| /* |
| * 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 "FloatQuad.h" |
| #include <wtf/MathExtras.h> |
| #include <wtf/Vector.h> |
| |
| namespace WebCore { |
| |
| float euclidianDistance(const FloatSize& delta) |
| { |
| return std::hypot(delta.width(), delta.height()); |
| } |
| |
| float euclidianDistance(const FloatPoint& p1, const FloatPoint& p2) |
| { |
| return euclidianDistance(p1 - p2); |
| } |
| |
| 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; |
| for (auto& rect : rects) |
| result.unite(rect); |
| return result; |
| } |
| |
| FloatRect unionRect(const Vector<FloatRect>& rects) |
| { |
| FloatRect result; |
| for (auto& rect : rects) |
| result.unite(rect); |
| return result; |
| } |
| |
| FloatRect unionRectIgnoringZeroRects(const Vector<FloatRect>& rects) |
| { |
| FloatRect result; |
| for (auto& rect : rects) |
| result.uniteIfNonZero(rect); |
| 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; |
| } |
| |
| FloatPoint midPoint(const FloatPoint& first, const FloatPoint& second) |
| { |
| return { (first.x() + second.x()) / 2, (first.y() + second.y()) / 2 }; |
| } |
| |
| static float dotProduct(const FloatSize& u, const FloatSize& v) |
| { |
| return u.width() * v.width() + u.height() * v.height(); |
| } |
| |
| static float angleBetweenVectors(const FloatSize& u, const FloatSize& v) |
| { |
| auto magnitudes = u.diagonalLength() * v.diagonalLength(); |
| return magnitudes ? acos(clampTo<float>(dotProduct(u, v) / magnitudes, -1, 1)) : 0; |
| } |
| |
| RotatedRect rotatedBoundingRectWithMinimumAngleOfRotation(const FloatQuad& quad, std::optional<float> minRotationInRadians) |
| { |
| constexpr auto twoPiFloat = 2 * piFloat; |
| |
| auto minRotationAmount = minRotationInRadians.value_or(std::numeric_limits<float>::epsilon()); |
| |
| auto leftMidPoint = midPoint(quad.p1(), quad.p4()); |
| auto rightMidPoint = midPoint(quad.p2(), quad.p3()); |
| auto widthVector = rightMidPoint - leftMidPoint; |
| |
| auto midPointToMidPointDistance = widthVector.diagonalLength(); |
| int signOfWidthVectorHeight = widthVector.height() < 0 ? -1 : 1; |
| auto angle = midPointToMidPointDistance ? signOfWidthVectorHeight * acos(widthVector.width() / midPointToMidPointDistance) : 0; |
| if (angle < 0) |
| angle += twoPiFloat; |
| |
| if (std::abs(angle) < minRotationAmount || std::abs(twoPiFloat - angle) < minRotationAmount) { |
| auto boundingBox = quad.boundingBox(); |
| return { boundingBox.center(), boundingBox.size(), 0 }; |
| } |
| |
| auto heightVector = FloatSize { widthVector.height(), -widthVector.width() }; |
| auto leftPerpendicularAngle = angleBetweenVectors(heightVector, quad.p1() - leftMidPoint); |
| auto rightPerpendicularAngle = angleBetweenVectors(heightVector, quad.p2() - rightMidPoint); |
| |
| auto leftHypotenuseLength = (leftMidPoint - quad.p1()).diagonalLength(); |
| auto rightHypotenuseLength = (rightMidPoint - quad.p2()).diagonalLength(); |
| |
| auto leftMargin = leftHypotenuseLength * sin(leftPerpendicularAngle); |
| auto rightMargin = rightHypotenuseLength * sin(rightPerpendicularAngle); |
| auto width = midPointToMidPointDistance + leftMargin + rightMargin; |
| auto height = 2 * std::max(leftHypotenuseLength * cos(leftPerpendicularAngle), rightHypotenuseLength * cos(rightPerpendicularAngle)); |
| |
| auto leftMidToCenterDistance = (midPointToMidPointDistance + rightMargin - leftMargin) / 2; |
| auto center = leftMidPoint + (widthVector * leftMidToCenterDistance / midPointToMidPointDistance); |
| return { center, { width, height }, angle }; |
| } |
| |
| } |