/*
 * Copyright (C) 2022 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_REGION3_HH_
#define GZ_MATH_REGION3_HH_

#include <cmath>
#include <limits>
#include <ostream>
#include <utility>

#include <gz/math/Interval.hh>
#include <gz/math/Vector3.hh>
#include <gz/math/config.hh>

namespace gz::math
{
  // Inline bracket to help doxygen filtering.
  inline namespace GZ_MATH_VERSION_NAMESPACE {
  //
  /// \class Region3 Region3.hh gz/math/Region3.hh
  /// \brief The Region3 class represents the cartesian product
  /// of intervals Ix ✕ Iy ✕ Iz, one per axis, yielding an
  /// axis-aligned region of R^3 space. It can be thought of as
  /// an intersection of halfspaces. Regions may be open or
  /// closed in their boundaries, if any.
  ///
  /// Note that the Region3 class is essentially a set R ⊆ R^3.
  /// For 3D solid box semantics, use the `AxisAlignedBox` class
  /// instead.
  ///
  /// ## Example
  ///
  /// \snippet examples/region3_example.cc complete
  template <typename T>
  class Region3
  {
    /// \brief An unbounded region (-∞, ∞) ✕ (-∞, ∞) ✕ (-∞, ∞)
    public: static const Region3<T> &Unbounded;

    /// \brief Constructor
    public: Region3() = default;

    /// \brief Constructor
    /// \param[in] _ix x-axis interval
    /// \param[in] _iy y-axis interval
    /// \param[in] _iz z-axis interval
    public: constexpr Region3(
        Interval<T> _ix, Interval<T> _iy, Interval<T> _iz)
    : ix(std::move(_ix)), iy(std::move(_iy)), iz(std::move(_iz))
    {
    }

    /// \brief Make an open region
    /// \param[in] _xLeft leftmost x-axis interval value
    /// \param[in] _xRight righmost x-axis interval value
    /// \param[in] _yLeft leftmost y-axis interval value
    /// \param[in] _yRight righmost y-axis interval value
    /// \param[in] _zLeft leftmost z-axis interval value
    /// \param[in] _zRight righmost z-axis interval value
    /// \return the (`_xLeft`, `_xRight`) ✕ (`_yLeft`, `_yRight`)
    ///  ✕ (`_zLeft`, `_zRight`) open region
    public: static constexpr Region3<T> Open(
        T _xLeft, T _yLeft, T _zLeft,
        T _xRight, T _yRight, T _zRight)
    {
      return Region3<T>(Interval<T>::Open(_xLeft, _xRight),
                        Interval<T>::Open(_yLeft, _yRight),
                        Interval<T>::Open(_zLeft, _zRight));
    }

    /// \brief Make a closed region
    /// \param[in] _xLeft leftmost x-axis interval value
    /// \param[in] _xRight righmost x-axis interval value
    /// \param[in] _yLeft leftmost y-axis interval value
    /// \param[in] _yRight righmost y-axis interval value
    /// \param[in] _zLeft leftmost z-axis interval value
    /// \param[in] _zRight righmost z-axis interval value
    /// \return the [`_xLeft`, `_xRight`] ✕ [`_yLeft`, `_yRight`]
    ///  ✕ [`_zLeft`, `_zRight`] closed region
    public: static constexpr Region3<T> Closed(
        T _xLeft, T _yLeft, T _zLeft,
        T _xRight, T _yRight, T _zRight)
    {
      return Region3<T>(Interval<T>::Closed(_xLeft, _xRight),
                        Interval<T>::Closed(_yLeft, _yRight),
                        Interval<T>::Closed(_zLeft, _zRight));
    }

    /// \brief Get the x-axis interval for the region
    /// \return the x-axis interval
    public: const Interval<T> &Ix() const { return this->ix; }

    /// \brief Get the y-axis interval for the region
    /// \return the y-axis interval
    public: const Interval<T> &Iy() const { return this->iy; }

    /// \brief Get the z-axis interval for the region
    /// \return the z-axis interval
    public: const Interval<T> &Iz() const { return this->iz; }

    /// \brief Check if the region is empty
    /// A region is empty if any of the intervals
    /// it is defined with (i.e. Ix, Iy, Iz) are.
    /// \return true if it is empty, false otherwise
    public: bool Empty() const
    {
      return this->ix.Empty() || this->iy.Empty() || this->iz.Empty();
    }

    /// \brief Check if the region contains `_point`
    /// \param[in] _point point to check for membership
    /// \return true if it is contained, false otherwise
    public: bool Contains(const Vector3<T> &_point) const
    {
      return (this->ix.Contains(_point.X()) &&
              this->iy.Contains(_point.Y()) &&
              this->iz.Contains(_point.Z()));
    }

    /// \brief Check if the region contains `_other` region
    /// \param[in] _other region to check for membership
    /// \return true if it is contained, false otherwise
    public: bool Contains(const Region3<T> &_other) const
    {
      return (this->ix.Contains(_other.ix) &&
              this->iy.Contains(_other.iy) &&
              this->iz.Contains(_other.iz));
    }

    /// \brief Check if the region intersects `_other` region
    /// \param[in] _other region to check for intersection
    /// \return true if it is contained, false otherwise
    public: bool Intersects(const Region3<T>& _other) const
    {
      return (this->ix.Intersects(_other.ix) &&
              this->iy.Intersects(_other.iy) &&
              this->iz.Intersects(_other.iz));
    }

    /// \brief Equality test operator
    /// \param _other region to check for equality
    /// \return true if regions are equal, false otherwise
    public: bool operator==(const Region3<T> &_other) const
    {
      return this->Contains(_other) && _other.Contains(*this);
    }

    /// \brief Inequality test operator
    /// \param _other region to check for inequality
    /// \return true if regions are unequal, false otherwise
    public: bool operator!=(const Region3<T> &_other) const
    {
      return !this->Contains(_other) || !_other.Contains(*this);
    }

    /// \brief Stream insertion operator
    /// \param _out output stream
    /// \param _r Region3 to output
    /// \return the stream
    public: friend std::ostream &operator<<(
      std::ostream &_out, const gz::math::Region3<T> &_r)
    {
      return _out <<_r.ix << " x " << _r.iy << " x " << _r.iz;
    }

    /// \brief The x-axis interval
    private: Interval<T> ix;
    /// \brief The y-axis interval
    private: Interval<T> iy;
    /// \brief The z-axis interval
    private: Interval<T> iz;
  };

  namespace detail {
     template<typename T>
     constexpr Region3<T> gUnboundedRegion3(
         Interval<T>::Open(-std::numeric_limits<T>::infinity(),
                           std::numeric_limits<T>::infinity()),
         Interval<T>::Open(-std::numeric_limits<T>::infinity(),
                           std::numeric_limits<T>::infinity()),
         Interval<T>::Open(-std::numeric_limits<T>::infinity(),
                           std::numeric_limits<T>::infinity()));
  }
  template<typename T>
  const Region3<T> &Region3<T>::Unbounded = detail::gUnboundedRegion3<T>;

  using Region3f = Region3<float>;
  using Region3d = Region3<double>;
  }  // namespace GZ_MATH_VERSION_NAMESPACE
}  // namespace gz::math
#endif  // GZ_MATH_REGION3_HH_
