[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #ifndef EIGEN_ROTATION2D_H
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| 11 | #define EIGEN_ROTATION2D_H
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| 12 |
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| 13 | namespace Eigen {
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| 14 |
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| 15 | /** \geometry_module \ingroup Geometry_Module
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| 16 | *
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| 17 | * \class Rotation2D
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| 18 | *
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| 19 | * \brief Represents a rotation/orientation in a 2 dimensional space.
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| 20 | *
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| 21 | * \param _Scalar the scalar type, i.e., the type of the coefficients
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| 22 | *
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| 23 | * This class is equivalent to a single scalar representing a counter clock wise rotation
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| 24 | * as a single angle in radian. It provides some additional features such as the automatic
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| 25 | * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar
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| 26 | * interface to Quaternion in order to facilitate the writing of generic algorithms
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| 27 | * dealing with rotations.
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| 28 | *
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| 29 | * \sa class Quaternion, class Transform
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| 30 | */
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| 31 |
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| 32 | namespace internal {
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| 33 |
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| 34 | template<typename _Scalar> struct traits<Rotation2D<_Scalar> >
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| 35 | {
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| 36 | typedef _Scalar Scalar;
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| 37 | };
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| 38 | } // end namespace internal
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| 39 |
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| 40 | template<typename _Scalar>
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| 41 | class Rotation2D : public RotationBase<Rotation2D<_Scalar>,2>
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| 42 | {
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| 43 | typedef RotationBase<Rotation2D<_Scalar>,2> Base;
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| 44 |
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| 45 | public:
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| 46 |
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| 47 | using Base::operator*;
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| 48 |
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| 49 | enum { Dim = 2 };
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| 50 | /** the scalar type of the coefficients */
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| 51 | typedef _Scalar Scalar;
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| 52 | typedef Matrix<Scalar,2,1> Vector2;
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| 53 | typedef Matrix<Scalar,2,2> Matrix2;
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| 54 |
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| 55 | protected:
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| 56 |
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| 57 | Scalar m_angle;
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| 58 |
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| 59 | public:
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| 60 |
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| 61 | /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
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| 62 | inline Rotation2D(const Scalar& a) : m_angle(a) {}
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| 63 |
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| 64 | /** Default constructor wihtout initialization. The represented rotation is undefined. */
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| 65 | Rotation2D() {}
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| 66 |
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| 67 | /** \returns the rotation angle */
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| 68 | inline Scalar angle() const { return m_angle; }
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| 69 |
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| 70 | /** \returns a read-write reference to the rotation angle */
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| 71 | inline Scalar& angle() { return m_angle; }
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| 72 |
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| 73 | /** \returns the inverse rotation */
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| 74 | inline Rotation2D inverse() const { return -m_angle; }
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| 75 |
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| 76 | /** Concatenates two rotations */
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| 77 | inline Rotation2D operator*(const Rotation2D& other) const
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| 78 | { return m_angle + other.m_angle; }
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| 79 |
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| 80 | /** Concatenates two rotations */
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| 81 | inline Rotation2D& operator*=(const Rotation2D& other)
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| 82 | { m_angle += other.m_angle; return *this; }
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| 83 |
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| 84 | /** Applies the rotation to a 2D vector */
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| 85 | Vector2 operator* (const Vector2& vec) const
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| 86 | { return toRotationMatrix() * vec; }
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| 87 |
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| 88 | template<typename Derived>
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| 89 | Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);
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| 90 | Matrix2 toRotationMatrix() const;
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| 91 |
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| 92 | /** \returns the spherical interpolation between \c *this and \a other using
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| 93 | * parameter \a t. It is in fact equivalent to a linear interpolation.
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| 94 | */
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| 95 | inline Rotation2D slerp(const Scalar& t, const Rotation2D& other) const
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| 96 | { return m_angle * (1-t) + other.angle() * t; }
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| 97 |
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| 98 | /** \returns \c *this with scalar type casted to \a NewScalarType
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| 99 | *
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| 100 | * Note that if \a NewScalarType is equal to the current scalar type of \c *this
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| 101 | * then this function smartly returns a const reference to \c *this.
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| 102 | */
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| 103 | template<typename NewScalarType>
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| 104 | inline typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type cast() const
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| 105 | { return typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); }
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| 106 |
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| 107 | /** Copy constructor with scalar type conversion */
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| 108 | template<typename OtherScalarType>
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| 109 | inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other)
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| 110 | {
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| 111 | m_angle = Scalar(other.angle());
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| 112 | }
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| 113 |
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| 114 | static inline Rotation2D Identity() { return Rotation2D(0); }
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| 115 |
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| 116 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision
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| 117 | * determined by \a prec.
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| 118 | *
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| 119 | * \sa MatrixBase::isApprox() */
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| 120 | bool isApprox(const Rotation2D& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
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| 121 | { return internal::isApprox(m_angle,other.m_angle, prec); }
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| 122 | };
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| 123 |
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| 124 | /** \ingroup Geometry_Module
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| 125 | * single precision 2D rotation type */
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| 126 | typedef Rotation2D<float> Rotation2Df;
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| 127 | /** \ingroup Geometry_Module
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| 128 | * double precision 2D rotation type */
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| 129 | typedef Rotation2D<double> Rotation2Dd;
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| 130 |
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| 131 | /** Set \c *this from a 2x2 rotation matrix \a mat.
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| 132 | * In other words, this function extract the rotation angle
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| 133 | * from the rotation matrix.
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| 134 | */
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| 135 | template<typename Scalar>
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| 136 | template<typename Derived>
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| 137 | Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
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| 138 | {
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| 139 | using std::atan2;
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| 140 | EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
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| 141 | m_angle = atan2(mat.coeff(1,0), mat.coeff(0,0));
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| 142 | return *this;
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| 143 | }
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| 144 |
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| 145 | /** Constructs and \returns an equivalent 2x2 rotation matrix.
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| 146 | */
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| 147 | template<typename Scalar>
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| 148 | typename Rotation2D<Scalar>::Matrix2
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| 149 | Rotation2D<Scalar>::toRotationMatrix(void) const
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| 150 | {
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| 151 | using std::sin;
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| 152 | using std::cos;
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| 153 | Scalar sinA = sin(m_angle);
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| 154 | Scalar cosA = cos(m_angle);
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| 155 | return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
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| 156 | }
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| 157 |
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| 158 | } // end namespace Eigen
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| 159 |
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| 160 | #endif // EIGEN_ROTATION2D_H
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