Eigen/src/Geometry/Rotation2D.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_ROTATION2D_H
#define EIGEN_ROTATION2D_H

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

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
 *
 * \class Rotation2D
 *
 * \brief Represents a rotation/orientation in a 2 dimensional space.
 *
 * \tparam Scalar_ the scalar type, i.e., the type of the coefficients
 *
 * This class is equivalent to a single scalar representing a counter clock wise rotation
 * as a single angle in radian. It provides some additional features such as the automatic
 * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar
 * interface to Quaternion in order to facilitate the writing of generic algorithms
 * dealing with rotations.
 *
 * \sa class Quaternion, class Transform
 */

namespace internal {

template <typename Scalar_>
struct traits<Rotation2D<Scalar_> > {
  typedef Scalar_ Scalar;
};
}  // end namespace internal

template <typename Scalar_>
class Rotation2D : public RotationBase<Rotation2D<Scalar_>, 2> {
  typedef RotationBase<Rotation2D<Scalar_>, 2> Base;

 public:
  using Base::operator*;

  enum { Dim = 2 };
  /** the scalar type of the coefficients */
  typedef Scalar_ Scalar;
  typedef Matrix<Scalar, 2, 1> Vector2;
  typedef Matrix<Scalar, 2, 2> Matrix2;

 protected:
  Scalar m_angle;

 public:
  /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
  EIGEN_DEVICE_FUNC explicit inline Rotation2D(const Scalar& a) : m_angle(a) {}

  /** Default constructor without initialization. The represented rotation is undefined. */
  EIGEN_DEVICE_FUNC Rotation2D() {}

  /** Construct a 2D rotation from a 2x2 rotation matrix \a mat.
   *
   * \sa fromRotationMatrix()
   */
  template <typename Derived>
  EIGEN_DEVICE_FUNC explicit Rotation2D(const MatrixBase<Derived>& m) {
    fromRotationMatrix(m.derived());
  }

  /** \returns the rotation angle */
  EIGEN_DEVICE_FUNC inline Scalar angle() const { return m_angle; }

  /** \returns a read-write reference to the rotation angle */
  EIGEN_DEVICE_FUNC inline Scalar& angle() { return m_angle; }

  /** \returns the rotation angle in [0,2pi] */
  EIGEN_DEVICE_FUNC inline Scalar smallestPositiveAngle() const {
    Scalar tmp = numext::fmod(m_angle, Scalar(2 * EIGEN_PI));
    return tmp < Scalar(0) ? tmp + Scalar(2 * EIGEN_PI) : tmp;
  }

  /** \returns the rotation angle in [-pi,pi] */
  EIGEN_DEVICE_FUNC inline Scalar smallestAngle() const {
    Scalar tmp = numext::fmod(m_angle, Scalar(2 * EIGEN_PI));
    if (tmp > Scalar(EIGEN_PI))
      tmp -= Scalar(2 * EIGEN_PI);
    else if (tmp < -Scalar(EIGEN_PI))
      tmp += Scalar(2 * EIGEN_PI);
    return tmp;
  }

  /** \returns the inverse rotation */
  EIGEN_DEVICE_FUNC inline Rotation2D inverse() const { return Rotation2D(-m_angle); }

  /** Concatenates two rotations */
  EIGEN_DEVICE_FUNC inline Rotation2D operator*(const Rotation2D& other) const {
    return Rotation2D(m_angle + other.m_angle);
  }

  /** Concatenates two rotations */
  EIGEN_DEVICE_FUNC inline Rotation2D& operator*=(const Rotation2D& other) {
    m_angle += other.m_angle;
    return *this;
  }

  /** Applies the rotation to a 2D vector */
  EIGEN_DEVICE_FUNC Vector2 operator*(const Vector2& vec) const { return toRotationMatrix() * vec; }

  template <typename Derived>
  EIGEN_DEVICE_FUNC Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);
  EIGEN_DEVICE_FUNC Matrix2 toRotationMatrix() const;

  /** Set \c *this from a 2x2 rotation matrix \a mat.
   * In other words, this function extract the rotation angle from the rotation matrix.
   *
   * This method is an alias for fromRotationMatrix()
   *
   * \sa fromRotationMatrix()
   */
  template <typename Derived>
  EIGEN_DEVICE_FUNC Rotation2D& operator=(const MatrixBase<Derived>& m) {
    return fromRotationMatrix(m.derived());
  }

  /** \returns the spherical interpolation between \c *this and \a other using
   * parameter \a t. It is in fact equivalent to a linear interpolation.
   */
  EIGEN_DEVICE_FUNC inline Rotation2D slerp(const Scalar& t, const Rotation2D& other) const {
    Scalar dist = Rotation2D(other.m_angle - m_angle).smallestAngle();
    return Rotation2D(m_angle + dist * t);
  }

  /** \returns \c *this with scalar type casted to \a NewScalarType
   *
   * Note that if \a NewScalarType is equal to the current scalar type of \c *this
   * then this function smartly returns a const reference to \c *this.
   */
  template <typename NewScalarType>
  EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Rotation2D, Rotation2D<NewScalarType> >::type cast()
      const {
    return typename internal::cast_return_type<Rotation2D, Rotation2D<NewScalarType> >::type(*this);
  }

  /** Copy constructor with scalar type conversion */
  template <typename OtherScalarType>
  EIGEN_DEVICE_FUNC inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other) {
    m_angle = Scalar(other.angle());
  }

  EIGEN_DEVICE_FUNC static inline Rotation2D Identity() { return Rotation2D(0); }

  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
   * determined by \a prec.
   *
   * \sa MatrixBase::isApprox() */
  EIGEN_DEVICE_FUNC bool isApprox(const Rotation2D& other, const typename NumTraits<Scalar>::Real& prec =
                                                               NumTraits<Scalar>::dummy_precision()) const {
    return internal::isApprox(m_angle, other.m_angle, prec);
  }
};

/** \ingroup Geometry_Module
 * single precision 2D rotation type */
typedef Rotation2D<float> Rotation2Df;
/** \ingroup Geometry_Module
 * double precision 2D rotation type */
typedef Rotation2D<double> Rotation2Dd;

/** Set \c *this from a 2x2 rotation matrix \a mat.
 * In other words, this function extract the rotation angle
 * from the rotation matrix.
 */
template <typename Scalar>
template <typename Derived>
EIGEN_DEVICE_FUNC Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat) {
  EIGEN_USING_STD(atan2)
  EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime == 2 && Derived::ColsAtCompileTime == 2,
                      YOU_MADE_A_PROGRAMMING_MISTAKE)
  m_angle = atan2(mat.coeff(1, 0), mat.coeff(0, 0));
  return *this;
}

/** Constructs and \returns an equivalent 2x2 rotation matrix.
 */
template <typename Scalar>
typename Rotation2D<Scalar>::Matrix2 EIGEN_DEVICE_FUNC Rotation2D<Scalar>::toRotationMatrix(void) const {
  EIGEN_USING_STD(sin)
  EIGEN_USING_STD(cos)
  Scalar sinA = sin(m_angle);
  Scalar cosA = cos(m_angle);
  return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
}

}  // end namespace Eigen

#endif  // EIGEN_ROTATION2D_H