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- // This file is part of Eigen, a lightweight C++ template library
- // for linear algebra.
- //
- // Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
- // Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.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_QUATERNION_H
- #define EIGEN_QUATERNION_H
- namespace Eigen {
- /***************************************************************************
- * Definition of QuaternionBase<Derived>
- * The implementation is at the end of the file
- ***************************************************************************/
- namespace internal {
- template<typename Other,
- int OtherRows=Other::RowsAtCompileTime,
- int OtherCols=Other::ColsAtCompileTime>
- struct quaternionbase_assign_impl;
- }
- /** \geometry_module \ingroup Geometry_Module
- * \class QuaternionBase
- * \brief Base class for quaternion expressions
- * \tparam Derived derived type (CRTP)
- * \sa class Quaternion
- */
- template<class Derived>
- class QuaternionBase : public RotationBase<Derived, 3>
- {
- public:
- typedef RotationBase<Derived, 3> Base;
- using Base::operator*;
- using Base::derived;
- typedef typename internal::traits<Derived>::Scalar Scalar;
- typedef typename NumTraits<Scalar>::Real RealScalar;
- typedef typename internal::traits<Derived>::Coefficients Coefficients;
- typedef typename Coefficients::CoeffReturnType CoeffReturnType;
- typedef typename internal::conditional<bool(internal::traits<Derived>::Flags&LvalueBit),
- Scalar&, CoeffReturnType>::type NonConstCoeffReturnType;
- enum {
- Flags = Eigen::internal::traits<Derived>::Flags
- };
- // typedef typename Matrix<Scalar,4,1> Coefficients;
- /** the type of a 3D vector */
- typedef Matrix<Scalar,3,1> Vector3;
- /** the equivalent rotation matrix type */
- typedef Matrix<Scalar,3,3> Matrix3;
- /** the equivalent angle-axis type */
- typedef AngleAxis<Scalar> AngleAxisType;
- /** \returns the \c x coefficient */
- EIGEN_DEVICE_FUNC inline CoeffReturnType x() const { return this->derived().coeffs().coeff(0); }
- /** \returns the \c y coefficient */
- EIGEN_DEVICE_FUNC inline CoeffReturnType y() const { return this->derived().coeffs().coeff(1); }
- /** \returns the \c z coefficient */
- EIGEN_DEVICE_FUNC inline CoeffReturnType z() const { return this->derived().coeffs().coeff(2); }
- /** \returns the \c w coefficient */
- EIGEN_DEVICE_FUNC inline CoeffReturnType w() const { return this->derived().coeffs().coeff(3); }
- /** \returns a reference to the \c x coefficient (if Derived is a non-const lvalue) */
- EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType x() { return this->derived().coeffs().x(); }
- /** \returns a reference to the \c y coefficient (if Derived is a non-const lvalue) */
- EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType y() { return this->derived().coeffs().y(); }
- /** \returns a reference to the \c z coefficient (if Derived is a non-const lvalue) */
- EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType z() { return this->derived().coeffs().z(); }
- /** \returns a reference to the \c w coefficient (if Derived is a non-const lvalue) */
- EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType w() { return this->derived().coeffs().w(); }
- /** \returns a read-only vector expression of the imaginary part (x,y,z) */
- EIGEN_DEVICE_FUNC inline const VectorBlock<const Coefficients,3> vec() const { return coeffs().template head<3>(); }
- /** \returns a vector expression of the imaginary part (x,y,z) */
- EIGEN_DEVICE_FUNC inline VectorBlock<Coefficients,3> vec() { return coeffs().template head<3>(); }
- /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
- EIGEN_DEVICE_FUNC inline const typename internal::traits<Derived>::Coefficients& coeffs() const { return derived().coeffs(); }
- /** \returns a vector expression of the coefficients (x,y,z,w) */
- EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Coefficients& coeffs() { return derived().coeffs(); }
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& operator=(const QuaternionBase<Derived>& other);
- template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const QuaternionBase<OtherDerived>& other);
- // disabled this copy operator as it is giving very strange compilation errors when compiling
- // test_stdvector with GCC 4.4.2. This looks like a GCC bug though, so feel free to re-enable it if it's
- // useful; however notice that we already have the templated operator= above and e.g. in MatrixBase
- // we didn't have to add, in addition to templated operator=, such a non-templated copy operator.
- // Derived& operator=(const QuaternionBase& other)
- // { return operator=<Derived>(other); }
- EIGEN_DEVICE_FUNC Derived& operator=(const AngleAxisType& aa);
- template<class OtherDerived> EIGEN_DEVICE_FUNC Derived& operator=(const MatrixBase<OtherDerived>& m);
- /** \returns a quaternion representing an identity rotation
- * \sa MatrixBase::Identity()
- */
- EIGEN_DEVICE_FUNC static inline Quaternion<Scalar> Identity() { return Quaternion<Scalar>(Scalar(1), Scalar(0), Scalar(0), Scalar(0)); }
- /** \sa QuaternionBase::Identity(), MatrixBase::setIdentity()
- */
- EIGEN_DEVICE_FUNC inline QuaternionBase& setIdentity() { coeffs() << Scalar(0), Scalar(0), Scalar(0), Scalar(1); return *this; }
- /** \returns the squared norm of the quaternion's coefficients
- * \sa QuaternionBase::norm(), MatrixBase::squaredNorm()
- */
- EIGEN_DEVICE_FUNC inline Scalar squaredNorm() const { return coeffs().squaredNorm(); }
- /** \returns the norm of the quaternion's coefficients
- * \sa QuaternionBase::squaredNorm(), MatrixBase::norm()
- */
- EIGEN_DEVICE_FUNC inline Scalar norm() const { return coeffs().norm(); }
- /** Normalizes the quaternion \c *this
- * \sa normalized(), MatrixBase::normalize() */
- EIGEN_DEVICE_FUNC inline void normalize() { coeffs().normalize(); }
- /** \returns a normalized copy of \c *this
- * \sa normalize(), MatrixBase::normalized() */
- EIGEN_DEVICE_FUNC inline Quaternion<Scalar> normalized() const { return Quaternion<Scalar>(coeffs().normalized()); }
- /** \returns the dot product of \c *this and \a other
- * Geometrically speaking, the dot product of two unit quaternions
- * corresponds to the cosine of half the angle between the two rotations.
- * \sa angularDistance()
- */
- template<class OtherDerived> EIGEN_DEVICE_FUNC inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); }
- template<class OtherDerived> EIGEN_DEVICE_FUNC Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const;
- /** \returns an equivalent 3x3 rotation matrix */
- EIGEN_DEVICE_FUNC Matrix3 toRotationMatrix() const;
- /** \returns the quaternion which transform \a a into \a b through a rotation */
- template<typename Derived1, typename Derived2>
- EIGEN_DEVICE_FUNC Derived& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
- template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const;
- template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*= (const QuaternionBase<OtherDerived>& q);
- /** \returns the quaternion describing the inverse rotation */
- EIGEN_DEVICE_FUNC Quaternion<Scalar> inverse() const;
- /** \returns the conjugated quaternion */
- EIGEN_DEVICE_FUNC Quaternion<Scalar> conjugate() const;
- template<class OtherDerived> EIGEN_DEVICE_FUNC Quaternion<Scalar> slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const;
- /** \returns \c true if \c *this is approximately equal to \a other, within the precision
- * determined by \a prec.
- *
- * \sa MatrixBase::isApprox() */
- template<class OtherDerived>
- EIGEN_DEVICE_FUNC bool isApprox(const QuaternionBase<OtherDerived>& other, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
- { return coeffs().isApprox(other.coeffs(), prec); }
- /** return the result vector of \a v through the rotation*/
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Vector3 _transformVector(const Vector3& v) const;
- #ifdef EIGEN_PARSED_BY_DOXYGEN
- /** \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<Derived,Quaternion<NewScalarType> >::type cast() const;
- #else
- template<typename NewScalarType>
- EIGEN_DEVICE_FUNC inline
- typename internal::enable_if<internal::is_same<Scalar,NewScalarType>::value,const Derived&>::type cast() const
- {
- return derived();
- }
- template<typename NewScalarType>
- EIGEN_DEVICE_FUNC inline
- typename internal::enable_if<!internal::is_same<Scalar,NewScalarType>::value,Quaternion<NewScalarType> >::type cast() const
- {
- return Quaternion<NewScalarType>(coeffs().template cast<NewScalarType>());
- }
- #endif
- #ifdef EIGEN_QUATERNIONBASE_PLUGIN
- # include EIGEN_QUATERNIONBASE_PLUGIN
- #endif
- protected:
- EIGEN_DEFAULT_COPY_CONSTRUCTOR(QuaternionBase)
- EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(QuaternionBase)
- };
- /***************************************************************************
- * Definition/implementation of Quaternion<Scalar>
- ***************************************************************************/
- /** \geometry_module \ingroup Geometry_Module
- *
- * \class Quaternion
- *
- * \brief The quaternion class used to represent 3D orientations and rotations
- *
- * \tparam _Scalar the scalar type, i.e., the type of the coefficients
- * \tparam _Options controls the memory alignment of the coefficients. Can be \# AutoAlign or \# DontAlign. Default is AutoAlign.
- *
- * This class represents a quaternion \f$ w+xi+yj+zk \f$ that is a convenient representation of
- * orientations and rotations of objects in three dimensions. Compared to other representations
- * like Euler angles or 3x3 matrices, quaternions offer the following advantages:
- * \li \b compact storage (4 scalars)
- * \li \b efficient to compose (28 flops),
- * \li \b stable spherical interpolation
- *
- * The following two typedefs are provided for convenience:
- * \li \c Quaternionf for \c float
- * \li \c Quaterniond for \c double
- *
- * \warning Operations interpreting the quaternion as rotation have undefined behavior if the quaternion is not normalized.
- *
- * \sa class AngleAxis, class Transform
- */
- namespace internal {
- template<typename _Scalar,int _Options>
- struct traits<Quaternion<_Scalar,_Options> >
- {
- typedef Quaternion<_Scalar,_Options> PlainObject;
- typedef _Scalar Scalar;
- typedef Matrix<_Scalar,4,1,_Options> Coefficients;
- enum{
- Alignment = internal::traits<Coefficients>::Alignment,
- Flags = LvalueBit
- };
- };
- }
- template<typename _Scalar, int _Options>
- class Quaternion : public QuaternionBase<Quaternion<_Scalar,_Options> >
- {
- public:
- typedef QuaternionBase<Quaternion<_Scalar,_Options> > Base;
- enum { NeedsAlignment = internal::traits<Quaternion>::Alignment>0 };
- typedef _Scalar Scalar;
- EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Quaternion)
- using Base::operator*=;
- typedef typename internal::traits<Quaternion>::Coefficients Coefficients;
- typedef typename Base::AngleAxisType AngleAxisType;
- /** Default constructor leaving the quaternion uninitialized. */
- EIGEN_DEVICE_FUNC inline Quaternion() {}
- /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from
- * its four coefficients \a w, \a x, \a y and \a z.
- *
- * \warning Note the order of the arguments: the real \a w coefficient first,
- * while internally the coefficients are stored in the following order:
- * [\c x, \c y, \c z, \c w]
- */
- EIGEN_DEVICE_FUNC inline Quaternion(const Scalar& w, const Scalar& x, const Scalar& y, const Scalar& z) : m_coeffs(x, y, z, w){}
- /** Constructs and initialize a quaternion from the array data */
- EIGEN_DEVICE_FUNC explicit inline Quaternion(const Scalar* data) : m_coeffs(data) {}
- /** Copy constructor */
- template<class Derived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion(const QuaternionBase<Derived>& other) { this->Base::operator=(other); }
- /** Constructs and initializes a quaternion from the angle-axis \a aa */
- EIGEN_DEVICE_FUNC explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
- /** Constructs and initializes a quaternion from either:
- * - a rotation matrix expression,
- * - a 4D vector expression representing quaternion coefficients.
- */
- template<typename Derived>
- EIGEN_DEVICE_FUNC explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
- /** Explicit copy constructor with scalar conversion */
- template<typename OtherScalar, int OtherOptions>
- EIGEN_DEVICE_FUNC explicit inline Quaternion(const Quaternion<OtherScalar, OtherOptions>& other)
- { m_coeffs = other.coeffs().template cast<Scalar>(); }
- EIGEN_DEVICE_FUNC static Quaternion UnitRandom();
- template<typename Derived1, typename Derived2>
- EIGEN_DEVICE_FUNC static Quaternion FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
- EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs;}
- EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;}
- EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(NeedsAlignment))
-
- #ifdef EIGEN_QUATERNION_PLUGIN
- # include EIGEN_QUATERNION_PLUGIN
- #endif
- protected:
- Coefficients m_coeffs;
-
- #ifndef EIGEN_PARSED_BY_DOXYGEN
- static EIGEN_STRONG_INLINE void _check_template_params()
- {
- EIGEN_STATIC_ASSERT( (_Options & DontAlign) == _Options,
- INVALID_MATRIX_TEMPLATE_PARAMETERS)
- }
- #endif
- };
- /** \ingroup Geometry_Module
- * single precision quaternion type */
- typedef Quaternion<float> Quaternionf;
- /** \ingroup Geometry_Module
- * double precision quaternion type */
- typedef Quaternion<double> Quaterniond;
- /***************************************************************************
- * Specialization of Map<Quaternion<Scalar>>
- ***************************************************************************/
- namespace internal {
- template<typename _Scalar, int _Options>
- struct traits<Map<Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
- {
- typedef Map<Matrix<_Scalar,4,1>, _Options> Coefficients;
- };
- }
- namespace internal {
- template<typename _Scalar, int _Options>
- struct traits<Map<const Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
- {
- typedef Map<const Matrix<_Scalar,4,1>, _Options> Coefficients;
- typedef traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> > TraitsBase;
- enum {
- Flags = TraitsBase::Flags & ~LvalueBit
- };
- };
- }
- /** \ingroup Geometry_Module
- * \brief Quaternion expression mapping a constant memory buffer
- *
- * \tparam _Scalar the type of the Quaternion coefficients
- * \tparam _Options see class Map
- *
- * This is a specialization of class Map for Quaternion. This class allows to view
- * a 4 scalar memory buffer as an Eigen's Quaternion object.
- *
- * \sa class Map, class Quaternion, class QuaternionBase
- */
- template<typename _Scalar, int _Options>
- class Map<const Quaternion<_Scalar>, _Options >
- : public QuaternionBase<Map<const Quaternion<_Scalar>, _Options> >
- {
- public:
- typedef QuaternionBase<Map<const Quaternion<_Scalar>, _Options> > Base;
- typedef _Scalar Scalar;
- typedef typename internal::traits<Map>::Coefficients Coefficients;
- EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
- using Base::operator*=;
- /** Constructs a Mapped Quaternion object from the pointer \a coeffs
- *
- * The pointer \a coeffs must reference the four coefficients of Quaternion in the following order:
- * \code *coeffs == {x, y, z, w} \endcode
- *
- * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */
- EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(const Scalar* coeffs) : m_coeffs(coeffs) {}
- EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;}
- protected:
- const Coefficients m_coeffs;
- };
- /** \ingroup Geometry_Module
- * \brief Expression of a quaternion from a memory buffer
- *
- * \tparam _Scalar the type of the Quaternion coefficients
- * \tparam _Options see class Map
- *
- * This is a specialization of class Map for Quaternion. This class allows to view
- * a 4 scalar memory buffer as an Eigen's Quaternion object.
- *
- * \sa class Map, class Quaternion, class QuaternionBase
- */
- template<typename _Scalar, int _Options>
- class Map<Quaternion<_Scalar>, _Options >
- : public QuaternionBase<Map<Quaternion<_Scalar>, _Options> >
- {
- public:
- typedef QuaternionBase<Map<Quaternion<_Scalar>, _Options> > Base;
- typedef _Scalar Scalar;
- typedef typename internal::traits<Map>::Coefficients Coefficients;
- EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
- using Base::operator*=;
- /** Constructs a Mapped Quaternion object from the pointer \a coeffs
- *
- * The pointer \a coeffs must reference the four coefficients of Quaternion in the following order:
- * \code *coeffs == {x, y, z, w} \endcode
- *
- * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */
- EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(Scalar* coeffs) : m_coeffs(coeffs) {}
- EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }
- EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }
- protected:
- Coefficients m_coeffs;
- };
- /** \ingroup Geometry_Module
- * Map an unaligned array of single precision scalars as a quaternion */
- typedef Map<Quaternion<float>, 0> QuaternionMapf;
- /** \ingroup Geometry_Module
- * Map an unaligned array of double precision scalars as a quaternion */
- typedef Map<Quaternion<double>, 0> QuaternionMapd;
- /** \ingroup Geometry_Module
- * Map a 16-byte aligned array of single precision scalars as a quaternion */
- typedef Map<Quaternion<float>, Aligned> QuaternionMapAlignedf;
- /** \ingroup Geometry_Module
- * Map a 16-byte aligned array of double precision scalars as a quaternion */
- typedef Map<Quaternion<double>, Aligned> QuaternionMapAlignedd;
- /***************************************************************************
- * Implementation of QuaternionBase methods
- ***************************************************************************/
- // Generic Quaternion * Quaternion product
- // This product can be specialized for a given architecture via the Arch template argument.
- namespace internal {
- template<int Arch, class Derived1, class Derived2, typename Scalar> struct quat_product
- {
- EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived1>& a, const QuaternionBase<Derived2>& b){
- return Quaternion<Scalar>
- (
- a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
- a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
- a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
- a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
- );
- }
- };
- }
- /** \returns the concatenation of two rotations as a quaternion-quaternion product */
- template <class Derived>
- template <class OtherDerived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar>
- QuaternionBase<Derived>::operator* (const QuaternionBase<OtherDerived>& other) const
- {
- EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value),
- YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
- return internal::quat_product<Architecture::Target, Derived, OtherDerived,
- typename internal::traits<Derived>::Scalar>::run(*this, other);
- }
- /** \sa operator*(Quaternion) */
- template <class Derived>
- template <class OtherDerived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
- {
- derived() = derived() * other.derived();
- return derived();
- }
- /** Rotation of a vector by a quaternion.
- * \remarks If the quaternion is used to rotate several points (>1)
- * then it is much more efficient to first convert it to a 3x3 Matrix.
- * Comparison of the operation cost for n transformations:
- * - Quaternion2: 30n
- * - Via a Matrix3: 24 + 15n
- */
- template <class Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename QuaternionBase<Derived>::Vector3
- QuaternionBase<Derived>::_transformVector(const Vector3& v) const
- {
- // Note that this algorithm comes from the optimization by hand
- // of the conversion to a Matrix followed by a Matrix/Vector product.
- // It appears to be much faster than the common algorithm found
- // in the literature (30 versus 39 flops). It also requires two
- // Vector3 as temporaries.
- Vector3 uv = this->vec().cross(v);
- uv += uv;
- return v + this->w() * uv + this->vec().cross(uv);
- }
- template<class Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<Derived>& other)
- {
- coeffs() = other.coeffs();
- return derived();
- }
- template<class Derived>
- template<class OtherDerived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
- {
- coeffs() = other.coeffs();
- return derived();
- }
- /** Set \c *this from an angle-axis \a aa and returns a reference to \c *this
- */
- template<class Derived>
- EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
- {
- EIGEN_USING_STD_MATH(cos)
- EIGEN_USING_STD_MATH(sin)
- Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
- this->w() = cos(ha);
- this->vec() = sin(ha) * aa.axis();
- return derived();
- }
- /** Set \c *this from the expression \a xpr:
- * - if \a xpr is a 4x1 vector, then \a xpr is assumed to be a quaternion
- * - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
- * and \a xpr is converted to a quaternion
- */
- template<class Derived>
- template<class MatrixDerived>
- EIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)
- {
- EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),
- YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
- internal::quaternionbase_assign_impl<MatrixDerived>::run(*this, xpr.derived());
- return derived();
- }
- /** Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to
- * be normalized, otherwise the result is undefined.
- */
- template<class Derived>
- EIGEN_DEVICE_FUNC inline typename QuaternionBase<Derived>::Matrix3
- QuaternionBase<Derived>::toRotationMatrix(void) const
- {
- // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
- // if not inlined then the cost of the return by value is huge ~ +35%,
- // however, not inlining this function is an order of magnitude slower, so
- // it has to be inlined, and so the return by value is not an issue
- Matrix3 res;
- const Scalar tx = Scalar(2)*this->x();
- const Scalar ty = Scalar(2)*this->y();
- const Scalar tz = Scalar(2)*this->z();
- const Scalar twx = tx*this->w();
- const Scalar twy = ty*this->w();
- const Scalar twz = tz*this->w();
- const Scalar txx = tx*this->x();
- const Scalar txy = ty*this->x();
- const Scalar txz = tz*this->x();
- const Scalar tyy = ty*this->y();
- const Scalar tyz = tz*this->y();
- const Scalar tzz = tz*this->z();
- res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);
- res.coeffRef(0,1) = txy-twz;
- res.coeffRef(0,2) = txz+twy;
- res.coeffRef(1,0) = txy+twz;
- res.coeffRef(1,1) = Scalar(1)-(txx+tzz);
- res.coeffRef(1,2) = tyz-twx;
- res.coeffRef(2,0) = txz-twy;
- res.coeffRef(2,1) = tyz+twx;
- res.coeffRef(2,2) = Scalar(1)-(txx+tyy);
- return res;
- }
- /** Sets \c *this to be a quaternion representing a rotation between
- * the two arbitrary vectors \a a and \a b. In other words, the built
- * rotation represent a rotation sending the line of direction \a a
- * to the line of direction \a b, both lines passing through the origin.
- *
- * \returns a reference to \c *this.
- *
- * Note that the two input vectors do \b not have to be normalized, and
- * do not need to have the same norm.
- */
- template<class Derived>
- template<typename Derived1, typename Derived2>
- EIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
- {
- EIGEN_USING_STD_MATH(sqrt)
- Vector3 v0 = a.normalized();
- Vector3 v1 = b.normalized();
- Scalar c = v1.dot(v0);
- // if dot == -1, vectors are nearly opposites
- // => accurately compute the rotation axis by computing the
- // intersection of the two planes. This is done by solving:
- // x^T v0 = 0
- // x^T v1 = 0
- // under the constraint:
- // ||x|| = 1
- // which yields a singular value problem
- if (c < Scalar(-1)+NumTraits<Scalar>::dummy_precision())
- {
- c = numext::maxi(c,Scalar(-1));
- Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
- JacobiSVD<Matrix<Scalar,2,3> > svd(m, ComputeFullV);
- Vector3 axis = svd.matrixV().col(2);
- Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
- this->w() = sqrt(w2);
- this->vec() = axis * sqrt(Scalar(1) - w2);
- return derived();
- }
- Vector3 axis = v0.cross(v1);
- Scalar s = sqrt((Scalar(1)+c)*Scalar(2));
- Scalar invs = Scalar(1)/s;
- this->vec() = axis * invs;
- this->w() = s * Scalar(0.5);
- return derived();
- }
- /** \returns a random unit quaternion following a uniform distribution law on SO(3)
- *
- * \note The implementation is based on http://planning.cs.uiuc.edu/node198.html
- */
- template<typename Scalar, int Options>
- EIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Quaternion<Scalar,Options>::UnitRandom()
- {
- EIGEN_USING_STD_MATH(sqrt)
- EIGEN_USING_STD_MATH(sin)
- EIGEN_USING_STD_MATH(cos)
- const Scalar u1 = internal::random<Scalar>(0, 1),
- u2 = internal::random<Scalar>(0, 2*EIGEN_PI),
- u3 = internal::random<Scalar>(0, 2*EIGEN_PI);
- const Scalar a = sqrt(1 - u1),
- b = sqrt(u1);
- return Quaternion (a * sin(u2), a * cos(u2), b * sin(u3), b * cos(u3));
- }
- /** Returns a quaternion representing a rotation between
- * the two arbitrary vectors \a a and \a b. In other words, the built
- * rotation represent a rotation sending the line of direction \a a
- * to the line of direction \a b, both lines passing through the origin.
- *
- * \returns resulting quaternion
- *
- * Note that the two input vectors do \b not have to be normalized, and
- * do not need to have the same norm.
- */
- template<typename Scalar, int Options>
- template<typename Derived1, typename Derived2>
- EIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Quaternion<Scalar,Options>::FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
- {
- Quaternion quat;
- quat.setFromTwoVectors(a, b);
- return quat;
- }
- /** \returns the multiplicative inverse of \c *this
- * Note that in most cases, i.e., if you simply want the opposite rotation,
- * and/or the quaternion is normalized, then it is enough to use the conjugate.
- *
- * \sa QuaternionBase::conjugate()
- */
- template <class Derived>
- EIGEN_DEVICE_FUNC inline Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Derived>::inverse() const
- {
- // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite() ??
- Scalar n2 = this->squaredNorm();
- if (n2 > Scalar(0))
- return Quaternion<Scalar>(conjugate().coeffs() / n2);
- else
- {
- // return an invalid result to flag the error
- return Quaternion<Scalar>(Coefficients::Zero());
- }
- }
- // Generic conjugate of a Quaternion
- namespace internal {
- template<int Arch, class Derived, typename Scalar> struct quat_conj
- {
- EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived>& q){
- return Quaternion<Scalar>(q.w(),-q.x(),-q.y(),-q.z());
- }
- };
- }
-
- /** \returns the conjugate of the \c *this which is equal to the multiplicative inverse
- * if the quaternion is normalized.
- * The conjugate of a quaternion represents the opposite rotation.
- *
- * \sa Quaternion2::inverse()
- */
- template <class Derived>
- EIGEN_DEVICE_FUNC inline Quaternion<typename internal::traits<Derived>::Scalar>
- QuaternionBase<Derived>::conjugate() const
- {
- return internal::quat_conj<Architecture::Target, Derived,
- typename internal::traits<Derived>::Scalar>::run(*this);
-
- }
- /** \returns the angle (in radian) between two rotations
- * \sa dot()
- */
- template <class Derived>
- template <class OtherDerived>
- EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar
- QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
- {
- EIGEN_USING_STD_MATH(atan2)
- Quaternion<Scalar> d = (*this) * other.conjugate();
- return Scalar(2) * atan2( d.vec().norm(), numext::abs(d.w()) );
- }
-
-
- /** \returns the spherical linear interpolation between the two quaternions
- * \c *this and \a other at the parameter \a t in [0;1].
- *
- * This represents an interpolation for a constant motion between \c *this and \a other,
- * see also http://en.wikipedia.org/wiki/Slerp.
- */
- template <class Derived>
- template <class OtherDerived>
- EIGEN_DEVICE_FUNC Quaternion<typename internal::traits<Derived>::Scalar>
- QuaternionBase<Derived>::slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const
- {
- EIGEN_USING_STD_MATH(acos)
- EIGEN_USING_STD_MATH(sin)
- const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon();
- Scalar d = this->dot(other);
- Scalar absD = numext::abs(d);
- Scalar scale0;
- Scalar scale1;
- if(absD>=one)
- {
- scale0 = Scalar(1) - t;
- scale1 = t;
- }
- else
- {
- // theta is the angle between the 2 quaternions
- Scalar theta = acos(absD);
- Scalar sinTheta = sin(theta);
- scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;
- scale1 = sin( ( t * theta) ) / sinTheta;
- }
- if(d<Scalar(0)) scale1 = -scale1;
- return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
- }
- namespace internal {
- // set from a rotation matrix
- template<typename Other>
- struct quaternionbase_assign_impl<Other,3,3>
- {
- typedef typename Other::Scalar Scalar;
- template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& a_mat)
- {
- const typename internal::nested_eval<Other,2>::type mat(a_mat);
- EIGEN_USING_STD_MATH(sqrt)
- // This algorithm comes from "Quaternion Calculus and Fast Animation",
- // Ken Shoemake, 1987 SIGGRAPH course notes
- Scalar t = mat.trace();
- if (t > Scalar(0))
- {
- t = sqrt(t + Scalar(1.0));
- q.w() = Scalar(0.5)*t;
- t = Scalar(0.5)/t;
- q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
- q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
- q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
- }
- else
- {
- Index i = 0;
- if (mat.coeff(1,1) > mat.coeff(0,0))
- i = 1;
- if (mat.coeff(2,2) > mat.coeff(i,i))
- i = 2;
- Index j = (i+1)%3;
- Index k = (j+1)%3;
- t = sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
- q.coeffs().coeffRef(i) = Scalar(0.5) * t;
- t = Scalar(0.5)/t;
- q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
- q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
- q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
- }
- }
- };
- // set from a vector of coefficients assumed to be a quaternion
- template<typename Other>
- struct quaternionbase_assign_impl<Other,4,1>
- {
- typedef typename Other::Scalar Scalar;
- template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& vec)
- {
- q.coeffs() = vec;
- }
- };
- } // end namespace internal
- } // end namespace Eigen
- #endif // EIGEN_QUATERNION_H
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