diff options
Diffstat (limited to 'eigen/Eigen/src/Geometry/Quaternion.h')
| -rw-r--r-- | eigen/Eigen/src/Geometry/Quaternion.h | 225 |
1 files changed, 130 insertions, 95 deletions
diff --git a/eigen/Eigen/src/Geometry/Quaternion.h b/eigen/Eigen/src/Geometry/Quaternion.h index e89ba80..f6ef1bc 100644 --- a/eigen/Eigen/src/Geometry/Quaternion.h +++ b/eigen/Eigen/src/Geometry/Quaternion.h @@ -34,8 +34,9 @@ struct quaternionbase_assign_impl; template<class Derived> class QuaternionBase : public RotationBase<Derived, 3> { + public: typedef RotationBase<Derived, 3> Base; -public: + using Base::operator*; using Base::derived; @@ -57,37 +58,37 @@ public: /** \returns the \c x coefficient */ - inline Scalar x() const { return this->derived().coeffs().coeff(0); } + EIGEN_DEVICE_FUNC inline Scalar x() const { return this->derived().coeffs().coeff(0); } /** \returns the \c y coefficient */ - inline Scalar y() const { return this->derived().coeffs().coeff(1); } + EIGEN_DEVICE_FUNC inline Scalar y() const { return this->derived().coeffs().coeff(1); } /** \returns the \c z coefficient */ - inline Scalar z() const { return this->derived().coeffs().coeff(2); } + EIGEN_DEVICE_FUNC inline Scalar z() const { return this->derived().coeffs().coeff(2); } /** \returns the \c w coefficient */ - inline Scalar w() const { return this->derived().coeffs().coeff(3); } + EIGEN_DEVICE_FUNC inline Scalar w() const { return this->derived().coeffs().coeff(3); } /** \returns a reference to the \c x coefficient */ - inline Scalar& x() { return this->derived().coeffs().coeffRef(0); } + EIGEN_DEVICE_FUNC inline Scalar& x() { return this->derived().coeffs().coeffRef(0); } /** \returns a reference to the \c y coefficient */ - inline Scalar& y() { return this->derived().coeffs().coeffRef(1); } + EIGEN_DEVICE_FUNC inline Scalar& y() { return this->derived().coeffs().coeffRef(1); } /** \returns a reference to the \c z coefficient */ - inline Scalar& z() { return this->derived().coeffs().coeffRef(2); } + EIGEN_DEVICE_FUNC inline Scalar& z() { return this->derived().coeffs().coeffRef(2); } /** \returns a reference to the \c w coefficient */ - inline Scalar& w() { return this->derived().coeffs().coeffRef(3); } + EIGEN_DEVICE_FUNC inline Scalar& w() { return this->derived().coeffs().coeffRef(3); } /** \returns a read-only vector expression of the imaginary part (x,y,z) */ - inline const VectorBlock<const Coefficients,3> vec() const { return coeffs().template head<3>(); } + 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) */ - inline VectorBlock<Coefficients,3> vec() { return coeffs().template head<3>(); } + 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) */ - inline const typename internal::traits<Derived>::Coefficients& coeffs() const { return derived().coeffs(); } + 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) */ - inline typename internal::traits<Derived>::Coefficients& coeffs() { return derived().coeffs(); } + EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Coefficients& coeffs() { return derived().coeffs(); } - EIGEN_STRONG_INLINE QuaternionBase<Derived>& operator=(const QuaternionBase<Derived>& other); - template<class OtherDerived> EIGEN_STRONG_INLINE Derived& operator=(const QuaternionBase<OtherDerived>& other); + 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 @@ -96,72 +97,72 @@ public: // Derived& operator=(const QuaternionBase& other) // { return operator=<Derived>(other); } - Derived& operator=(const AngleAxisType& aa); - template<class OtherDerived> Derived& operator=(const MatrixBase<OtherDerived>& m); + 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() */ - static inline Quaternion<Scalar> Identity() { return Quaternion<Scalar>(Scalar(1), Scalar(0), Scalar(0), Scalar(0)); } + EIGEN_DEVICE_FUNC static inline Quaternion<Scalar> Identity() { return Quaternion<Scalar>(Scalar(1), Scalar(0), Scalar(0), Scalar(0)); } /** \sa QuaternionBase::Identity(), MatrixBase::setIdentity() */ - inline QuaternionBase& setIdentity() { coeffs() << Scalar(0), Scalar(0), Scalar(0), Scalar(1); return *this; } + 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() */ - inline Scalar squaredNorm() const { return coeffs().squaredNorm(); } + EIGEN_DEVICE_FUNC inline Scalar squaredNorm() const { return coeffs().squaredNorm(); } /** \returns the norm of the quaternion's coefficients * \sa QuaternionBase::squaredNorm(), MatrixBase::norm() */ - inline Scalar norm() const { return coeffs().norm(); } + EIGEN_DEVICE_FUNC inline Scalar norm() const { return coeffs().norm(); } /** Normalizes the quaternion \c *this * \sa normalized(), MatrixBase::normalize() */ - inline void normalize() { coeffs().normalize(); } + EIGEN_DEVICE_FUNC inline void normalize() { coeffs().normalize(); } /** \returns a normalized copy of \c *this * \sa normalize(), MatrixBase::normalized() */ - inline Quaternion<Scalar> normalized() const { return Quaternion<Scalar>(coeffs().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> inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); } + template<class OtherDerived> EIGEN_DEVICE_FUNC inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); } - template<class OtherDerived> Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const; + template<class OtherDerived> EIGEN_DEVICE_FUNC Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const; /** \returns an equivalent 3x3 rotation matrix */ - Matrix3 toRotationMatrix() const; + EIGEN_DEVICE_FUNC Matrix3 toRotationMatrix() const; /** \returns the quaternion which transform \a a into \a b through a rotation */ template<typename Derived1, typename Derived2> - Derived& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b); + EIGEN_DEVICE_FUNC Derived& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b); - template<class OtherDerived> EIGEN_STRONG_INLINE Quaternion<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const; - template<class OtherDerived> EIGEN_STRONG_INLINE Derived& operator*= (const QuaternionBase<OtherDerived>& q); + 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 */ - Quaternion<Scalar> inverse() const; + EIGEN_DEVICE_FUNC Quaternion<Scalar> inverse() const; /** \returns the conjugated quaternion */ - Quaternion<Scalar> conjugate() const; + EIGEN_DEVICE_FUNC Quaternion<Scalar> conjugate() const; - template<class OtherDerived> Quaternion<Scalar> slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) 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> - bool isApprox(const QuaternionBase<OtherDerived>& other, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const + 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_STRONG_INLINE Vector3 _transformVector(const Vector3& v) const; + /** return the result vector of \a v through the rotation*/ + EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Vector3 _transformVector(const Vector3& v) const; /** \returns \c *this with scalar type casted to \a NewScalarType * @@ -169,7 +170,7 @@ public: * then this function smartly returns a const reference to \c *this. */ template<typename NewScalarType> - inline typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const + EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const { return typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type(derived()); } @@ -216,8 +217,8 @@ struct traits<Quaternion<_Scalar,_Options> > typedef _Scalar Scalar; typedef Matrix<_Scalar,4,1,_Options> Coefficients; enum{ - IsAligned = internal::traits<Coefficients>::Flags & AlignedBit, - Flags = IsAligned ? (AlignedBit | LvalueBit) : LvalueBit + Alignment = internal::traits<Coefficients>::Alignment, + Flags = LvalueBit }; }; } @@ -225,10 +226,10 @@ struct traits<Quaternion<_Scalar,_Options> > template<typename _Scalar, int _Options> class Quaternion : public QuaternionBase<Quaternion<_Scalar,_Options> > { +public: typedef QuaternionBase<Quaternion<_Scalar,_Options> > Base; - enum { IsAligned = internal::traits<Quaternion>::IsAligned }; + enum { NeedsAlignment = internal::traits<Quaternion>::Alignment>0 }; -public: typedef _Scalar Scalar; EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Quaternion) @@ -238,7 +239,7 @@ public: typedef typename Base::AngleAxisType AngleAxisType; /** Default constructor leaving the quaternion uninitialized. */ - inline Quaternion() {} + 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. @@ -247,36 +248,42 @@ public: * while internally the coefficients are stored in the following order: * [\c x, \c y, \c z, \c w] */ - inline Quaternion(const Scalar& w, const Scalar& x, const Scalar& y, const Scalar& z) : m_coeffs(x, y, z, 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 */ - inline Quaternion(const Scalar* data) : m_coeffs(data) {} + EIGEN_DEVICE_FUNC explicit inline Quaternion(const Scalar* data) : m_coeffs(data) {} /** Copy constructor */ - template<class Derived> EIGEN_STRONG_INLINE Quaternion(const QuaternionBase<Derived>& other) { this->Base::operator=(other); } + 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 */ - explicit inline Quaternion(const AngleAxisType& aa) { *this = 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> - explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; } + EIGEN_DEVICE_FUNC explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; } /** Explicit copy constructor with scalar conversion */ template<typename OtherScalar, int OtherOptions> - explicit inline Quaternion(const Quaternion<OtherScalar, OtherOptions>& other) + 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> - static Quaternion FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b); + EIGEN_DEVICE_FUNC static Quaternion FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b); - inline Coefficients& coeffs() { return m_coeffs;} - inline const Coefficients& coeffs() const { return m_coeffs;} + 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(IsAligned)) + EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(NeedsAlignment)) + +#ifdef EIGEN_QUATERNION_PLUGIN +# include EIGEN_QUATERNION_PLUGIN +#endif protected: Coefficients m_coeffs; @@ -336,9 +343,9 @@ 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; - public: typedef _Scalar Scalar; typedef typename internal::traits<Map>::Coefficients Coefficients; EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map) @@ -350,9 +357,9 @@ class Map<const Quaternion<_Scalar>, _Options > * \code *coeffs == {x, y, z, w} \endcode * * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */ - EIGEN_STRONG_INLINE Map(const Scalar* coeffs) : m_coeffs(coeffs) {} + EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(const Scalar* coeffs) : m_coeffs(coeffs) {} - inline const Coefficients& coeffs() const { return m_coeffs;} + EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;} protected: const Coefficients m_coeffs; @@ -373,9 +380,9 @@ template<typename _Scalar, int _Options> class Map<Quaternion<_Scalar>, _Options > : public QuaternionBase<Map<Quaternion<_Scalar>, _Options> > { + public: typedef QuaternionBase<Map<Quaternion<_Scalar>, _Options> > Base; - public: typedef _Scalar Scalar; typedef typename internal::traits<Map>::Coefficients Coefficients; EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map) @@ -387,10 +394,10 @@ class Map<Quaternion<_Scalar>, _Options > * \code *coeffs == {x, y, z, w} \endcode * * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */ - EIGEN_STRONG_INLINE Map(Scalar* coeffs) : m_coeffs(coeffs) {} + EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(Scalar* coeffs) : m_coeffs(coeffs) {} - inline Coefficients& coeffs() { return m_coeffs; } - inline const Coefficients& coeffs() const { return m_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; @@ -418,7 +425,7 @@ typedef Map<Quaternion<double>, Aligned> QuaternionMapAlignedd; namespace internal { template<int Arch, class Derived1, class Derived2, typename Scalar, int _Options> struct quat_product { - static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived1>& a, const QuaternionBase<Derived2>& b){ + 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(), @@ -433,20 +440,20 @@ template<int Arch, class Derived1, class Derived2, typename Scalar, int _Options /** \returns the concatenation of two rotations as a quaternion-quaternion product */ template <class Derived> template <class OtherDerived> -EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar> +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, - internal::traits<Derived>::IsAligned && internal::traits<OtherDerived>::IsAligned>::run(*this, other); + EIGEN_PLAIN_ENUM_MIN(internal::traits<Derived>::Alignment, internal::traits<OtherDerived>::Alignment)>::run(*this, other); } /** \sa operator*(Quaternion) */ template <class Derived> template <class OtherDerived> -EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other) +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other) { derived() = derived() * other.derived(); return derived(); @@ -460,7 +467,7 @@ EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const Quaterni * - Via a Matrix3: 24 + 15n */ template <class Derived> -EIGEN_STRONG_INLINE typename QuaternionBase<Derived>::Vector3 +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 @@ -474,7 +481,7 @@ QuaternionBase<Derived>::_transformVector(const Vector3& v) const } template<class Derived> -EIGEN_STRONG_INLINE QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<Derived>& other) +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<Derived>& other) { coeffs() = other.coeffs(); return derived(); @@ -482,7 +489,7 @@ EIGEN_STRONG_INLINE QuaternionBase<Derived>& QuaternionBase<Derived>::operator=( template<class Derived> template<class OtherDerived> -EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other) +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other) { coeffs() = other.coeffs(); return derived(); @@ -491,10 +498,10 @@ EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const Quaternion /** Set \c *this from an angle-axis \a aa and returns a reference to \c *this */ template<class Derived> -EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa) +EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa) { - using std::cos; - using std::sin; + 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(); @@ -509,7 +516,7 @@ EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisT template<class Derived> template<class MatrixDerived> -inline Derived& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr) +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) @@ -521,7 +528,7 @@ inline Derived& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerive * be normalized, otherwise the result is undefined. */ template<class Derived> -inline typename QuaternionBase<Derived>::Matrix3 +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 !!) @@ -568,10 +575,9 @@ QuaternionBase<Derived>::toRotationMatrix(void) const */ template<class Derived> template<typename Derived1, typename Derived2> -inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b) +EIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b) { - using std::max; - using std::sqrt; + EIGEN_USING_STD_MATH(sqrt) Vector3 v0 = a.normalized(); Vector3 v1 = b.normalized(); Scalar c = v1.dot(v0); @@ -586,7 +592,7 @@ inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Deri // which yields a singular value problem if (c < Scalar(-1)+NumTraits<Scalar>::dummy_precision()) { - c = (max)(c,Scalar(-1)); + 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); @@ -605,6 +611,24 @@ inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Deri 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 @@ -618,7 +642,7 @@ inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Deri */ template<typename Scalar, int Options> template<typename Derived1, typename Derived2> -Quaternion<Scalar,Options> Quaternion<Scalar,Options>::FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b) +EIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Quaternion<Scalar,Options>::FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b) { Quaternion quat; quat.setFromTwoVectors(a, b); @@ -633,7 +657,7 @@ Quaternion<Scalar,Options> Quaternion<Scalar,Options>::FromTwoVectors(const Matr * \sa QuaternionBase::conjugate() */ template <class Derived> -inline Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Derived>::inverse() const +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(); @@ -646,6 +670,16 @@ inline Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Der } } +// Generic conjugate of a Quaternion +namespace internal { +template<int Arch, class Derived, typename Scalar, int _Options> 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. @@ -653,10 +687,13 @@ inline Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Der * \sa Quaternion2::inverse() */ template <class Derived> -inline Quaternion<typename internal::traits<Derived>::Scalar> +EIGEN_DEVICE_FUNC inline Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Derived>::conjugate() const { - return Quaternion<Scalar>(this->w(),-this->x(),-this->y(),-this->z()); + return internal::quat_conj<Architecture::Target, Derived, + typename internal::traits<Derived>::Scalar, + internal::traits<Derived>::Alignment>::run(*this); + } /** \returns the angle (in radian) between two rotations @@ -664,13 +701,12 @@ QuaternionBase<Derived>::conjugate() const */ template <class Derived> template <class OtherDerived> -inline typename internal::traits<Derived>::Scalar +EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const { - using std::atan2; - using std::abs; + EIGEN_USING_STD_MATH(atan2) Quaternion<Scalar> d = (*this) * other.conjugate(); - return Scalar(2) * atan2( d.vec().norm(), abs(d.w()) ); + return Scalar(2) * atan2( d.vec().norm(), numext::abs(d.w()) ); } @@ -683,15 +719,14 @@ QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& oth */ template <class Derived> template <class OtherDerived> -Quaternion<typename internal::traits<Derived>::Scalar> +EIGEN_DEVICE_FUNC Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Derived>::slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const { - using std::acos; - using std::sin; - using std::abs; - static const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon(); + 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 = abs(d); + Scalar absD = numext::abs(d); Scalar scale0; Scalar scale1; @@ -722,10 +757,10 @@ template<typename Other> struct quaternionbase_assign_impl<Other,3,3> { typedef typename Other::Scalar Scalar; - typedef DenseIndex Index; - template<class Derived> static inline void run(QuaternionBase<Derived>& q, const Other& mat) + template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& a_mat) { - using std::sqrt; + 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(); @@ -740,13 +775,13 @@ struct quaternionbase_assign_impl<Other,3,3> } else { - DenseIndex i = 0; + 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; - DenseIndex j = (i+1)%3; - DenseIndex k = (j+1)%3; + 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; @@ -763,7 +798,7 @@ template<typename Other> struct quaternionbase_assign_impl<Other,4,1> { typedef typename Other::Scalar Scalar; - template<class Derived> static inline void run(QuaternionBase<Derived>& q, const Other& vec) + template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& vec) { q.coeffs() = vec; } |