Line2.hh

Go to the documentation of this file.

/*
 * Copyright (C) 2014 Open Source Robotics Foundation
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 *
*/
#ifndef GZ_MATH_LINE2_HH_
#define GZ_MATH_LINE2_HH_
 
#include <algorithm>
#include <gz/math/Vector2.hh>
#include <gz/math/config.hh>
 
namespace gz::math
{
  // Inline bracket to help doxygen filtering.
  inline namespace GZ_MATH_VERSION_NAMESPACE {
  //
  template<typename T>
  class Line2
  {
    public: Line2(const math::Vector2<T> &_ptA, const math::Vector2<T> &_ptB)
    {
      this->Set(_ptA, _ptB);
    }
 
    public: Line2(T _x1, T _y1, T _x2, T _y2)
    {
      this->Set(_x1, _y1, _x2, _y2);
    }
 
    public: void Set(const math::Vector2<T> &_ptA,
                     const math::Vector2<T> &_ptB)
    {
      this->pts[0] = _ptA;
      this->pts[1] = _ptB;
    }
 
    public: void Set(T _x1, T _y1, T _x2, T _y2)
    {
      this->pts[0].Set(_x1, _y1);
      this->pts[1].Set(_x2, _y2);
    }
 
    public: T CrossProduct(const Line2<T> &_line) const
    {
      return (this->pts[0].X() - this->pts[1].X()) *
             (_line[0].Y() -_line[1].Y()) -
             (this->pts[0].Y() - this->pts[1].Y()) *
             (_line[0].X() - _line[1].X());
    }
 
    //  (_pt.y - a.y) * (b.x - a.x) - (_pt.x - a.x) * (b.y - a.y)
    public: T CrossProduct(const Vector2<T> &_pt) const
    {
      return (_pt.Y() - this->pts[0].Y()) *
             (this->pts[1].X() - this->pts[0].X()) -
             (_pt.X() - this->pts[0].X()) *
             (this->pts[1].Y() - this->pts[0].Y());
    }
 
    public: bool Collinear(const math::Vector2<T> &_pt,
                           double _epsilon = 1e-6) const
    {
      return math::equal(this->CrossProduct(_pt),
          static_cast<T>(0), static_cast<T>(_epsilon));
    }
 
    public: bool Parallel(const math::Line2<T> &_line,
                          double _epsilon = 1e-6) const
    {
      return math::equal(this->CrossProduct(_line),
          static_cast<T>(0), static_cast<T>(_epsilon));
    }
 
    public: bool Collinear(const math::Line2<T> &_line,
                           double _epsilon = 1e-6) const
    {
      return this->Parallel(_line, _epsilon) &&
             this->Intersect(_line, _epsilon);
    }
 
    public: bool OnSegment(const math::Vector2<T> &_pt,
                           double _epsilon = 1e-6) const
    {
      return this->Collinear(_pt, _epsilon) && this->Within(_pt, _epsilon);
    }
 
    public: bool Within(const math::Vector2<T> &_pt,
                        double _epsilon = 1e-6) const
    {
      auto eps = static_cast<T>(_epsilon);
      return _pt.X() <= std::max(this->pts[0].X(),
                                 this->pts[1].X()) + eps &&
             _pt.X() >= std::min(this->pts[0].X(),
                                 this->pts[1].X()) - eps &&
             _pt.Y() <= std::max(this->pts[0].Y(),
                                 this->pts[1].Y()) + eps &&
             _pt.Y() >= std::min(this->pts[0].Y(),
                                 this->pts[1].Y()) - eps;
    }
 
    public: bool Intersect(const Line2<T> &_line,
                           double _epsilon = 1e-6) const
    {
      math::Vector2<T> ignore;
      return this->Intersect(_line, ignore, _epsilon);
    }
 
    public: bool Intersect(const Line2<T> &_line, math::Vector2<T> &_pt,
                           double _epsilon = 1e-6) const
    {
      T d = this->CrossProduct(_line);
 
      // d is zero if the two line are collinear. Must check special
      // cases.
      if (math::equal(d, static_cast<T>(0), static_cast<T>(_epsilon)))
      {
        // Check if _line's starting point is on the line.
        if (this->Within(_line[0], _epsilon))
        {
          _pt = _line[0];
          return true;
        }
        // Check if _line's ending point is on the line.
        else if (this->Within(_line[1], _epsilon))
        {
          _pt = _line[1];
          return true;
        }
        // Other wise return false.
        else
          return false;
      }
 
      _pt.X((_line[0].X() - _line[1].X()) *
            (this->pts[0].X() * this->pts[1].Y() -
             this->pts[0].Y() * this->pts[1].X()) -
            (this->pts[0].X() - this->pts[1].X()) *
            (_line[0].X() * _line[1].Y() - _line[0].Y() * _line[1].X()));
 
      _pt.Y((_line[0].Y() - _line[1].Y()) *
            (this->pts[0].X() * this->pts[1].Y() -
             this->pts[0].Y() * this->pts[1].X()) -
            (this->pts[0].Y() - this->pts[1].Y()) *
            (_line[0].X() * _line[1].Y() - _line[0].Y() * _line[1].X()));
 
      _pt /= d;
 
      if (_pt.X() < std::min(this->pts[0].X(), this->pts[1].X()) ||
          _pt.X() > std::max(this->pts[0].X(), this->pts[1].X()) ||
          _pt.X() < std::min(_line[0].X(), _line[1].X()) ||
          _pt.X() > std::max(_line[0].X(), _line[1].X()))
      {
        return false;
      }
 
      if (_pt.Y() < std::min(this->pts[0].Y(), this->pts[1].Y()) ||
          _pt.Y() > std::max(this->pts[0].Y(), this->pts[1].Y()) ||
          _pt.Y() < std::min(_line[0].Y(), _line[1].Y()) ||
          _pt.Y() > std::max(_line[0].Y(), _line[1].Y()))
      {
        return false;
      }
 
      return true;
    }
 
    public: T Length() const
    {
      return static_cast<T>(this->pts[0].Distance(this->pts[1]));
    }
 
    public: double Slope() const
    {
      if (math::equal(this->pts[1].X(), this->pts[0].X()))
        return NAN_D;
 
      return (this->pts[1].Y() - this->pts[0].Y()) /
             static_cast<double>(this->pts[1].X() - this->pts[0].X());
    }
 
    public: bool operator==(const Line2<T> &_line) const
    {
      return this->pts[0] == _line[0] && this->pts[1] == _line[1];
    }
 
    public: bool operator!=(const Line2<T> &_line) const
    {
      return !(*this == _line);
    }
 
    public: math::Vector2<T> operator[](size_t _index) const
    {
      return this->pts[clamp(_index, GZ_ZERO_SIZE_T, GZ_ONE_SIZE_T)];
    }
 
    public: friend std::ostream &operator<<(
                std::ostream &_out, const Line2<T> &_line)
    {
      _out << _line[0] << " " << _line[1];
      return _out;
    }
 
    private: math::Vector2<T> pts[2];
  };
 
 
  typedef Line2<int> Line2i;
  typedef Line2<double> Line2d;
  typedef Line2<float> Line2f;
  }  // namespace GZ_MATH_VERSION_NAMESPACE
}  // namespace gz::math
#endif  // GZ_MATH_LINE2_HH_