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 */

#ifndef DART_MATH_CONFIGURATIONSPACE_HPP_
#define DART_MATH_CONFIGURATIONSPACE_HPP_

#include <Eigen/Dense>
#include "dart/math/Geometry.hpp"
#include "dart/math/MathTypes.hpp"

namespace dart {
namespace math {

//==============================================================================
template <std::size_t Dimension>
struct RealVectorSpace
{
  static constexpr std::size_t NumDofs = Dimension;
  static constexpr int NumDofsEigen = static_cast<int>(Dimension);

  using TangentSpace = RealVectorSpace<NumDofs>;

  using Point = Eigen::Matrix<double, NumDofs, 1>;
  using EuclideanPoint = Eigen::Matrix<double, NumDofs, 1>;
  using Vector = Eigen::Matrix<double, NumDofs, 1>;
  using Matrix = Eigen::Matrix<double, NumDofs, NumDofs>;
  using JacobianMatrix = Eigen::Matrix<double, 6, NumDofs>;
};

//==============================================================================
//
// These namespace-level definitions are required to enable ODR-use of static
// constexpr member variables.
//
// See this StackOverflow answer: http://stackoverflow.com/a/14396189/111426
//
template <std::size_t Dimension>
constexpr std::size_t RealVectorSpace<Dimension>::NumDofs;
template <std::size_t Dimension>
constexpr int RealVectorSpace<Dimension>::NumDofsEigen;

using NullSpace = RealVectorSpace<0u>;
using R1Space = RealVectorSpace<1u>;
using R2Space = RealVectorSpace<2u>;
using R3Space = RealVectorSpace<3u>;

//==============================================================================
struct SO3Space
{
  static constexpr std::size_t NumDofs = 3u;
  static constexpr int NumDofsEigen = 3;

  using TangentSpace = RealVectorSpace<NumDofs>;

  using Point = Eigen::Matrix3d;
  using EuclideanPoint = Eigen::Vector3d;
  using Vector = Eigen::Vector3d;
  using Matrix = Eigen::Matrix3d;
  using JacobianMatrix = Eigen::Matrix<double, 6, NumDofs>;
};

//==============================================================================
struct SE3Space
{
  static constexpr std::size_t NumDofs = 6u;
  static constexpr int NumDofsEigen = 6;

  using TangentSpace = RealVectorSpace<NumDofs>;

  using Point = Eigen::Isometry3d;
  using EuclideanPoint = Eigen::Vector6d;
  using Vector = Eigen::Vector6d;
  using Matrix = Eigen::Matrix6d;
  using JacobianMatrix = Eigen::Matrix6d;
};

struct MapsToManifoldPoint
{
};

//==============================================================================
template <typename SpaceT>
typename SpaceT::Matrix inverse(const typename SpaceT::Matrix& mat);

//==============================================================================
template <typename SpaceT>
typename SpaceT::EuclideanPoint toEuclideanPoint(
    const typename SpaceT::Point& point);

//==============================================================================
template <typename SpaceT>
typename SpaceT::Point toManifoldPoint(
    const typename SpaceT::EuclideanPoint& point);

//==============================================================================
template <typename SpaceT>
typename SpaceT::Point integratePosition(
    const typename SpaceT::Point& pos,
    const typename SpaceT::Vector& vel,
    double dt);

//==============================================================================
template <typename SpaceT>
typename SpaceT::Vector integrateVelocity(
    const typename SpaceT::Vector& vel,
    const typename SpaceT::Vector& acc,
    double dt);

} // namespace math
} // namespace dart

#include "dart/math/detail/ConfigurationSpace.hpp"

#endif // DART_MATH_CONFIGURATIONSPACE_HPP_
