blob: 6e5ac0bd45db73b47d318a7d4b3aef0f42af0078 [file] [log] [blame]
// 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 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.
DCHECK_NE(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.
DCHECK(h1.ShouldBeClipped() ^ h2.ShouldBeClipped());
// ...or any positive non-zero small epsilon
SkMScalar w = 0.00001f;
SkMScalar t = (w - h1.w()) / (h2.w() - h1.w());
SkMScalar x = (SK_MScalar1 - t) * h1.x() + t * h2.x();
SkMScalar y = (SK_MScalar1 - t) * h1.y() + t * h2.y();
SkMScalar z = (SK_MScalar1 - 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 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(
ComputeClippedPointForEdge(h1, h2).CartesianPoint2d(),
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(
ComputeClippedPointForEdge(h2, h3).CartesianPoint2d(),
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(
ComputeClippedPointForEdge(h3, h4).CartesianPoint2d(),
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(
ComputeClippedPointForEdge(h4, h1).CartesianPoint2d(),
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(
ComputeClippedPointForEdge(h1, h2).CartesianPoint3d(),
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(
ComputeClippedPointForEdge(h2, h3).CartesianPoint3d(),
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(
ComputeClippedPointForEdge(h3, h4).CartesianPoint3d(),
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(
ComputeClippedPointForEdge(h4, h1).CartesianPoint3d(),
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,
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 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());
}
scoped_ptr<base::Value> MathUtil::AsValue(const gfx::Size& s) {
scoped_ptr<base::DictionaryValue> res(new base::DictionaryValue());
res->SetDouble("width", s.width());
res->SetDouble("height", s.height());
return res.Pass();
}
scoped_ptr<base::Value> MathUtil::AsValue(const gfx::Rect& r) {
scoped_ptr<base::ListValue> res(new base::ListValue());
res->AppendInteger(r.x());
res->AppendInteger(r.y());
res->AppendInteger(r.width());
res->AppendInteger(r.height());
return res.Pass();
}
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;
}
scoped_ptr<base::Value> MathUtil::AsValue(const gfx::PointF& pt) {
scoped_ptr<base::ListValue> res(new base::ListValue());
res->AppendDouble(pt.x());
res->AppendDouble(pt.y());
return res.Pass();
}
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::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