blob: fc885a41414fdb6d4b0906c5a4c790934f057e1b [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>
#ifdef __SSE__
#include <xmmintrin.h>
#endif
#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 bool IsNearlyTheSame(float f, float g) {
// The idea behind this is to use this fraction of the larger of the
// two numbers as the limit of the difference. This breaks down near
// zero, so we reuse this as the minimum absolute size we will use
// for the base of the scale too.
static const float epsilon_scale = 0.00001f;
return std::abs(f - g) <
epsilon_scale *
std::max(std::max(std::abs(f), std::abs(g)), epsilon_scale);
}
static inline bool IsNearlyTheSame(const gfx::PointF& lhs,
const gfx::PointF& rhs) {
return IsNearlyTheSame(lhs.x(), rhs.x()) && IsNearlyTheSame(lhs.y(), rhs.y());
}
static inline bool IsNearlyTheSame(const gfx::Point3F& lhs,
const gfx::Point3F& rhs) {
return IsNearlyTheSame(lhs.x(), rhs.x()) &&
IsNearlyTheSame(lhs.y(), rhs.y()) && IsNearlyTheSame(lhs.z(), rhs.z());
}
static inline void AddVertexToClippedQuad3d(const gfx::Point3F& new_vertex,
gfx::Point3F clipped_quad[6],
int* num_vertices_in_clipped_quad) {
if (*num_vertices_in_clipped_quad > 0 &&
IsNearlyTheSame(clipped_quad[*num_vertices_in_clipped_quad - 1],
new_vertex))
return;
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));
}
bool MathUtil::MapClippedQuad3d(const gfx::Transform& transform,
const gfx::QuadF& src_quad,
gfx::Point3F clipped_quad[6],
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);
}
if (*num_vertices_in_clipped_quad > 2 &&
IsNearlyTheSame(clipped_quad[0],
clipped_quad[*num_vertices_in_clipped_quad - 1]))
*num_vertices_in_clipped_quad -= 1;
DCHECK_LE(*num_vertices_in_clipped_quad, 6);
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::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::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));
}
ScopedSubnormalFloatDisabler::ScopedSubnormalFloatDisabler() {
#ifdef __SSE__
// Turn on "subnormals are zero" and "flush to zero" CSR flags.
orig_state_ = _mm_getcsr();
_mm_setcsr(orig_state_ | 0x8040);
#endif
}
ScopedSubnormalFloatDisabler::~ScopedSubnormalFloatDisabler() {
#ifdef __SSE__
_mm_setcsr(orig_state_);
#endif
}
bool MathUtil::IsFloatNearlyTheSame(float left, float right) {
return IsNearlyTheSame(left, right);
}
bool MathUtil::IsNearlyTheSameForTesting(const gfx::PointF& left,
const gfx::PointF& right) {
return IsNearlyTheSame(left, right);
}
bool MathUtil::IsNearlyTheSameForTesting(const gfx::Point3F& left,
const gfx::Point3F& right) {
return IsNearlyTheSame(left, right);
}
} // namespace cc