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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.


/** \geometry_module \ingroup Geometry_Module
  * \class Rotation2D
  * \brief Represents a rotation/orientation in a 2 dimensional space.
  * \param _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 {

00047 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;


  using Base::operator*;

  enum { Dim = 2 };
  /** the scalar type of the coefficients */
00064   typedef _Scalar Scalar;
  typedef Matrix<Scalar,2,1> Vector2;
  typedef Matrix<Scalar,2,2> Matrix2;


  Scalar m_angle;


  /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
00075   inline Rotation2D(Scalar a) : m_angle(a) {}

  /** \returns the rotation angle */
00078   inline Scalar angle() const { return m_angle; }

  /** \returns a read-write reference to the rotation angle */
00081   inline Scalar& angle() { return m_angle; }

  /** \returns the inverse rotation */
00084   inline Rotation2D inverse() const { return -m_angle; }

  /** Concatenates two rotations */
00087   inline Rotation2D operator*(const Rotation2D& other) const
  { return m_angle + other.m_angle; }

  /** Concatenates two rotations */
00091   inline Rotation2D& operator*=(const Rotation2D& other)
  { return m_angle += other.m_angle; return *this; }

  /** Applies the rotation to a 2D vector */
00095   Vector2 operator* (const Vector2& vec) const
  { return toRotationMatrix() * vec; }

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

  /** \returns the spherical interpolation between \c *this and \a other using
    * parameter \a t. It is in fact equivalent to a linear interpolation.
00105   inline Rotation2D slerp(Scalar t, const Rotation2D& other) const
  { return m_angle * (1-t) + other.angle() * 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>
00114   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>
00119   inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other)
    m_angle = Scalar(other.angle());

  inline static 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() */
00130   bool isApprox(const Rotation2D& other, 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 */
00136 typedef Rotation2D<float> Rotation2Df;
/** \ingroup Geometry_Module
  * double precision 2D rotation type */
00139 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>
Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
  EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
  m_angle = internal::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
Rotation2D<Scalar>::toRotationMatrix(void) const
  Scalar sinA = internal::sin(m_angle);
  Scalar cosA = internal::cos(m_angle);
  return (Matrix2() << cosA, -sinA, sinA, cosA).finished();


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