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Rotation2D.h
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Rotation2D.h
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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(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

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