| // This file is part of Eigen, a lightweight C++ template library |
| // for linear algebra. |
| // |
| // Copyright (C) 2008 Gael Guennebaud <g.gael@free.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/>. |
| |
| #ifndef EIGEN_ROTATION2D_H |
| #define EIGEN_ROTATION2D_H |
| |
| /** \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 |
| */ |
| template<typename _Scalar> struct ei_traits<Rotation2D<_Scalar> > |
| { |
| typedef _Scalar Scalar; |
| }; |
| |
| 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. */ |
| inline Rotation2D(Scalar a) : m_angle(a) {} |
| |
| /** \returns the rotation angle */ |
| inline Scalar angle() const { return m_angle; } |
| |
| /** \returns a read-write reference to the rotation angle */ |
| inline Scalar& angle() { return m_angle; } |
| |
| /** \returns the inverse rotation */ |
| inline Rotation2D inverse() const { return -m_angle; } |
| |
| /** Concatenates two rotations */ |
| inline Rotation2D operator*(const Rotation2D& other) const |
| { return m_angle + other.m_angle; } |
| |
| /** Concatenates two rotations */ |
| inline Rotation2D& operator*=(const Rotation2D& other) |
| { return m_angle += other.m_angle; } |
| |
| /** Applies the rotation to a 2D vector */ |
| 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. |
| */ |
| 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> |
| inline typename ei_cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type cast() const |
| { return typename ei_cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); } |
| |
| /** Copy constructor with scalar type conversion */ |
| template<typename OtherScalarType> |
| inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other) |
| { |
| m_angle = Scalar(other.angle()); |
| } |
| |
| /** \returns \c true if \c *this is approximately equal to \a other, within the precision |
| * determined by \a prec. |
| * |
| * \sa MatrixBase::isApprox() */ |
| bool isApprox(const Rotation2D& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const |
| { return ei_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> |
| 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 = ei_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 = ei_sin(m_angle); |
| Scalar cosA = ei_cos(m_angle); |
| return (Matrix2() << cosA, -sinA, sinA, cosA).finished(); |
| } |
| |
| #endif // EIGEN_ROTATION2D_H |