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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>
- //
- // 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
- 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 wihtout 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_MATH(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_MATH(sin)
- EIGEN_USING_STD_MATH(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
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