src/cobalt/math/quad_f.cc

// Copyright (c) 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 "cobalt/math/quad_f.h"

#include <limits>

#include "base/stringprintf.h"

namespace cobalt {
namespace math {

void QuadF::operator=(const RectF& rect) {
  p1_ = PointF(rect.x(), rect.y());
  p2_ = PointF(rect.right(), rect.y());
  p3_ = PointF(rect.right(), rect.bottom());
  p4_ = PointF(rect.x(), rect.bottom());
}

std::string QuadF::ToString() const {
  return base::StringPrintf("%s;%s;%s;%s", p1_.ToString().c_str(),
                            p2_.ToString().c_str(), p3_.ToString().c_str(),
                            p4_.ToString().c_str());
}

static inline bool WithinEpsilon(float a, float b) {
  return std::abs(a - b) < std::numeric_limits<float>::epsilon();
}

bool QuadF::IsRectilinear() const {
  return (WithinEpsilon(p1_.x(), p2_.x()) && WithinEpsilon(p2_.y(), p3_.y()) &&
          WithinEpsilon(p3_.x(), p4_.x()) && WithinEpsilon(p4_.y(), p1_.y())) ||
         (WithinEpsilon(p1_.y(), p2_.y()) && WithinEpsilon(p2_.x(), p3_.x()) &&
          WithinEpsilon(p3_.y(), p4_.y()) && WithinEpsilon(p4_.x(), p1_.x()));
}

bool QuadF::IsCounterClockwise() const {
  // This math computes the signed area of the quad. Positive area
  // indicates the quad is clockwise; negative area indicates the quad is
  // counter-clockwise. Note carefully: this is backwards from conventional
  // math because our geometric space uses screen coordiantes with y-axis
  // pointing downards.
  // Reference: http://mathworld.wolfram.com/PolygonArea.html.
  // The equation can be written:
  // Signed area = determinant1 + determinant2 + determinant3 + determinant4
  // In practise, Refactoring the computation of adding determinants so that
  // reducing the number of operations. The equation is:
  // Signed area = element1 + element2 - element3 - element4

  float p24 = p2_.y() - p4_.y();
  float p31 = p3_.y() - p1_.y();

  // Up-cast to double so this cannot overflow.
  double element1 = static_cast<double>(p1_.x()) * p24;
  double element2 = static_cast<double>(p2_.x()) * p31;
  double element3 = static_cast<double>(p3_.x()) * p24;
  double element4 = static_cast<double>(p4_.x()) * p31;

  return element1 + element2 < element3 + element4;
}

static inline bool PointIsInTriangle(const PointF& point, const PointF& r1,
                                     const PointF& r2, const PointF& r3) {
  // Translate point and triangle so that point lies at origin.
  // Then checking if the origin is contained in the translated triangle.
  // The origin O lies inside ABC if and only if the triangles OAB, OBC,
  // and OCA are all either clockwise or counterclockwise.
  // This algorithm is from Real-Time Collision Detection (Chaper 5.4.2).

  Vector2dF a = r1 - point;
  Vector2dF b = r2 - point;
  Vector2dF c = r3 - point;

  double u = CrossProduct(b, c);
  double v = CrossProduct(c, a);
  double w = CrossProduct(a, b);
  return ((u * v < 0) || ((u * w) < 0) || ((v * w) < 0)) ? false : true;
}

bool QuadF::Contains(const PointF& point) const {
  return PointIsInTriangle(point, p1_, p2_, p3_) ||
         PointIsInTriangle(point, p1_, p3_, p4_);
}

void QuadF::Scale(float x_scale, float y_scale) {
  p1_.Scale(x_scale, y_scale);
  p2_.Scale(x_scale, y_scale);
  p3_.Scale(x_scale, y_scale);
  p4_.Scale(x_scale, y_scale);
}

void QuadF::operator+=(const Vector2dF& rhs) {
  p1_ += rhs;
  p2_ += rhs;
  p3_ += rhs;
  p4_ += rhs;
}

void QuadF::operator-=(const Vector2dF& rhs) {
  p1_ -= rhs;
  p2_ -= rhs;
  p3_ -= rhs;
  p4_ -= rhs;
}

QuadF operator+(const QuadF& lhs, const Vector2dF& rhs) {
  QuadF result = lhs;
  result += rhs;
  return result;
}

QuadF operator-(const QuadF& lhs, const Vector2dF& rhs) {
  QuadF result = lhs;
  result -= rhs;
  return result;
}

}  // namespace math
}  // namespace cobalt