// Copyright 2012 The Chromium Authors. All rights reserved. // Use of this source code is governed by a BSD-style license that can be // found in the LICENSE file. #include "config.h" #include "CCMathUtil.h" #include "FloatPoint.h" #include "FloatQuad.h" #include "IntRect.h" #include using WebKit::WebTransformationMatrix; namespace cc { static HomogeneousCoordinate projectHomogeneousPoint(const WebTransformationMatrix& transform, const FloatPoint& p) { // In this case, the layer we are trying to project onto is perpendicular to ray // (point p and z-axis direction) that we are trying to project. This happens when the // layer is rotated so that it is infinitesimally thin, or when it is co-planar with // the camera origin -- i.e. when the layer is invisible anyway. if (!transform.m33()) return HomogeneousCoordinate(0, 0, 0, 1); double x = p.x(); double y = p.y(); double z = -(transform.m13() * x + transform.m23() * y + transform.m43()) / transform.m33(); // implicit definition of w = 1; double outX = x * transform.m11() + y * transform.m21() + z * transform.m31() + transform.m41(); double outY = x * transform.m12() + y * transform.m22() + z * transform.m32() + transform.m42(); double outZ = x * transform.m13() + y * transform.m23() + z * transform.m33() + transform.m43(); double outW = x * transform.m14() + y * transform.m24() + z * transform.m34() + transform.m44(); return HomogeneousCoordinate(outX, outY, outZ, outW); } static HomogeneousCoordinate mapHomogeneousPoint(const WebTransformationMatrix& transform, const FloatPoint3D& p) { double x = p.x(); double y = p.y(); double z = p.z(); // implicit definition of w = 1; double outX = x * transform.m11() + y * transform.m21() + z * transform.m31() + transform.m41(); double outY = x * transform.m12() + y * transform.m22() + z * transform.m32() + transform.m42(); double outZ = x * transform.m13() + y * transform.m23() + z * transform.m33() + transform.m43(); double outW = x * transform.m14() + y * transform.m24() + z * transform.m34() + transform.m44(); return HomogeneousCoordinate(outX, outY, outZ, outW); } static HomogeneousCoordinate computeClippedPointForEdge(const HomogeneousCoordinate& h1, const HomogeneousCoordinate& h2) { // Points h1 and h2 form a line in 4d, and any point on that line can be represented // as an interpolation between h1 and h2: // p = (1-t) h1 + (t) h2 // // We want to compute point p such that p.w == epsilon, where epsilon is a small // non-zero number. (but the smaller the number is, the higher the risk of overflow) // To do this, we solve for t in the following equation: // p.w = epsilon = (1-t) * h1.w + (t) * h2.w // // Once paramter t is known, the rest of p can be computed via p = (1-t) h1 + (t) h2. // Technically this is a special case of the following assertion, but its a good idea to keep it an explicit sanity check here. ASSERT(h2.w != h1.w); // Exactly one of h1 or h2 (but not both) must be on the negative side of the w plane when this is called. ASSERT(h1.shouldBeClipped() ^ h2.shouldBeClipped()); double w = 0.00001; // or any positive non-zero small epsilon double t = (w - h1.w) / (h2.w - h1.w); double x = (1-t) * h1.x + t * h2.x; double y = (1-t) * h1.y + t * h2.y; double z = (1-t) * h1.z + t * h2.z; return HomogeneousCoordinate(x, y, z, w); } static inline void expandBoundsToIncludePoint(float& xmin, float& xmax, float& ymin, float& ymax, const FloatPoint& p) { xmin = std::min(p.x(), xmin); xmax = std::max(p.x(), xmax); ymin = std::min(p.y(), ymin); ymax = std::max(p.y(), ymax); } static inline void addVertexToClippedQuad(const FloatPoint& newVertex, FloatPoint clippedQuad[8], int& numVerticesInClippedQuad) { clippedQuad[numVerticesInClippedQuad] = newVertex; numVerticesInClippedQuad++; } IntRect CCMathUtil::mapClippedRect(const WebTransformationMatrix& transform, const IntRect& srcRect) { return enclosingIntRect(mapClippedRect(transform, FloatRect(srcRect))); } FloatRect CCMathUtil::mapClippedRect(const WebTransformationMatrix& transform, const FloatRect& srcRect) { if (transform.isIdentityOrTranslation()) { FloatRect mappedRect(srcRect); mappedRect.move(static_cast(transform.m41()), static_cast(transform.m42())); return mappedRect; } // Apply the transform, but retain the result in homogeneous coordinates. FloatQuad q = FloatQuad(FloatRect(srcRect)); HomogeneousCoordinate h1 = mapHomogeneousPoint(transform, q.p1()); HomogeneousCoordinate h2 = mapHomogeneousPoint(transform, q.p2()); HomogeneousCoordinate h3 = mapHomogeneousPoint(transform, q.p3()); HomogeneousCoordinate h4 = mapHomogeneousPoint(transform, q.p4()); return computeEnclosingClippedRect(h1, h2, h3, h4); } FloatRect CCMathUtil::projectClippedRect(const WebTransformationMatrix& transform, const FloatRect& srcRect) { // Perform the projection, but retain the result in homogeneous coordinates. FloatQuad q = FloatQuad(FloatRect(srcRect)); HomogeneousCoordinate h1 = projectHomogeneousPoint(transform, q.p1()); HomogeneousCoordinate h2 = projectHomogeneousPoint(transform, q.p2()); HomogeneousCoordinate h3 = projectHomogeneousPoint(transform, q.p3()); HomogeneousCoordinate h4 = projectHomogeneousPoint(transform, q.p4()); return computeEnclosingClippedRect(h1, h2, h3, h4); } void CCMathUtil::mapClippedQuad(const WebTransformationMatrix& transform, const FloatQuad& srcQuad, FloatPoint clippedQuad[8], int& numVerticesInClippedQuad) { HomogeneousCoordinate h1 = mapHomogeneousPoint(transform, srcQuad.p1()); HomogeneousCoordinate h2 = mapHomogeneousPoint(transform, srcQuad.p2()); HomogeneousCoordinate h3 = mapHomogeneousPoint(transform, srcQuad.p3()); HomogeneousCoordinate h4 = mapHomogeneousPoint(transform, srcQuad.p4()); // The order of adding the vertices to the array is chosen so that clockwise / counter-clockwise orientation is retained. numVerticesInClippedQuad = 0; if (!h1.shouldBeClipped()) addVertexToClippedQuad(h1.cartesianPoint2d(), clippedQuad, numVerticesInClippedQuad); if (h1.shouldBeClipped() ^ h2.shouldBeClipped()) addVertexToClippedQuad(computeClippedPointForEdge(h1, h2).cartesianPoint2d(), clippedQuad, numVerticesInClippedQuad); if (!h2.shouldBeClipped()) addVertexToClippedQuad(h2.cartesianPoint2d(), clippedQuad, numVerticesInClippedQuad); if (h2.shouldBeClipped() ^ h3.shouldBeClipped()) addVertexToClippedQuad(computeClippedPointForEdge(h2, h3).cartesianPoint2d(), clippedQuad, numVerticesInClippedQuad); if (!h3.shouldBeClipped()) addVertexToClippedQuad(h3.cartesianPoint2d(), clippedQuad, numVerticesInClippedQuad); if (h3.shouldBeClipped() ^ h4.shouldBeClipped()) addVertexToClippedQuad(computeClippedPointForEdge(h3, h4).cartesianPoint2d(), clippedQuad, numVerticesInClippedQuad); if (!h4.shouldBeClipped()) addVertexToClippedQuad(h4.cartesianPoint2d(), clippedQuad, numVerticesInClippedQuad); if (h4.shouldBeClipped() ^ h1.shouldBeClipped()) addVertexToClippedQuad(computeClippedPointForEdge(h4, h1).cartesianPoint2d(), clippedQuad, numVerticesInClippedQuad); ASSERT(numVerticesInClippedQuad <= 8); } FloatRect CCMathUtil::computeEnclosingRectOfVertices(FloatPoint vertices[], int numVertices) { if (numVertices < 2) return FloatRect(); float xmin = std::numeric_limits::max(); float xmax = -std::numeric_limits::max(); float ymin = std::numeric_limits::max(); float ymax = -std::numeric_limits::max(); for (int i = 0; i < numVertices; ++i) expandBoundsToIncludePoint(xmin, xmax, ymin, ymax, vertices[i]); return FloatRect(FloatPoint(xmin, ymin), FloatSize(xmax - xmin, ymax - ymin)); } FloatRect CCMathUtil::computeEnclosingClippedRect(const HomogeneousCoordinate& h1, const HomogeneousCoordinate& h2, const HomogeneousCoordinate& h3, const HomogeneousCoordinate& h4) { // This function performs clipping as necessary and computes the enclosing 2d // FloatRect of the vertices. Doing these two steps simultaneously allows us to avoid // the overhead of storing an unknown number of clipped vertices. // If no vertices on the quad are clipped, then we can simply return the enclosing rect directly. bool somethingClipped = h1.shouldBeClipped() || h2.shouldBeClipped() || h3.shouldBeClipped() || h4.shouldBeClipped(); if (!somethingClipped) { FloatQuad mappedQuad = FloatQuad(h1.cartesianPoint2d(), h2.cartesianPoint2d(), h3.cartesianPoint2d(), h4.cartesianPoint2d()); return mappedQuad.boundingBox(); } bool everythingClipped = h1.shouldBeClipped() && h2.shouldBeClipped() && h3.shouldBeClipped() && h4.shouldBeClipped(); if (everythingClipped) return FloatRect(); float xmin = std::numeric_limits::max(); float xmax = -std::numeric_limits::max(); float ymin = std::numeric_limits::max(); float ymax = -std::numeric_limits::max(); if (!h1.shouldBeClipped()) expandBoundsToIncludePoint(xmin, xmax, ymin, ymax, h1.cartesianPoint2d()); if (h1.shouldBeClipped() ^ h2.shouldBeClipped()) expandBoundsToIncludePoint(xmin, xmax, ymin, ymax, computeClippedPointForEdge(h1, h2).cartesianPoint2d()); if (!h2.shouldBeClipped()) expandBoundsToIncludePoint(xmin, xmax, ymin, ymax, h2.cartesianPoint2d()); if (h2.shouldBeClipped() ^ h3.shouldBeClipped()) expandBoundsToIncludePoint(xmin, xmax, ymin, ymax, computeClippedPointForEdge(h2, h3).cartesianPoint2d()); if (!h3.shouldBeClipped()) expandBoundsToIncludePoint(xmin, xmax, ymin, ymax, h3.cartesianPoint2d()); if (h3.shouldBeClipped() ^ h4.shouldBeClipped()) expandBoundsToIncludePoint(xmin, xmax, ymin, ymax, computeClippedPointForEdge(h3, h4).cartesianPoint2d()); if (!h4.shouldBeClipped()) expandBoundsToIncludePoint(xmin, xmax, ymin, ymax, h4.cartesianPoint2d()); if (h4.shouldBeClipped() ^ h1.shouldBeClipped()) expandBoundsToIncludePoint(xmin, xmax, ymin, ymax, computeClippedPointForEdge(h4, h1).cartesianPoint2d()); return FloatRect(FloatPoint(xmin, ymin), FloatSize(xmax - xmin, ymax - ymin)); } FloatQuad CCMathUtil::mapQuad(const WebTransformationMatrix& transform, const FloatQuad& q, bool& clipped) { if (transform.isIdentityOrTranslation()) { FloatQuad mappedQuad(q); mappedQuad.move(static_cast(transform.m41()), static_cast(transform.m42())); clipped = false; return mappedQuad; } HomogeneousCoordinate h1 = mapHomogeneousPoint(transform, q.p1()); HomogeneousCoordinate h2 = mapHomogeneousPoint(transform, q.p2()); HomogeneousCoordinate h3 = mapHomogeneousPoint(transform, q.p3()); HomogeneousCoordinate h4 = mapHomogeneousPoint(transform, q.p4()); clipped = h1.shouldBeClipped() || h2.shouldBeClipped() || h3.shouldBeClipped() || h4.shouldBeClipped(); // Result will be invalid if clipped == true. But, compute it anyway just in case, to emulate existing behavior. return FloatQuad(h1.cartesianPoint2d(), h2.cartesianPoint2d(), h3.cartesianPoint2d(), h4.cartesianPoint2d()); } FloatPoint CCMathUtil::mapPoint(const WebTransformationMatrix& transform, const FloatPoint& p, bool& clipped) { HomogeneousCoordinate h = mapHomogeneousPoint(transform, p); if (h.w > 0) { clipped = false; return h.cartesianPoint2d(); } // The cartesian coordinates will be invalid after dividing by w. clipped = true; // Avoid dividing by w if w == 0. if (!h.w) return FloatPoint(); // This return value will be invalid because clipped == true, but (1) users of this // code should be ignoring the return value when clipped == true anyway, and (2) this // behavior is more consistent with existing behavior of WebKit transforms if the user // really does not ignore the return value. return h.cartesianPoint2d(); } FloatPoint3D CCMathUtil::mapPoint(const WebTransformationMatrix& transform, const FloatPoint3D& p, bool& clipped) { HomogeneousCoordinate h = mapHomogeneousPoint(transform, p); if (h.w > 0) { clipped = false; return h.cartesianPoint3d(); } // The cartesian coordinates will be invalid after dividing by w. clipped = true; // Avoid dividing by w if w == 0. if (!h.w) return FloatPoint3D(); // This return value will be invalid because clipped == true, but (1) users of this // code should be ignoring the return value when clipped == true anyway, and (2) this // behavior is more consistent with existing behavior of WebKit transforms if the user // really does not ignore the return value. return h.cartesianPoint3d(); } FloatQuad CCMathUtil::projectQuad(const WebTransformationMatrix& transform, const FloatQuad& q, bool& clipped) { FloatQuad projectedQuad; bool clippedPoint; projectedQuad.setP1(projectPoint(transform, q.p1(), clippedPoint)); clipped = clippedPoint; projectedQuad.setP2(projectPoint(transform, q.p2(), clippedPoint)); clipped |= clippedPoint; projectedQuad.setP3(projectPoint(transform, q.p3(), clippedPoint)); clipped |= clippedPoint; projectedQuad.setP4(projectPoint(transform, q.p4(), clippedPoint)); clipped |= clippedPoint; return projectedQuad; } FloatPoint CCMathUtil::projectPoint(const WebTransformationMatrix& transform, const FloatPoint& p, bool& clipped) { HomogeneousCoordinate h = projectHomogeneousPoint(transform, p); if (h.w > 0) { // The cartesian coordinates will be valid in this case. clipped = false; return h.cartesianPoint2d(); } // The cartesian coordinates will be invalid after dividing by w. clipped = true; // Avoid dividing by w if w == 0. if (!h.w) return FloatPoint(); // This return value will be invalid because clipped == true, but (1) users of this // code should be ignoring the return value when clipped == true anyway, and (2) this // behavior is more consistent with existing behavior of WebKit transforms if the user // really does not ignore the return value. return h.cartesianPoint2d(); } void CCMathUtil::flattenTransformTo2d(WebTransformationMatrix& transform) { // Set both the 3rd row and 3rd column to (0, 0, 1, 0). // // One useful interpretation of doing this operation: // - For x and y values, the new transform behaves effectively like an orthographic // projection was added to the matrix sequence. // - For z values, the new transform overrides any effect that the transform had on // z, and instead it preserves the z value for any points that are transformed. // - Because of linearity of transforms, this flattened transform also preserves the // effect that any subsequent (post-multiplied) transforms would have on z values. // transform.setM13(0); transform.setM23(0); transform.setM31(0); transform.setM32(0); transform.setM33(1); transform.setM34(0); transform.setM43(0); } float CCMathUtil::smallestAngleBetweenVectors(const FloatSize& v1, const FloatSize& v2) { float dotProduct = (v1.width() * v2.width() + v1.height() * v2.height()) / (v1.diagonalLength() * v2.diagonalLength()); // Clamp to compensate for rounding errors. dotProduct = std::max(-1.f, std::min(1.f, dotProduct)); return rad2deg(acosf(dotProduct)); } FloatSize CCMathUtil::projectVector(const FloatSize& source, const FloatSize& destination) { float sourceDotDestination = source.width() * destination.width() + source.height() * destination.height(); float projectedLength = sourceDotDestination / destination.diagonalLengthSquared(); return FloatSize(projectedLength * destination.width(), projectedLength * destination.height()); } } // namespace cc