| // 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 "cc/base/math_util.h" |
| |
| #include <algorithm> |
| #include <cmath> |
| #include <limits> |
| |
| #include "base/trace_event/trace_event_argument.h" |
| #include "base/values.h" |
| #include "ui/gfx/geometry/quad_f.h" |
| #include "ui/gfx/geometry/rect.h" |
| #include "ui/gfx/geometry/rect_conversions.h" |
| #include "ui/gfx/geometry/rect_f.h" |
| #include "ui/gfx/geometry/vector2d_f.h" |
| #include "ui/gfx/geometry/vector3d_f.h" |
| #include "ui/gfx/transform.h" |
| |
| namespace cc { |
| |
| const double MathUtil::kPiDouble = 3.14159265358979323846; |
| const float MathUtil::kPiFloat = 3.14159265358979323846f; |
| |
| static HomogeneousCoordinate ProjectHomogeneousPoint( |
| const gfx::Transform& transform, |
| const gfx::PointF& p) { |
| SkMScalar z = |
| -(transform.matrix().get(2, 0) * p.x() + |
| transform.matrix().get(2, 1) * p.y() + transform.matrix().get(2, 3)) / |
| transform.matrix().get(2, 2); |
| |
| // 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 (!std::isfinite(z)) |
| return HomogeneousCoordinate(0.0, 0.0, 0.0, 1.0); |
| |
| HomogeneousCoordinate result(p.x(), p.y(), z, 1.0); |
| transform.matrix().mapMScalars(result.vec, result.vec); |
| return result; |
| } |
| |
| static HomogeneousCoordinate ProjectHomogeneousPoint( |
| const gfx::Transform& transform, |
| const gfx::PointF& p, |
| bool* clipped) { |
| HomogeneousCoordinate h = ProjectHomogeneousPoint(transform, p); |
| *clipped = h.w() <= 0; |
| return h; |
| } |
| |
| static HomogeneousCoordinate MapHomogeneousPoint( |
| const gfx::Transform& transform, |
| const gfx::Point3F& p) { |
| HomogeneousCoordinate result(p.x(), p.y(), p.z(), 1.0); |
| transform.matrix().mapMScalars(result.vec, result.vec); |
| return result; |
| } |
| |
| static void homogenousLimitAtZero(SkMScalar a1, |
| SkMScalar w1, |
| SkMScalar a2, |
| SkMScalar w2, |
| float t, |
| float* limit) { |
| // This is the tolerance for detecting an eyepoint-aligned edge. |
| static const float kStationaryPointEplison = 0.00001f; |
| // This needs to be big enough to not be the limit of clipping, but not so |
| // big that using it as a size destroys the offset in a rect. |
| static const float kInfiniteCoordinate = 1000000.0f; |
| |
| if (std::abs(a1 * w2 / w1 / a2 - 1.0f) > kStationaryPointEplison) { |
| // We are going to explode towards an infity, but we choose the one that |
| // corresponds to the one on the positive side of w. |
| if (((1.0f - t) * a1 + t * a2) > 0) { |
| *limit = kInfiniteCoordinate; |
| } else { |
| *limit = -kInfiniteCoordinate; |
| } |
| } else { |
| *limit = a1 / w1; // (== a2 / w2) && == (1.0f - t) * a1 / w1 + t * a2 / w2 |
| } |
| } |
| |
| static gfx::PointF ComputeClippedCartesianPoint2dForEdge( |
| 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 the limit in 2 space of |
| // x = ((1-t) h1.x + (t) h2.x) / ((1-t) h1.w + (t) h2.w) |
| // y = ((1-t) h1.y + (t) h2.y) / ((1-t) h1.w + (t) h2.w) |
| // as ((1-t) h1.w + (t) h2.w) -> 0+ |
| |
| // The only answers to this are h1.x/h1.w == h2.x/h2.w, +/- infinity |
| // i.e., either the coordinate is not moving, or is trending to one |
| // infinity or the other. |
| |
| float t = h1.w() / (h1.w() - h2.w()); |
| float x; |
| float y; |
| |
| homogenousLimitAtZero(h1.x(), h1.w(), h2.x(), h2.w(), t, &x); |
| homogenousLimitAtZero(h1.y(), h1.w(), h2.y(), h2.w(), t, &y); |
| |
| return gfx::PointF(x, y); |
| } |
| |
| static gfx::Point3F ComputeClippedCartesianPoint3dForEdge( |
| 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 the limit in 3 space of |
| // x = ((1-t) h1.x + (t) h2.x) / ((1-t) h1.w + (t) h2.w) |
| // y = ((1-t) h1.y + (t) h2.y) / ((1-t) h1.w + (t) h2.w) |
| // z = ((1-t) h1.z + (t) h2.z) / ((1-t) h1.w + (t) h2.w) |
| // as ((1-t) h1.w + (t) h2.w) -> 0+ |
| |
| // The only answers to this are h1.x/h1.w == h2.x/h2.w, +/- infinity |
| // i.e., either the coordinate is not moving, or is trending to one |
| // infinity or the other. |
| |
| float t = h1.w() / (h1.w() - h2.w()); |
| float x; |
| float y; |
| float z; |
| |
| homogenousLimitAtZero(h1.x(), h1.w(), h2.x(), h2.w(), t, &x); |
| homogenousLimitAtZero(h1.y(), h1.w(), h2.y(), h2.w(), t, &y); |
| homogenousLimitAtZero(h1.z(), h1.w(), h2.z(), h2.w(), t, &z); |
| |
| return gfx::Point3F(x, y, z); |
| } |
| |
| static inline void ExpandBoundsToIncludePoint(float* xmin, |
| float* xmax, |
| float* ymin, |
| float* ymax, |
| const gfx::PointF& 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 gfx::PointF& new_vertex, |
| gfx::PointF clipped_quad[8], |
| int* num_vertices_in_clipped_quad) { |
| clipped_quad[*num_vertices_in_clipped_quad] = new_vertex; |
| (*num_vertices_in_clipped_quad)++; |
| } |
| |
| static inline void AddVertexToClippedQuad3d(const gfx::Point3F& new_vertex, |
| gfx::Point3F clipped_quad[8], |
| int* num_vertices_in_clipped_quad) { |
| clipped_quad[*num_vertices_in_clipped_quad] = new_vertex; |
| (*num_vertices_in_clipped_quad)++; |
| } |
| |
| gfx::Rect MathUtil::MapEnclosingClippedRect(const gfx::Transform& transform, |
| const gfx::Rect& src_rect) { |
| if (transform.IsIdentityOrIntegerTranslation()) { |
| gfx::Vector2d offset(static_cast<int>(transform.matrix().getFloat(0, 3)), |
| static_cast<int>(transform.matrix().getFloat(1, 3))); |
| return src_rect + offset; |
| } |
| gfx::RectF mapped_rect = MapClippedRect(transform, gfx::RectF(src_rect)); |
| |
| // gfx::ToEnclosingRect crashes if called on a RectF with any NaN coordinate. |
| if (std::isnan(mapped_rect.x()) || std::isnan(mapped_rect.y()) || |
| std::isnan(mapped_rect.right()) || std::isnan(mapped_rect.bottom())) |
| return gfx::Rect(); |
| |
| return gfx::ToEnclosingRect(mapped_rect); |
| } |
| |
| gfx::RectF MathUtil::MapClippedRect(const gfx::Transform& transform, |
| const gfx::RectF& src_rect) { |
| if (transform.IsIdentityOrTranslation()) { |
| gfx::Vector2dF offset(transform.matrix().getFloat(0, 3), |
| transform.matrix().getFloat(1, 3)); |
| return src_rect + offset; |
| } |
| |
| // Apply the transform, but retain the result in homogeneous coordinates. |
| |
| SkMScalar quad[4 * 2]; // input: 4 x 2D points |
| quad[0] = src_rect.x(); |
| quad[1] = src_rect.y(); |
| quad[2] = src_rect.right(); |
| quad[3] = src_rect.y(); |
| quad[4] = src_rect.right(); |
| quad[5] = src_rect.bottom(); |
| quad[6] = src_rect.x(); |
| quad[7] = src_rect.bottom(); |
| |
| SkMScalar result[4 * 4]; // output: 4 x 4D homogeneous points |
| transform.matrix().map2(quad, 4, result); |
| |
| HomogeneousCoordinate hc0(result[0], result[1], result[2], result[3]); |
| HomogeneousCoordinate hc1(result[4], result[5], result[6], result[7]); |
| HomogeneousCoordinate hc2(result[8], result[9], result[10], result[11]); |
| HomogeneousCoordinate hc3(result[12], result[13], result[14], result[15]); |
| return ComputeEnclosingClippedRect(hc0, hc1, hc2, hc3); |
| } |
| |
| gfx::Rect MathUtil::ProjectEnclosingClippedRect(const gfx::Transform& transform, |
| const gfx::Rect& src_rect) { |
| if (transform.IsIdentityOrIntegerTranslation()) { |
| gfx::Vector2d offset(static_cast<int>(transform.matrix().getFloat(0, 3)), |
| static_cast<int>(transform.matrix().getFloat(1, 3))); |
| return src_rect + offset; |
| } |
| gfx::RectF projected_rect = |
| ProjectClippedRect(transform, gfx::RectF(src_rect)); |
| |
| // gfx::ToEnclosingRect crashes if called on a RectF with any NaN coordinate. |
| if (std::isnan(projected_rect.x()) || std::isnan(projected_rect.y()) || |
| std::isnan(projected_rect.right()) || std::isnan(projected_rect.bottom())) |
| return gfx::Rect(); |
| |
| return gfx::ToEnclosingRect(projected_rect); |
| } |
| |
| gfx::RectF MathUtil::ProjectClippedRect(const gfx::Transform& transform, |
| const gfx::RectF& src_rect) { |
| if (transform.IsIdentityOrTranslation()) { |
| gfx::Vector2dF offset(transform.matrix().getFloat(0, 3), |
| transform.matrix().getFloat(1, 3)); |
| return src_rect + offset; |
| } |
| |
| // Perform the projection, but retain the result in homogeneous coordinates. |
| gfx::QuadF q = gfx::QuadF(src_rect); |
| 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); |
| } |
| |
| gfx::Rect MathUtil::MapEnclosedRectWith2dAxisAlignedTransform( |
| const gfx::Transform& transform, |
| const gfx::Rect& rect) { |
| DCHECK(transform.Preserves2dAxisAlignment()); |
| |
| if (transform.IsIdentityOrIntegerTranslation()) { |
| gfx::Vector2d offset(static_cast<int>(transform.matrix().getFloat(0, 3)), |
| static_cast<int>(transform.matrix().getFloat(1, 3))); |
| return rect + offset; |
| } |
| if (transform.IsIdentityOrTranslation()) { |
| gfx::Vector2dF offset(transform.matrix().getFloat(0, 3), |
| transform.matrix().getFloat(1, 3)); |
| return gfx::ToEnclosedRect(gfx::RectF(rect) + offset); |
| } |
| |
| SkMScalar quad[2 * 2]; // input: 2 x 2D points |
| quad[0] = rect.x(); |
| quad[1] = rect.y(); |
| quad[2] = rect.right(); |
| quad[3] = rect.bottom(); |
| |
| SkMScalar result[4 * 2]; // output: 2 x 4D homogeneous points |
| transform.matrix().map2(quad, 2, result); |
| |
| HomogeneousCoordinate hc0(result[0], result[1], result[2], result[3]); |
| HomogeneousCoordinate hc1(result[4], result[5], result[6], result[7]); |
| DCHECK(!hc0.ShouldBeClipped()); |
| DCHECK(!hc1.ShouldBeClipped()); |
| |
| gfx::PointF top_left(hc0.CartesianPoint2d()); |
| gfx::PointF bottom_right(hc1.CartesianPoint2d()); |
| return gfx::ToEnclosedRect(gfx::BoundingRect(top_left, bottom_right)); |
| } |
| |
| void MathUtil::MapClippedQuad(const gfx::Transform& transform, |
| const gfx::QuadF& src_quad, |
| gfx::PointF clipped_quad[8], |
| int* num_vertices_in_clipped_quad) { |
| HomogeneousCoordinate h1 = |
| MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p1())); |
| HomogeneousCoordinate h2 = |
| MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p2())); |
| HomogeneousCoordinate h3 = |
| MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p3())); |
| HomogeneousCoordinate h4 = |
| MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p4())); |
| |
| // The order of adding the vertices to the array is chosen so that |
| // clockwise / counter-clockwise orientation is retained. |
| |
| *num_vertices_in_clipped_quad = 0; |
| |
| if (!h1.ShouldBeClipped()) { |
| AddVertexToClippedQuad( |
| h1.CartesianPoint2d(), clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (h1.ShouldBeClipped() ^ h2.ShouldBeClipped()) { |
| AddVertexToClippedQuad(ComputeClippedCartesianPoint2dForEdge(h1, h2), |
| clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (!h2.ShouldBeClipped()) { |
| AddVertexToClippedQuad( |
| h2.CartesianPoint2d(), clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (h2.ShouldBeClipped() ^ h3.ShouldBeClipped()) { |
| AddVertexToClippedQuad(ComputeClippedCartesianPoint2dForEdge(h2, h3), |
| clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (!h3.ShouldBeClipped()) { |
| AddVertexToClippedQuad( |
| h3.CartesianPoint2d(), clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (h3.ShouldBeClipped() ^ h4.ShouldBeClipped()) { |
| AddVertexToClippedQuad(ComputeClippedCartesianPoint2dForEdge(h3, h4), |
| clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (!h4.ShouldBeClipped()) { |
| AddVertexToClippedQuad( |
| h4.CartesianPoint2d(), clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (h4.ShouldBeClipped() ^ h1.ShouldBeClipped()) { |
| AddVertexToClippedQuad(ComputeClippedCartesianPoint2dForEdge(h4, h1), |
| clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| DCHECK_LE(*num_vertices_in_clipped_quad, 8); |
| } |
| |
| bool MathUtil::MapClippedQuad3d(const gfx::Transform& transform, |
| const gfx::QuadF& src_quad, |
| gfx::Point3F clipped_quad[8], |
| int* num_vertices_in_clipped_quad) { |
| HomogeneousCoordinate h1 = |
| MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p1())); |
| HomogeneousCoordinate h2 = |
| MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p2())); |
| HomogeneousCoordinate h3 = |
| MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p3())); |
| HomogeneousCoordinate h4 = |
| MapHomogeneousPoint(transform, gfx::Point3F(src_quad.p4())); |
| |
| // The order of adding the vertices to the array is chosen so that |
| // clockwise / counter-clockwise orientation is retained. |
| |
| *num_vertices_in_clipped_quad = 0; |
| |
| if (!h1.ShouldBeClipped()) { |
| AddVertexToClippedQuad3d( |
| h1.CartesianPoint3d(), clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (h1.ShouldBeClipped() ^ h2.ShouldBeClipped()) { |
| AddVertexToClippedQuad3d(ComputeClippedCartesianPoint3dForEdge(h1, h2), |
| clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (!h2.ShouldBeClipped()) { |
| AddVertexToClippedQuad3d( |
| h2.CartesianPoint3d(), clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (h2.ShouldBeClipped() ^ h3.ShouldBeClipped()) { |
| AddVertexToClippedQuad3d(ComputeClippedCartesianPoint3dForEdge(h2, h3), |
| clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (!h3.ShouldBeClipped()) { |
| AddVertexToClippedQuad3d( |
| h3.CartesianPoint3d(), clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (h3.ShouldBeClipped() ^ h4.ShouldBeClipped()) { |
| AddVertexToClippedQuad3d(ComputeClippedCartesianPoint3dForEdge(h3, h4), |
| clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (!h4.ShouldBeClipped()) { |
| AddVertexToClippedQuad3d( |
| h4.CartesianPoint3d(), clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| if (h4.ShouldBeClipped() ^ h1.ShouldBeClipped()) { |
| AddVertexToClippedQuad3d(ComputeClippedCartesianPoint3dForEdge(h4, h1), |
| clipped_quad, num_vertices_in_clipped_quad); |
| } |
| |
| DCHECK_LE(*num_vertices_in_clipped_quad, 8); |
| return (*num_vertices_in_clipped_quad >= 4); |
| } |
| |
| gfx::RectF MathUtil::ComputeEnclosingRectOfVertices( |
| const gfx::PointF vertices[], |
| int num_vertices) { |
| if (num_vertices < 2) |
| return gfx::RectF(); |
| |
| float xmin = std::numeric_limits<float>::max(); |
| float xmax = -std::numeric_limits<float>::max(); |
| float ymin = std::numeric_limits<float>::max(); |
| float ymax = -std::numeric_limits<float>::max(); |
| |
| for (int i = 0; i < num_vertices; ++i) |
| ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, vertices[i]); |
| |
| return gfx::RectF(gfx::PointF(xmin, ymin), |
| gfx::SizeF(xmax - xmin, ymax - ymin)); |
| } |
| |
| gfx::RectF MathUtil::ComputeEnclosingClippedRect( |
| const HomogeneousCoordinate& h1, |
| const HomogeneousCoordinate& h2, |
| const HomogeneousCoordinate& h3, |
| const HomogeneousCoordinate& h4) { |
| // This function performs clipping as necessary and computes the enclosing 2d |
| // gfx::RectF 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 something_clipped = h1.ShouldBeClipped() || h2.ShouldBeClipped() || |
| h3.ShouldBeClipped() || h4.ShouldBeClipped(); |
| if (!something_clipped) { |
| gfx::QuadF mapped_quad = gfx::QuadF(h1.CartesianPoint2d(), |
| h2.CartesianPoint2d(), |
| h3.CartesianPoint2d(), |
| h4.CartesianPoint2d()); |
| return mapped_quad.BoundingBox(); |
| } |
| |
| bool everything_clipped = h1.ShouldBeClipped() && h2.ShouldBeClipped() && |
| h3.ShouldBeClipped() && h4.ShouldBeClipped(); |
| if (everything_clipped) |
| return gfx::RectF(); |
| |
| float xmin = std::numeric_limits<float>::max(); |
| float xmax = -std::numeric_limits<float>::max(); |
| float ymin = std::numeric_limits<float>::max(); |
| float ymax = -std::numeric_limits<float>::max(); |
| |
| if (!h1.ShouldBeClipped()) |
| ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, |
| h1.CartesianPoint2d()); |
| |
| if (h1.ShouldBeClipped() ^ h2.ShouldBeClipped()) |
| ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, |
| ComputeClippedCartesianPoint2dForEdge(h1, h2)); |
| |
| if (!h2.ShouldBeClipped()) |
| ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, |
| h2.CartesianPoint2d()); |
| |
| if (h2.ShouldBeClipped() ^ h3.ShouldBeClipped()) |
| ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, |
| ComputeClippedCartesianPoint2dForEdge(h2, h3)); |
| |
| if (!h3.ShouldBeClipped()) |
| ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, |
| h3.CartesianPoint2d()); |
| |
| if (h3.ShouldBeClipped() ^ h4.ShouldBeClipped()) |
| ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, |
| ComputeClippedCartesianPoint2dForEdge(h3, h4)); |
| |
| if (!h4.ShouldBeClipped()) |
| ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, |
| h4.CartesianPoint2d()); |
| |
| if (h4.ShouldBeClipped() ^ h1.ShouldBeClipped()) |
| ExpandBoundsToIncludePoint(&xmin, &xmax, &ymin, &ymax, |
| ComputeClippedCartesianPoint2dForEdge(h4, h1)); |
| |
| return gfx::RectF(gfx::PointF(xmin, ymin), |
| gfx::SizeF(xmax - xmin, ymax - ymin)); |
| } |
| |
| gfx::QuadF MathUtil::MapQuad(const gfx::Transform& transform, |
| const gfx::QuadF& q, |
| bool* clipped) { |
| if (transform.IsIdentityOrTranslation()) { |
| gfx::QuadF mapped_quad(q); |
| mapped_quad += gfx::Vector2dF(transform.matrix().getFloat(0, 3), |
| transform.matrix().getFloat(1, 3)); |
| *clipped = false; |
| return mapped_quad; |
| } |
| |
| HomogeneousCoordinate h1 = |
| MapHomogeneousPoint(transform, gfx::Point3F(q.p1())); |
| HomogeneousCoordinate h2 = |
| MapHomogeneousPoint(transform, gfx::Point3F(q.p2())); |
| HomogeneousCoordinate h3 = |
| MapHomogeneousPoint(transform, gfx::Point3F(q.p3())); |
| HomogeneousCoordinate h4 = |
| MapHomogeneousPoint(transform, gfx::Point3F(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 gfx::QuadF(h1.CartesianPoint2d(), |
| h2.CartesianPoint2d(), |
| h3.CartesianPoint2d(), |
| h4.CartesianPoint2d()); |
| } |
| |
| gfx::QuadF MathUtil::MapQuad3d(const gfx::Transform& transform, |
| const gfx::QuadF& q, |
| gfx::Point3F* p, |
| bool* clipped) { |
| if (transform.IsIdentityOrTranslation()) { |
| gfx::QuadF mapped_quad(q); |
| mapped_quad += gfx::Vector2dF(transform.matrix().getFloat(0, 3), |
| transform.matrix().getFloat(1, 3)); |
| *clipped = false; |
| p[0] = gfx::Point3F(mapped_quad.p1().x(), mapped_quad.p1().y(), 0.0f); |
| p[1] = gfx::Point3F(mapped_quad.p2().x(), mapped_quad.p2().y(), 0.0f); |
| p[2] = gfx::Point3F(mapped_quad.p3().x(), mapped_quad.p3().y(), 0.0f); |
| p[3] = gfx::Point3F(mapped_quad.p4().x(), mapped_quad.p4().y(), 0.0f); |
| return mapped_quad; |
| } |
| |
| HomogeneousCoordinate h1 = |
| MapHomogeneousPoint(transform, gfx::Point3F(q.p1())); |
| HomogeneousCoordinate h2 = |
| MapHomogeneousPoint(transform, gfx::Point3F(q.p2())); |
| HomogeneousCoordinate h3 = |
| MapHomogeneousPoint(transform, gfx::Point3F(q.p3())); |
| HomogeneousCoordinate h4 = |
| MapHomogeneousPoint(transform, gfx::Point3F(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. |
| p[0] = h1.CartesianPoint3d(); |
| p[1] = h2.CartesianPoint3d(); |
| p[2] = h3.CartesianPoint3d(); |
| p[3] = h4.CartesianPoint3d(); |
| |
| return gfx::QuadF(h1.CartesianPoint2d(), |
| h2.CartesianPoint2d(), |
| h3.CartesianPoint2d(), |
| h4.CartesianPoint2d()); |
| } |
| |
| gfx::PointF MathUtil::MapPoint(const gfx::Transform& transform, |
| const gfx::PointF& p, |
| bool* clipped) { |
| HomogeneousCoordinate h = MapHomogeneousPoint(transform, gfx::Point3F(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 gfx::PointF(); |
| |
| // 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(); |
| } |
| |
| gfx::Point3F MathUtil::MapPoint(const gfx::Transform& transform, |
| const gfx::Point3F& 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 gfx::Point3F(); |
| |
| // 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(); |
| } |
| |
| gfx::QuadF MathUtil::ProjectQuad(const gfx::Transform& transform, |
| const gfx::QuadF& q, |
| bool* clipped) { |
| gfx::QuadF projected_quad; |
| bool clipped_point; |
| projected_quad.set_p1(ProjectPoint(transform, q.p1(), &clipped_point)); |
| *clipped = clipped_point; |
| projected_quad.set_p2(ProjectPoint(transform, q.p2(), &clipped_point)); |
| *clipped |= clipped_point; |
| projected_quad.set_p3(ProjectPoint(transform, q.p3(), &clipped_point)); |
| *clipped |= clipped_point; |
| projected_quad.set_p4(ProjectPoint(transform, q.p4(), &clipped_point)); |
| *clipped |= clipped_point; |
| |
| return projected_quad; |
| } |
| |
| gfx::PointF MathUtil::ProjectPoint(const gfx::Transform& transform, |
| const gfx::PointF& p, |
| bool* clipped) { |
| HomogeneousCoordinate h = ProjectHomogeneousPoint(transform, p, clipped); |
| // Avoid dividing by w if w == 0. |
| if (!h.w()) |
| return gfx::PointF(); |
| |
| // This return value will be invalid if 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(); |
| } |
| |
| gfx::Point3F MathUtil::ProjectPoint3D(const gfx::Transform& transform, |
| const gfx::PointF& p, |
| bool* clipped) { |
| HomogeneousCoordinate h = ProjectHomogeneousPoint(transform, p, clipped); |
| if (!h.w()) |
| return gfx::Point3F(); |
| return h.CartesianPoint3d(); |
| } |
| |
| gfx::RectF MathUtil::ScaleRectProportional(const gfx::RectF& input_outer_rect, |
| const gfx::RectF& scale_outer_rect, |
| const gfx::RectF& scale_inner_rect) { |
| gfx::RectF output_inner_rect = input_outer_rect; |
| float scale_rect_to_input_scale_x = |
| scale_outer_rect.width() / input_outer_rect.width(); |
| float scale_rect_to_input_scale_y = |
| scale_outer_rect.height() / input_outer_rect.height(); |
| |
| gfx::Vector2dF top_left_diff = |
| scale_inner_rect.origin() - scale_outer_rect.origin(); |
| gfx::Vector2dF bottom_right_diff = |
| scale_inner_rect.bottom_right() - scale_outer_rect.bottom_right(); |
| output_inner_rect.Inset(top_left_diff.x() / scale_rect_to_input_scale_x, |
| top_left_diff.y() / scale_rect_to_input_scale_y, |
| -bottom_right_diff.x() / scale_rect_to_input_scale_x, |
| -bottom_right_diff.y() / scale_rect_to_input_scale_y); |
| return output_inner_rect; |
| } |
| |
| static inline bool NearlyZero(double value) { |
| return std::abs(value) < std::numeric_limits<double>::epsilon(); |
| } |
| |
| static inline float ScaleOnAxis(double a, double b, double c) { |
| if (NearlyZero(b) && NearlyZero(c)) |
| return std::abs(a); |
| if (NearlyZero(a) && NearlyZero(c)) |
| return std::abs(b); |
| if (NearlyZero(a) && NearlyZero(b)) |
| return std::abs(c); |
| |
| // Do the sqrt as a double to not lose precision. |
| return static_cast<float>(std::sqrt(a * a + b * b + c * c)); |
| } |
| |
| gfx::Vector2dF MathUtil::ComputeTransform2dScaleComponents( |
| const gfx::Transform& transform, |
| float fallback_value) { |
| if (transform.HasPerspective()) |
| return gfx::Vector2dF(fallback_value, fallback_value); |
| float x_scale = ScaleOnAxis(transform.matrix().getDouble(0, 0), |
| transform.matrix().getDouble(1, 0), |
| transform.matrix().getDouble(2, 0)); |
| float y_scale = ScaleOnAxis(transform.matrix().getDouble(0, 1), |
| transform.matrix().getDouble(1, 1), |
| transform.matrix().getDouble(2, 1)); |
| return gfx::Vector2dF(x_scale, y_scale); |
| } |
| |
| float MathUtil::SmallestAngleBetweenVectors(const gfx::Vector2dF& v1, |
| const gfx::Vector2dF& v2) { |
| double dot_product = gfx::DotProduct(v1, v2) / v1.Length() / v2.Length(); |
| // Clamp to compensate for rounding errors. |
| dot_product = std::max(-1.0, std::min(1.0, dot_product)); |
| return static_cast<float>(Rad2Deg(std::acos(dot_product))); |
| } |
| |
| gfx::Vector2dF MathUtil::ProjectVector(const gfx::Vector2dF& source, |
| const gfx::Vector2dF& destination) { |
| float projected_length = |
| gfx::DotProduct(source, destination) / destination.LengthSquared(); |
| return gfx::Vector2dF(projected_length * destination.x(), |
| projected_length * destination.y()); |
| } |
| |
| std::unique_ptr<base::Value> MathUtil::AsValue(const gfx::Size& s) { |
| std::unique_ptr<base::DictionaryValue> res(new base::DictionaryValue()); |
| res->SetDouble("width", s.width()); |
| res->SetDouble("height", s.height()); |
| return std::move(res); |
| } |
| |
| std::unique_ptr<base::Value> MathUtil::AsValue(const gfx::Rect& r) { |
| std::unique_ptr<base::ListValue> res(new base::ListValue()); |
| res->AppendInteger(r.x()); |
| res->AppendInteger(r.y()); |
| res->AppendInteger(r.width()); |
| res->AppendInteger(r.height()); |
| return std::move(res); |
| } |
| |
| bool MathUtil::FromValue(const base::Value* raw_value, gfx::Rect* out_rect) { |
| const base::ListValue* value = nullptr; |
| if (!raw_value->GetAsList(&value)) |
| return false; |
| |
| if (value->GetSize() != 4) |
| return false; |
| |
| int x, y, w, h; |
| bool ok = true; |
| ok &= value->GetInteger(0, &x); |
| ok &= value->GetInteger(1, &y); |
| ok &= value->GetInteger(2, &w); |
| ok &= value->GetInteger(3, &h); |
| if (!ok) |
| return false; |
| |
| *out_rect = gfx::Rect(x, y, w, h); |
| return true; |
| } |
| |
| std::unique_ptr<base::Value> MathUtil::AsValue(const gfx::PointF& pt) { |
| std::unique_ptr<base::ListValue> res(new base::ListValue()); |
| res->AppendDouble(pt.x()); |
| res->AppendDouble(pt.y()); |
| return std::move(res); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::Size& s, |
| base::trace_event::TracedValue* res) { |
| res->BeginDictionary(name); |
| res->SetDouble("width", s.width()); |
| res->SetDouble("height", s.height()); |
| res->EndDictionary(); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::SizeF& s, |
| base::trace_event::TracedValue* res) { |
| res->BeginDictionary(name); |
| res->SetDouble("width", s.width()); |
| res->SetDouble("height", s.height()); |
| res->EndDictionary(); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::Rect& r, |
| base::trace_event::TracedValue* res) { |
| res->BeginArray(name); |
| res->AppendInteger(r.x()); |
| res->AppendInteger(r.y()); |
| res->AppendInteger(r.width()); |
| res->AppendInteger(r.height()); |
| res->EndArray(); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::Point& pt, |
| base::trace_event::TracedValue* res) { |
| res->BeginArray(name); |
| res->AppendInteger(pt.x()); |
| res->AppendInteger(pt.y()); |
| res->EndArray(); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::PointF& pt, |
| base::trace_event::TracedValue* res) { |
| res->BeginArray(name); |
| res->AppendDouble(pt.x()); |
| res->AppendDouble(pt.y()); |
| res->EndArray(); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::Point3F& pt, |
| base::trace_event::TracedValue* res) { |
| res->BeginArray(name); |
| res->AppendDouble(pt.x()); |
| res->AppendDouble(pt.y()); |
| res->AppendDouble(pt.z()); |
| res->EndArray(); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::Vector2d& v, |
| base::trace_event::TracedValue* res) { |
| res->BeginArray(name); |
| res->AppendInteger(v.x()); |
| res->AppendInteger(v.y()); |
| res->EndArray(); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::Vector2dF& v, |
| base::trace_event::TracedValue* res) { |
| res->BeginArray(name); |
| res->AppendDouble(v.x()); |
| res->AppendDouble(v.y()); |
| res->EndArray(); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::ScrollOffset& v, |
| base::trace_event::TracedValue* res) { |
| res->BeginArray(name); |
| res->AppendDouble(v.x()); |
| res->AppendDouble(v.y()); |
| res->EndArray(); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::QuadF& q, |
| base::trace_event::TracedValue* res) { |
| res->BeginArray(name); |
| res->AppendDouble(q.p1().x()); |
| res->AppendDouble(q.p1().y()); |
| res->AppendDouble(q.p2().x()); |
| res->AppendDouble(q.p2().y()); |
| res->AppendDouble(q.p3().x()); |
| res->AppendDouble(q.p3().y()); |
| res->AppendDouble(q.p4().x()); |
| res->AppendDouble(q.p4().y()); |
| res->EndArray(); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::RectF& rect, |
| base::trace_event::TracedValue* res) { |
| res->BeginArray(name); |
| res->AppendDouble(rect.x()); |
| res->AppendDouble(rect.y()); |
| res->AppendDouble(rect.width()); |
| res->AppendDouble(rect.height()); |
| res->EndArray(); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::Transform& transform, |
| base::trace_event::TracedValue* res) { |
| res->BeginArray(name); |
| const SkMatrix44& m = transform.matrix(); |
| for (int row = 0; row < 4; ++row) { |
| for (int col = 0; col < 4; ++col) |
| res->AppendDouble(m.getDouble(row, col)); |
| } |
| res->EndArray(); |
| } |
| |
| void MathUtil::AddToTracedValue(const char* name, |
| const gfx::BoxF& box, |
| base::trace_event::TracedValue* res) { |
| res->BeginArray(name); |
| res->AppendInteger(box.x()); |
| res->AppendInteger(box.y()); |
| res->AppendInteger(box.z()); |
| res->AppendInteger(box.width()); |
| res->AppendInteger(box.height()); |
| res->AppendInteger(box.depth()); |
| res->EndArray(); |
| } |
| |
| double MathUtil::AsDoubleSafely(double value) { |
| return std::min(value, std::numeric_limits<double>::max()); |
| } |
| |
| float MathUtil::AsFloatSafely(float value) { |
| return std::min(value, std::numeric_limits<float>::max()); |
| } |
| |
| gfx::Vector3dF MathUtil::GetXAxis(const gfx::Transform& transform) { |
| return gfx::Vector3dF(transform.matrix().getFloat(0, 0), |
| transform.matrix().getFloat(1, 0), |
| transform.matrix().getFloat(2, 0)); |
| } |
| |
| gfx::Vector3dF MathUtil::GetYAxis(const gfx::Transform& transform) { |
| return gfx::Vector3dF(transform.matrix().getFloat(0, 1), |
| transform.matrix().getFloat(1, 1), |
| transform.matrix().getFloat(2, 1)); |
| } |
| |
| } // namespace cc |
