Eigen/src/Geometry/RotationBase.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_ROTATIONBASE_H
#define EIGEN_ROTATIONBASE_H

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

// forward declaration
namespace internal {
template <typename RotationDerived, typename MatrixType, bool IsVector = MatrixType::IsVectorAtCompileTime>
struct rotation_base_generic_product_selector;
}

/** \class RotationBase
 *
 * \brief Common base class for compact rotation representations
 *
 * \tparam Derived is the derived type, i.e., a rotation type
 * \tparam Dim_ the dimension of the space
 */
template <typename Derived, int Dim_>
class RotationBase {
 public:
  enum { Dim = Dim_ };
  /** the scalar type of the coefficients */
  typedef typename internal::traits<Derived>::Scalar Scalar;

  /** corresponding linear transformation matrix type */
  typedef Matrix<Scalar, Dim, Dim> RotationMatrixType;
  typedef Matrix<Scalar, Dim, 1> VectorType;

 public:
  EIGEN_DEVICE_FUNC inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
  EIGEN_DEVICE_FUNC inline Derived& derived() { return *static_cast<Derived*>(this); }

  /** \returns an equivalent rotation matrix */
  EIGEN_DEVICE_FUNC inline RotationMatrixType toRotationMatrix() const { return derived().toRotationMatrix(); }

  /** \returns an equivalent rotation matrix
   * This function is added to be conform with the Transform class' naming scheme.
   */
  EIGEN_DEVICE_FUNC inline RotationMatrixType matrix() const { return derived().toRotationMatrix(); }

  /** \returns the inverse rotation */
  EIGEN_DEVICE_FUNC inline Derived inverse() const { return derived().inverse(); }

  /** \returns the concatenation of the rotation \c *this with a translation \a t */
  EIGEN_DEVICE_FUNC inline Transform<Scalar, Dim, Isometry> operator*(const Translation<Scalar, Dim>& t) const {
    return Transform<Scalar, Dim, Isometry>(*this) * t;
  }

  /** \returns the concatenation of the rotation \c *this with a uniform scaling \a s */
  EIGEN_DEVICE_FUNC inline RotationMatrixType operator*(const UniformScaling<Scalar>& s) const {
    return toRotationMatrix() * s.factor();
  }

  /** \returns the concatenation of the rotation \c *this with a generic expression \a e
   * \a e can be:
   *  - a DimxDim linear transformation matrix
   *  - a DimxDim diagonal matrix (axis aligned scaling)
   *  - a vector of size Dim
   */
  template <typename OtherDerived>
  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
      typename internal::rotation_base_generic_product_selector<Derived, OtherDerived,
                                                                OtherDerived::IsVectorAtCompileTime>::ReturnType
      operator*(const EigenBase<OtherDerived>& e) const {
    return internal::rotation_base_generic_product_selector<Derived, OtherDerived>::run(derived(), e.derived());
  }

  /** \returns the concatenation of a linear transformation \a l with the rotation \a r */
  template <typename OtherDerived>
  friend EIGEN_DEVICE_FUNC inline RotationMatrixType operator*(const EigenBase<OtherDerived>& l, const Derived& r) {
    return l.derived() * r.toRotationMatrix();
  }

  /** \returns the concatenation of a scaling \a l with the rotation \a r */
  EIGEN_DEVICE_FUNC friend inline Transform<Scalar, Dim, Affine> operator*(const DiagonalMatrix<Scalar, Dim>& l,
                                                                           const Derived& r) {
    Transform<Scalar, Dim, Affine> res(r);
    res.linear().applyOnTheLeft(l);
    return res;
  }

  /** \returns the concatenation of the rotation \c *this with a transformation \a t */
  template <int Mode, int Options>
  EIGEN_DEVICE_FUNC inline Transform<Scalar, Dim, Mode> operator*(
      const Transform<Scalar, Dim, Mode, Options>& t) const {
    return toRotationMatrix() * t;
  }

  template <typename OtherVectorType>
  EIGEN_DEVICE_FUNC inline VectorType _transformVector(const OtherVectorType& v) const {
    return toRotationMatrix() * v;
  }
};

namespace internal {

// implementation of the generic product rotation * matrix
template <typename RotationDerived, typename MatrixType>
struct rotation_base_generic_product_selector<RotationDerived, MatrixType, false> {
  enum { Dim = RotationDerived::Dim };
  typedef Matrix<typename RotationDerived::Scalar, Dim, Dim> ReturnType;
  EIGEN_DEVICE_FUNC static inline ReturnType run(const RotationDerived& r, const MatrixType& m) {
    return r.toRotationMatrix() * m;
  }
};

template <typename RotationDerived, typename Scalar, int Dim, int MaxDim>
struct rotation_base_generic_product_selector<RotationDerived, DiagonalMatrix<Scalar, Dim, MaxDim>, false> {
  typedef Transform<Scalar, Dim, Affine> ReturnType;
  EIGEN_DEVICE_FUNC static inline ReturnType run(const RotationDerived& r,
                                                 const DiagonalMatrix<Scalar, Dim, MaxDim>& m) {
    ReturnType res(r);
    res.linear() *= m;
    return res;
  }
};

template <typename RotationDerived, typename OtherVectorType>
struct rotation_base_generic_product_selector<RotationDerived, OtherVectorType, true> {
  enum { Dim = RotationDerived::Dim };
  typedef Matrix<typename RotationDerived::Scalar, Dim, 1> ReturnType;
  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE ReturnType run(const RotationDerived& r, const OtherVectorType& v) {
    return r._transformVector(v);
  }
};

}  // end namespace internal

/** \geometry_module
 *
 * \brief Constructs a Dim x Dim rotation matrix from the rotation \a r
 */
template <typename Scalar_, int Rows_, int Cols_, int Storage_, int MaxRows_, int MaxCols_>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC Matrix<Scalar_, Rows_, Cols_, Storage_, MaxRows_, MaxCols_>::Matrix(
    const RotationBase<OtherDerived, ColsAtCompileTime>& r) {
  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix, int(OtherDerived::Dim), int(OtherDerived::Dim))
  *this = r.toRotationMatrix();
}

/** \geometry_module
 *
 * \brief Set a Dim x Dim rotation matrix from the rotation \a r
 */
template <typename Scalar_, int Rows_, int Cols_, int Storage_, int MaxRows_, int MaxCols_>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC Matrix<Scalar_, Rows_, Cols_, Storage_, MaxRows_, MaxCols_>&
Matrix<Scalar_, Rows_, Cols_, Storage_, MaxRows_, MaxCols_>::operator=(
    const RotationBase<OtherDerived, ColsAtCompileTime>& r) {
  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix, int(OtherDerived::Dim), int(OtherDerived::Dim))
  return *this = r.toRotationMatrix();
}

namespace internal {

/** \internal
 *
 * Helper function to return an arbitrary rotation object to a rotation matrix.
 *
 * \tparam Scalar the numeric type of the matrix coefficients
 * \tparam Dim the dimension of the current space
 *
 * It returns a Dim x Dim fixed size matrix.
 *
 * Default specializations are provided for:
 *   - any scalar type (2D),
 *   - any matrix expression,
 *   - any type based on RotationBase (e.g., Quaternion, AngleAxis, Rotation2D)
 *
 * Currently toRotationMatrix is only used by Transform.
 *
 * \sa class Transform, class Rotation2D, class Quaternion, class AngleAxis
 */
template <typename Scalar, int Dim>
EIGEN_DEVICE_FUNC static inline Matrix<Scalar, 2, 2> toRotationMatrix(const Scalar& s) {
  EIGEN_STATIC_ASSERT(Dim == 2, YOU_MADE_A_PROGRAMMING_MISTAKE)
  return Rotation2D<Scalar>(s).toRotationMatrix();
}

template <typename Scalar, int Dim, typename OtherDerived>
EIGEN_DEVICE_FUNC static inline Matrix<Scalar, Dim, Dim> toRotationMatrix(const RotationBase<OtherDerived, Dim>& r) {
  return r.toRotationMatrix();
}

template <typename Scalar, int Dim, typename OtherDerived>
EIGEN_DEVICE_FUNC static inline const MatrixBase<OtherDerived>& toRotationMatrix(const MatrixBase<OtherDerived>& mat) {
  EIGEN_STATIC_ASSERT(OtherDerived::RowsAtCompileTime == Dim && OtherDerived::ColsAtCompileTime == Dim,
                      YOU_MADE_A_PROGRAMMING_MISTAKE)
  return mat;
}

}  // end namespace internal

}  // end namespace Eigen

#endif  // EIGEN_ROTATIONBASE_H