destRect.width() / aspectRatio - destRect.height();
159 destRect.inflateY(dy / 2);
160 } else {
161 float dx = destRect.height() * aspectRatio - destRect.width();
162 destRect.inflateX(dx / 2);
163 }
164 return destRect;
165}
166
167FloatSize sizeWithAreaAndAspectRatio(float area, float aspectRatio)
168{
169 auto scaledWidth = std::sqrt(area * aspectRatio);
170 return { scaledWidth, scaledWidth / aspectRatio };
171}
172
173bool ellipseContainsPoint(const FloatPoint& center, const FloatSize& radii, const FloatPoint& point)
174{
175 if (radii.width() <= 0 || radii.height() <= 0)
176 return false;
177
178 // First, offset the query point so that the ellipse is effectively centered at the origin.
179 FloatPoint transformedPoint(point);
180 transformedPoint.move(-center.x(), -center.y());
181
182 // If the point lies outside of the bounding box determined by the radii of the ellipse, it can't possibly
183 // be contained within the ellipse, so bail early.
184 if (transformedPoint.x() < -radii.width() || transformedPoint.x() > radii.width() || transformedPoint.y() < -radii.height() || transformedPoint.y() > radii.height())
185 return false;
186
187 // Let (x, y) represent the translated point, and let (Rx, Ry) represent the radii of an ellipse centered at the origin.
188 // (x, y) is contained within the ellipse if, after scaling the ellipse to be a unit circle, the identically scaled
189 // point lies within that unit circle. In other words, the squared distance (x/Rx)^2 + (y/Ry)^2 of the transformed point
190 // to the origin is no greater than 1. This is equivalent to checking whether or not the point (xRy, yRx) lies within a
191 // circle of radius RxRy.
192 transformedPoint.scale(radii.height(), radii.width());
193 auto transformedRadius = radii.width() * radii.height();
194
195 // We can bail early if |xRy| + |yRx| <= RxRy to avoid additional multiplications, since that means the Manhattan distance
196 // of the transformed point is less than the radius, so the point must lie within the transformed circle.
197 return std::abs(transformedPoint.x()) + std::abs(transformedPoint.y()) <= transformedRadius || transformedPoint.lengthSquared() <= transformedRadius * transformedRadius;
198}
199
200}
201