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/*
* Copyright (C) 2014 Apple Inc. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY APPLE INC. AND ITS CONTRIBUTORS ``AS IS''
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO,
* THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
* PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR ITS CONTRIBUTORS
* BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
* THE POSSIBILITY OF SUCH DAMAGE.
*/
#include "config.h"
#include "GeometryUtilities.h"
#include <wtf/Vector.h>
namespace WebCore {
float euclidianDistance(const FloatPoint& p1, const FloatPoint& p2)
{
FloatSize delta = p1 - p2;
return std::hypot(delta.width(), delta.height());
}
float findSlope(const FloatPoint& p1, const FloatPoint& p2, float& c)
{
if (p2.x() == p1.x())
return std::numeric_limits<float>::infinity();
// y = mx + c
float slope = (p2.y() - p1.y()) / (p2.x() - p1.x());
c = p1.y() - slope * p1.x();
return slope;
}
bool findIntersection(const FloatPoint& p1, const FloatPoint& p2, const FloatPoint& d1, const FloatPoint& d2, FloatPoint& intersection)
{
float pOffset = 0;
float pSlope = findSlope(p1, p2, pOffset);
float dOffset = 0;
float dSlope = findSlope(d1, d2, dOffset);
if (dSlope == pSlope)
return false;
if (pSlope == std::numeric_limits<float>::infinity()) {
intersection.setX(p1.x());
intersection.setY(dSlope * intersection.x() + dOffset);
return true;
}
if (dSlope == std::numeric_limits<float>::infinity()) {
intersection.setX(d1.x());
intersection.setY(pSlope * intersection.x() + pOffset);
return true;
}
// Find x at intersection, where ys overlap; x = (c' - c) / (m - m')
intersection.setX((dOffset - pOffset) / (pSlope - dSlope));
intersection.setY(pSlope * intersection.x() + pOffset);
return true;
}
IntRect unionRect(const Vector<IntRect>& rects)
{
IntRect result;
size_t count = rects.size();
for (size_t i = 0; i < count; ++i)
result.unite(rects[i]);
return result;
}
FloatRect unionRect(const Vector<FloatRect>& rects)
{
FloatRect result;
size_t count = rects.size();
for (size_t i = 0; i < count; ++i)
result.unite(rects[i]);
return result;
}
FloatPoint mapPoint(FloatPoint p, const FloatRect& srcRect, const FloatRect& destRect)
{
if (!srcRect.width() || !srcRect.height())
return p;
float widthScale = destRect.width() / srcRect.width();
float heightScale = destRect.height() / srcRect.height();
return {
destRect.x() + (p.x() - srcRect.x()) * widthScale,
destRect.y() + (p.y() - srcRect.y()) * heightScale
};
}
FloatRect mapRect(const FloatRect& r, const FloatRect& srcRect, const FloatRect& destRect)
{
if (!srcRect.width() || !srcRect.height())
return FloatRect();
float widthScale = destRect.width() / srcRect.width();
float heightScale = destRect.height() / srcRect.height();
return {
destRect.x() + (r.x() - srcRect.x()) * widthScale,
destRect.y() + (r.y() - srcRect.y()) * heightScale,
r.width() * widthScale,
r.height() * heightScale
};
}
FloatRect largestRectWithAspectRatioInsideRect(float aspectRatio, const FloatRect& srcRect)
{
FloatRect destRect = srcRect;
if (aspectRatio > srcRect.size().aspectRatio()) {
float dy = destRect.width() / aspectRatio - destRect.height();
destRect.inflateY(dy / 2);
} else {
float dx = destRect.height() * aspectRatio - destRect.width();
destRect.inflateX(dx / 2);
}
return destRect;
}
FloatRect boundsOfRotatingRect(const FloatRect& r)
{
// Compute the furthest corner from the origin.
float maxCornerDistance = euclidianDistance(FloatPoint(), r.minXMinYCorner());
maxCornerDistance = std::max(maxCornerDistance, euclidianDistance(FloatPoint(), r.maxXMinYCorner()));
maxCornerDistance = std::max(maxCornerDistance, euclidianDistance(FloatPoint(), r.minXMaxYCorner()));
maxCornerDistance = std::max(maxCornerDistance, euclidianDistance(FloatPoint(), r.maxXMaxYCorner()));
return FloatRect(-maxCornerDistance, -maxCornerDistance, 2 * maxCornerDistance, 2 * maxCornerDistance);
}
FloatRect smallestRectWithAspectRatioAroundRect(float aspectRatio, const FloatRect& srcRect)
{
FloatRect destRect = srcRect;
if (aspectRatio < srcRect.size().aspectRatio()) {
float dy = destRect.width() / aspectRatio - destRect.height();
destRect.inflateY(dy / 2);
} else {
float dx = destRect.height() * aspectRatio - destRect.width();
destRect.inflateX(dx / 2);
}
return destRect;
}
FloatSize sizeWithAreaAndAspectRatio(float area, float aspectRatio)
{
auto scaledWidth = std::sqrt(area * aspectRatio);
return { scaledWidth, scaledWidth / aspectRatio };
}
bool ellipseContainsPoint(const FloatPoint& center, const FloatSize& radii, const FloatPoint& point)
{
if (radii.width() <= 0 || radii.height() <= 0)
return false;
// First, offset the query point so that the ellipse is effectively centered at the origin.
FloatPoint transformedPoint(point);
transformedPoint.move(-center.x(), -center.y());
// If the point lies outside of the bounding box determined by the radii of the ellipse, it can't possibly
// be contained within the ellipse, so bail early.
if (transformedPoint.x() < -radii.width() || transformedPoint.x() > radii.width() || transformedPoint.y() < -radii.height() || transformedPoint.y() > radii.height())
return false;
// Let (x, y) represent the translated point, and let (Rx, Ry) represent the radii of an ellipse centered at the origin.
// (x, y) is contained within the ellipse if, after scaling the ellipse to be a unit circle, the identically scaled
// point lies within that unit circle. In other words, the squared distance (x/Rx)^2 + (y/Ry)^2 of the transformed point
// to the origin is no greater than 1. This is equivalent to checking whether or not the point (xRy, yRx) lies within a
// circle of radius RxRy.
transformedPoint.scale(radii.height(), radii.width());
auto transformedRadius = radii.width() * radii.height();
// We can bail early if |xRy| + |yRx| <= RxRy to avoid additional multiplications, since that means the Manhattan distance
// of the transformed point is less than the radius, so the point must lie within the transformed circle.
return std::abs(transformedPoint.x()) + std::abs(transformedPoint.y()) <= transformedRadius || transformedPoint.lengthSquared() <= transformedRadius * transformedRadius;
}
}