ConfigurationSpace.hpp

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#ifndef DART_MATH_DETAIL_CONFIGURATIONSPACE_H_
#define DART_MATH_DETAIL_CONFIGURATIONSPACE_H_
 
#include "dart/math/ConfigurationSpace.hpp"
 
#include "dart/math/Geometry.hpp"
 
namespace dart {
namespace math {
 
namespace detail {
 
template <bool>
struct Range;
 
//==============================================================================
template <typename MatrixType, int Size, typename Enable = Range<true>>
struct inverseImpl
{
  static void run(const MatrixType& matrix, MatrixType& result)
  {
    result = matrix.ldlt().solve(MatrixType::Identity());
  }
};
 
//==============================================================================
template <typename MatrixType, int Size>
struct inverseImpl<MatrixType, Size, Range<(0 <= Size && Size <= 4)>>
{
  static void run(const MatrixType& matrix, MatrixType& result)
  {
    result = matrix.inverse();
  }
};
 
//==============================================================================
template <typename SpaceT>
struct toEuclideanPointImpl
{
  static typename SpaceT::EuclideanPoint run(
      const typename SpaceT::Point& point)
  {
    return point;
  }
};
 
//==============================================================================
template <>
struct toEuclideanPointImpl<SO3Space>
{
  static typename SO3Space::EuclideanPoint run(
      const typename SO3Space::Point& point)
  {
    return math::logMap(point);
  }
};
 
//==============================================================================
template <>
struct toEuclideanPointImpl<SE3Space>
{
  static typename SE3Space::EuclideanPoint run(
      const typename SE3Space::Point& point)
  {
    Eigen::Vector6d x;
 
    x.head<3>() = math::logMap(point.linear());
    x.tail<3>() = point.translation();
 
    return x;
  }
};
 
//==============================================================================
template <typename SpaceT>
struct toManifoldPointImpl
{
  static typename SpaceT::Point run(
      const typename SpaceT::EuclideanPoint& point)
  {
    return point;
  }
};
 
//==============================================================================
template <>
struct toManifoldPointImpl<SO3Space>
{
  static typename SO3Space::Point run(
      const typename SO3Space::EuclideanPoint& point)
  {
    return math::expMapRot(point);
  }
};
 
//==============================================================================
template <>
struct toManifoldPointImpl<SE3Space>
{
  static typename SE3Space::Point run(
      const typename SE3Space::EuclideanPoint& point)
  {
    Eigen::Isometry3d tf(Eigen::Isometry3d::Identity());
 
    tf.linear() = math::expMapRot(point.head<3>());
    tf.translation() = point.tail<3>();
 
    return tf;
  }
};
 
//==============================================================================
template <typename SpaceT>
struct integratePositionImpl
{
  static typename SpaceT::Point run(
      const typename SpaceT::Point& pos,
      const typename SpaceT::Vector& vel,
      double dt)
  {
    return pos + dt * vel;
  }
};
 
//==============================================================================
template <>
struct integratePositionImpl<SO3Space>
{
  static typename SO3Space::Point run(
      const typename SO3Space::Point& pos,
      const typename SO3Space::Vector& vel,
      double dt)
  {
    return pos * toManifoldPoint<SO3Space>(vel * dt);
  }
};
 
//==============================================================================
template <>
struct integratePositionImpl<SE3Space>
{
  static typename SE3Space::Point run(
      const typename SE3Space::Point& pos,
      const typename SE3Space::Vector& vel,
      double dt)
  {
    return pos * toManifoldPoint<SE3Space>(vel * dt);
  }
};
 
} // namespace detail
 
//==============================================================================
template <typename SpaceT>
typename SpaceT::Matrix inverse(const typename SpaceT::Matrix& mat)
{
  typename SpaceT::Matrix res;
 
  detail::inverseImpl<typename SpaceT::Matrix, SpaceT::NumDofsEigen>::run(
      mat, res);
 
  return res;
}
 
//==============================================================================
template <typename SpaceT>
typename SpaceT::EuclideanPoint toEuclideanPoint(
    const typename SpaceT::Point& point)
{
  return detail::toEuclideanPointImpl<SpaceT>::run(point);
}
 
//==============================================================================
template <typename SpaceT>
typename SpaceT::Point toManifoldPoint(
    const typename SpaceT::EuclideanPoint& point)
{
  return detail::toManifoldPointImpl<SpaceT>::run(point);
}
 
//==============================================================================
template <typename SpaceT>
typename SpaceT::Point integratePosition(
    const typename SpaceT::Point& pos,
    const typename SpaceT::Vector& vel,
    double dt)
{
  return detail::integratePositionImpl<SpaceT>::run(pos, vel, dt);
}
 
//==============================================================================
template <typename SpaceT>
typename SpaceT::Vector integrateVelocity(
    const typename SpaceT::Vector& vel,
    const typename SpaceT::Vector& acc,
    double dt)
{
  return vel + acc * dt;
}
 
} // namespace math
} // namespace dart
 
#endif // DART_MATH_DETAIL_CONFIGURATIONSPACE_H_