cc/base/math_util.cc

// 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/values.h"
#include "ui/gfx/quad_f.h"
#include "ui/gfx/rect.h"
#include "ui/gfx/rect_conversions.h"
#include "ui/gfx/rect_f.h"
#include "ui/gfx/transform.h"
#include "ui/gfx/vector2d_f.h"

namespace cc {

const double MathUtil::kPiDouble = 3.14159265358979323846;
const float MathUtil::kPiFloat = 3.14159265358979323846f;

static HomogeneousCoordinate ProjectHomogeneousPoint(
    const gfx::Transform& transform,
    gfx::PointF 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.matrix().get(2, 2))
    return HomogeneousCoordinate(0.0, 0.0, 0.0, 1.0);

  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);
  HomogeneousCoordinate result(p.x(), p.y(), z, 1.0);
  transform.matrix().mapMScalars(result.vec, result.vec);
  return result;
}

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());

  SkMScalar w = 0.00001;  // or any positive non-zero small epsilon

  SkMScalar t = (w - h1.w()) / (h2.w() - h1.w());

  SkMScalar x = (1 - t) * h1.x() + t * h2.x();
  SkMScalar y = (1 - t) * h1.y() + t * h2.y();
  SkMScalar 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,
                                              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(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)++;
}

gfx::Rect MathUtil::MapClippedRect(const gfx::Transform& transform,
                                   gfx::Rect src_rect) {
  return gfx::ToEnclosingRect(MapClippedRect(transform, gfx::RectF(src_rect)));
}

gfx::RectF MathUtil::MapClippedRect(const gfx::Transform& transform,
                                    const gfx::RectF& src_rect) {
  if (transform.IsIdentityOrTranslation())
    return src_rect +
           gfx::Vector2dF(
               static_cast<float>(transform.matrix().getDouble(0, 3)),
               static_cast<float>(transform.matrix().getDouble(1, 3)));

  // Apply the transform, but retain the result in homogeneous coordinates.

  double 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();

  double 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::RectF MathUtil::ProjectClippedRect(const gfx::Transform& transform,
                                        const gfx::RectF& src_rect) {
  if (transform.IsIdentityOrTranslation()) {
    return src_rect +
           gfx::Vector2dF(
               static_cast<float>(transform.matrix().getDouble(0, 3)),
               static_cast<float>(transform.matrix().getDouble(1, 3)));
  }

  // 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);
}

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);
}

gfx::RectF MathUtil::ComputeEnclosingRectOfVertices(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(static_cast<float>(transform.matrix().getDouble(0, 3)),
                       static_cast<float>(transform.matrix().getDouble(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,
                               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,
                                   gfx::PointF 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 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();
}

static inline float ScaleOnAxis(double a, double b, double c) {
  return 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(gfx::Vector2dF v1,
                                            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(gfx::Vector2dF source,
                                       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(gfx::Size s) {
  scoped_ptr<base::DictionaryValue> res(new base::DictionaryValue());
  res->SetDouble("width", s.width());
  res->SetDouble("height", s.height());
  return res.PassAs<base::Value>();
}

scoped_ptr<base::Value> MathUtil::AsValue(gfx::SizeF s) {
  scoped_ptr<base::DictionaryValue> res(new base::DictionaryValue());
  res->SetDouble("width", s.width());
  res->SetDouble("height", s.height());
  return res.PassAs<base::Value>();
}

scoped_ptr<base::Value> MathUtil::AsValue(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.PassAs<base::Value>();
}

bool MathUtil::FromValue(const base::Value* raw_value, gfx::Rect* out_rect) {
  const base::ListValue* value = NULL;
  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(gfx::PointF pt) {
  scoped_ptr<base::ListValue> res(new base::ListValue());
  res->AppendDouble(pt.x());
  res->AppendDouble(pt.y());
  return res.PassAs<base::Value>();
}

scoped_ptr<base::Value> MathUtil::AsValue(const gfx::QuadF& q) {
  scoped_ptr<base::ListValue> res(new base::ListValue());
  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());
  return res.PassAs<base::Value>();
}

scoped_ptr<base::Value> MathUtil::AsValue(const gfx::RectF& rect) {
  scoped_ptr<base::ListValue> res(new base::ListValue());
  res->AppendDouble(rect.x());
  res->AppendDouble(rect.y());
  res->AppendDouble(rect.width());
  res->AppendDouble(rect.height());
  return res.PassAs<base::Value>();
}

scoped_ptr<base::Value> MathUtil::AsValue(const gfx::Transform& transform) {
  scoped_ptr<base::ListValue> res(new base::ListValue());
  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));
  }
  return res.PassAs<base::Value>();
}

scoped_ptr<base::Value> MathUtil::AsValueSafely(double value) {
  return scoped_ptr<base::Value>(base::Value::CreateDoubleValue(
      std::min(value, std::numeric_limits<double>::max())));
}

scoped_ptr<base::Value> MathUtil::AsValueSafely(float value) {
  return scoped_ptr<base::Value>(base::Value::CreateDoubleValue(
      std::min(value, std::numeric_limits<float>::max())));
}

}  // namespace cc