11 #ifndef EIGEN_QUATERNION_H 12 #define EIGEN_QUATERNION_H 22 template<
typename Other,
23 int OtherRows=Other::RowsAtCompileTime,
24 int OtherCols=Other::ColsAtCompileTime>
25 struct quaternionbase_assign_impl;
34 template<
class Derived>
35 class QuaternionBase :
public RotationBase<Derived, 3>
38 typedef RotationBase<Derived, 3> Base;
40 using Base::operator*;
43 typedef typename internal::traits<Derived>::Scalar Scalar;
44 typedef typename NumTraits<Scalar>::Real RealScalar;
45 typedef typename internal::traits<Derived>::Coefficients Coefficients;
46 typedef typename Coefficients::CoeffReturnType CoeffReturnType;
47 typedef typename internal::conditional<bool(internal::traits<Derived>::Flags&
LvalueBit),
48 Scalar&, CoeffReturnType>::type NonConstCoeffReturnType;
52 Flags = Eigen::internal::traits<Derived>::Flags
66 EIGEN_DEVICE_FUNC
inline CoeffReturnType
x()
const {
return this->derived().coeffs().coeff(0); }
68 EIGEN_DEVICE_FUNC
inline CoeffReturnType
y()
const {
return this->derived().coeffs().coeff(1); }
70 EIGEN_DEVICE_FUNC
inline CoeffReturnType
z()
const {
return this->derived().coeffs().coeff(2); }
72 EIGEN_DEVICE_FUNC
inline CoeffReturnType
w()
const {
return this->derived().coeffs().coeff(3); }
75 EIGEN_DEVICE_FUNC
inline NonConstCoeffReturnType
x() {
return this->derived().coeffs().x(); }
77 EIGEN_DEVICE_FUNC
inline NonConstCoeffReturnType
y() {
return this->derived().coeffs().y(); }
79 EIGEN_DEVICE_FUNC
inline NonConstCoeffReturnType
z() {
return this->derived().coeffs().z(); }
81 EIGEN_DEVICE_FUNC
inline NonConstCoeffReturnType
w() {
return this->derived().coeffs().w(); }
90 EIGEN_DEVICE_FUNC
inline const typename internal::traits<Derived>::Coefficients&
coeffs()
const {
return derived().coeffs(); }
93 EIGEN_DEVICE_FUNC
inline typename internal::traits<Derived>::Coefficients&
coeffs() {
return derived().coeffs(); }
105 EIGEN_DEVICE_FUNC Derived& operator=(
const AngleAxisType& aa);
120 EIGEN_DEVICE_FUNC
inline Scalar
squaredNorm()
const {
return coeffs().squaredNorm(); }
125 EIGEN_DEVICE_FUNC
inline Scalar
norm()
const {
return coeffs().norm(); }
129 EIGEN_DEVICE_FUNC
inline void normalize() { coeffs().normalize(); }
144 EIGEN_DEVICE_FUNC Matrix3 toRotationMatrix()
const;
147 template<
typename Derived1,
typename Derived2>
165 template<
class OtherDerived>
167 {
return coeffs().isApprox(other.coeffs(), prec); }
170 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Vector3 _transformVector(
const Vector3& v)
const;
177 template<
typename NewScalarType>
178 EIGEN_DEVICE_FUNC
inline typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type
cast()
const 180 return typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type(derived());
183 #ifdef EIGEN_QUATERNIONBASE_PLUGIN 184 # include EIGEN_QUATERNIONBASE_PLUGIN 218 template<
typename _Scalar,
int _Options>
219 struct traits<Quaternion<_Scalar,_Options> >
222 typedef _Scalar Scalar;
225 Alignment = internal::traits<Coefficients>::Alignment,
231 template<
typename _Scalar,
int _Options>
236 enum { NeedsAlignment = internal::traits<Quaternion>::Alignment>0 };
238 typedef _Scalar Scalar;
240 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(
Quaternion)
241 using Base::operator*=;
243 typedef typename internal::traits<Quaternion>::Coefficients Coefficients;
244 typedef typename Base::AngleAxisType AngleAxisType;
256 EIGEN_DEVICE_FUNC
inline Quaternion(
const Scalar& w,
const Scalar& x,
const Scalar& y,
const Scalar& z) : m_coeffs(x, y, z, w){}
259 EIGEN_DEVICE_FUNC
explicit inline Quaternion(
const Scalar* data) : m_coeffs(data) {}
265 EIGEN_DEVICE_FUNC
explicit inline Quaternion(
const AngleAxisType& aa) { *
this = aa; }
271 template<
typename Derived>
275 template<
typename OtherScalar,
int OtherOptions>
277 { m_coeffs = other.coeffs().template cast<Scalar>(); }
279 EIGEN_DEVICE_FUNC
static Quaternion UnitRandom();
281 template<
typename Derived1,
typename Derived2>
284 EIGEN_DEVICE_FUNC
inline Coefficients& coeffs() {
return m_coeffs;}
285 EIGEN_DEVICE_FUNC
inline const Coefficients& coeffs()
const {
return m_coeffs;}
287 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(
bool(NeedsAlignment))
289 #ifdef EIGEN_QUATERNION_PLUGIN 290 # include EIGEN_QUATERNION_PLUGIN 294 Coefficients m_coeffs;
296 #ifndef EIGEN_PARSED_BY_DOXYGEN 297 static EIGEN_STRONG_INLINE
void _check_template_params()
299 EIGEN_STATIC_ASSERT( (_Options &
DontAlign) == _Options,
300 INVALID_MATRIX_TEMPLATE_PARAMETERS)
317 template<
typename _Scalar,
int _Options>
318 struct traits<Map<Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
325 template<
typename _Scalar,
int _Options>
326 struct traits<Map<const Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
329 typedef traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> > TraitsBase;
347 template<
typename _Scalar,
int _Options>
349 :
public QuaternionBase<Map<const Quaternion<_Scalar>, _Options> >
354 typedef _Scalar Scalar;
355 typedef typename internal::traits<Map>::Coefficients Coefficients;
356 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(
Map)
357 using Base::operator*=;
365 EIGEN_DEVICE_FUNC
explicit EIGEN_STRONG_INLINE
Map(
const Scalar* coeffs) : m_coeffs(coeffs) {}
367 EIGEN_DEVICE_FUNC
inline const Coefficients& coeffs()
const {
return m_coeffs;}
370 const Coefficients m_coeffs;
384 template<
typename _Scalar,
int _Options>
391 typedef _Scalar Scalar;
392 typedef typename internal::traits<Map>::Coefficients Coefficients;
393 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(
Map)
394 using Base::operator*=;
402 EIGEN_DEVICE_FUNC
explicit EIGEN_STRONG_INLINE
Map(Scalar* coeffs) : m_coeffs(coeffs) {}
404 EIGEN_DEVICE_FUNC
inline Coefficients& coeffs() {
return m_coeffs; }
405 EIGEN_DEVICE_FUNC
inline const Coefficients& coeffs()
const {
return m_coeffs; }
408 Coefficients m_coeffs;
431 template<
int Arch,
class Derived1,
class Derived2,
typename Scalar>
struct quat_product
436 a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
437 a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
438 a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
439 a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
446 template <
class Derived>
447 template <
class OtherDerived>
451 EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value),
452 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
453 return internal::quat_product<Architecture::Target, Derived, OtherDerived,
454 typename internal::traits<Derived>::Scalar>::run(*
this, other);
458 template <
class Derived>
459 template <
class OtherDerived>
462 derived() = derived() * other.derived();
473 template <
class Derived>
482 Vector3 uv = this->vec().cross(v);
484 return v + this->w() * uv + this->vec().cross(uv);
487 template<
class Derived>
490 coeffs() = other.coeffs();
494 template<
class Derived>
495 template<
class OtherDerived>
498 coeffs() = other.coeffs();
504 template<
class Derived>
507 EIGEN_USING_STD_MATH(
cos)
508 EIGEN_USING_STD_MATH(
sin)
509 Scalar ha = Scalar(0.5)*aa.
angle();
511 this->vec() =
sin(ha) * aa.
axis();
521 template<
class Derived>
522 template<
class MatrixDerived>
525 EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),
526 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
527 internal::quaternionbase_assign_impl<MatrixDerived>::run(*
this, xpr.
derived());
534 template<
class Derived>
544 const Scalar tx = Scalar(2)*this->x();
545 const Scalar ty = Scalar(2)*this->y();
546 const Scalar tz = Scalar(2)*this->z();
547 const Scalar twx = tx*this->w();
548 const Scalar twy = ty*this->w();
549 const Scalar twz = tz*this->w();
550 const Scalar txx = tx*this->x();
551 const Scalar txy = ty*this->x();
552 const Scalar txz = tz*this->x();
553 const Scalar tyy = ty*this->y();
554 const Scalar tyz = tz*this->y();
555 const Scalar tzz = tz*this->z();
557 res.
coeffRef(0,0) = Scalar(1)-(tyy+tzz);
561 res.
coeffRef(1,1) = Scalar(1)-(txx+tzz);
565 res.
coeffRef(2,2) = Scalar(1)-(txx+tyy);
580 template<
class Derived>
581 template<
typename Derived1,
typename Derived2>
584 EIGEN_USING_STD_MATH(
sqrt)
587 Scalar c = v1.dot(v0);
599 c = numext::maxi(c,Scalar(-1));
602 Vector3 axis = svd.
matrixV().col(2);
604 Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
605 this->w() =
sqrt(w2);
606 this->vec() = axis *
sqrt(Scalar(1) - w2);
609 Vector3 axis = v0.cross(v1);
610 Scalar s =
sqrt((Scalar(1)+c)*Scalar(2));
611 Scalar invs = Scalar(1)/s;
612 this->vec() = axis * invs;
613 this->w() = s * Scalar(0.5);
622 template<
typename Scalar,
int Options>
625 EIGEN_USING_STD_MATH(
sqrt)
626 EIGEN_USING_STD_MATH(
sin)
627 EIGEN_USING_STD_MATH(
cos)
628 const Scalar u1 = internal::random<Scalar>(0, 1),
629 u2 = internal::random<Scalar>(0, 2*EIGEN_PI),
630 u3 = internal::random<Scalar>(0, 2*EIGEN_PI);
631 const Scalar a =
sqrt(1 - u1),
647 template<
typename Scalar,
int Options>
648 template<
typename Derived1,
typename Derived2>
663 template <
class Derived>
667 Scalar n2 = this->squaredNorm();
679 template<
int Arch,
class Derived,
typename Scalar>
struct quat_conj
693 template <
class Derived>
697 return internal::quat_conj<Architecture::Target, Derived,
698 typename internal::traits<Derived>::Scalar>::run(*
this);
705 template <
class Derived>
706 template <
class OtherDerived>
707 EIGEN_DEVICE_FUNC
inline typename internal::traits<Derived>::Scalar
710 EIGEN_USING_STD_MATH(atan2)
712 return Scalar(2) * atan2( d.
vec().norm(), numext::abs(d.
w()) );
723 template <
class Derived>
724 template <
class OtherDerived>
728 EIGEN_USING_STD_MATH(
acos)
729 EIGEN_USING_STD_MATH(
sin)
731 Scalar d = this->dot(other);
732 Scalar absD = numext::abs(d);
739 scale0 = Scalar(1) - t;
745 Scalar theta =
acos(absD);
746 Scalar sinTheta =
sin(theta);
748 scale0 =
sin( ( Scalar(1) - t ) * theta) / sinTheta;
749 scale1 =
sin( ( t * theta) ) / sinTheta;
751 if(d<Scalar(0)) scale1 = -scale1;
759 template<
typename Other>
760 struct quaternionbase_assign_impl<Other,3,3>
762 typedef typename Other::Scalar Scalar;
763 template<
class Derived> EIGEN_DEVICE_FUNC
static inline void run(
QuaternionBase<Derived>& q,
const Other& a_mat)
765 const typename internal::nested_eval<Other,2>::type mat(a_mat);
766 EIGEN_USING_STD_MATH(
sqrt)
769 Scalar t = mat.trace();
772 t =
sqrt(t + Scalar(1.0));
773 q.w() = Scalar(0.5)*t;
775 q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
776 q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
777 q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
782 if (mat.coeff(1,1) > mat.coeff(0,0))
784 if (mat.coeff(2,2) > mat.coeff(i,i))
789 t =
sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
790 q.coeffs().coeffRef(i) = Scalar(0.5) * t;
792 q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
793 q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
794 q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
800 template<
typename Other>
801 struct quaternionbase_assign_impl<Other,4,1>
803 typedef typename Other::Scalar Scalar;
814 #endif // EIGEN_QUATERNION_H const Vector3 & axis() const
Definition: AngleAxis.h:96
NonConstCoeffReturnType x()
Definition: Quaternion.h:75
Definition: Constants.h:326
CoeffReturnType w() const
Definition: Quaternion.h:72
NonConstCoeffReturnType y()
Definition: Quaternion.h:77
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:94
Matrix< Scalar, 3, 1 > Vector3
Definition: Quaternion.h:57
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)
bool isApprox(const QuaternionBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: Quaternion.h:166
Scalar angle() const
Definition: AngleAxis.h:91
Quaternion< double > Quaterniond
Definition: Quaternion.h:310
const unsigned int LvalueBit
Definition: Constants.h:139
Scalar dot(const QuaternionBase< OtherDerived > &other) const
Definition: Quaternion.h:139
Namespace containing all symbols from the Eigen library.
Definition: Core:306
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:150
const PlainObject normalized() const
Definition: Dot.h:124
Scalar norm() const
Definition: Quaternion.h:125
internal::cast_return_type< Derived, Quaternion< NewScalarType > >::type cast() const
Definition: Quaternion.h:178
AngleAxis< Scalar > AngleAxisType
Definition: Quaternion.h:61
Derived & derived()
Definition: EigenBase.h:45
Quaternion()
Definition: Quaternion.h:247
NonConstCoeffReturnType w()
Definition: Quaternion.h:81
Derived & operator*=(const QuaternionBase< OtherDerived > &q)
Definition: Quaternion.h:460
static Quaternion< Scalar > Identity()
Definition: Quaternion.h:111
NonConstCoeffReturnType z()
Definition: Quaternion.h:79
Map(const Scalar *coeffs)
Definition: Quaternion.h:365
void normalize()
Definition: Quaternion.h:129
Derived & setFromTwoVectors(const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
Definition: Quaternion.h:582
Scalar & coeffRef(Index rowId, Index colId)
Definition: PlainObjectBase.h:183
CoeffReturnType z() const
Definition: Quaternion.h:70
Expression of a fixed-size or dynamic-size sub-vector.
Definition: ForwardDeclarations.h:87
Scalar squaredNorm() const
Definition: Quaternion.h:120
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_acos_op< typename Derived::Scalar >, const Derived > acos(const Eigen::ArrayBase< Derived > &x)
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_inverse_op< typename Derived::Scalar >, const Derived > inverse(const Eigen::ArrayBase< Derived > &x)
internal::traits< Derived >::Coefficients & coeffs()
Definition: Quaternion.h:93
const VectorBlock< const Coefficients, 3 > vec() const
Definition: Quaternion.h:84
static Quaternion UnitRandom()
Definition: Quaternion.h:623
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_cos_op< typename Derived::Scalar >, const Derived > cos(const Eigen::ArrayBase< Derived > &x)
const Product< MatrixDerived, PermutationDerived, AliasFreeProduct > operator*(const MatrixBase< MatrixDerived > &matrix, const PermutationBase< PermutationDerived > &permutation)
Definition: PermutationMatrix.h:543
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
Map(Scalar *coeffs)
Definition: Quaternion.h:402
Definition: Constants.h:235
Quaternion(const Quaternion< OtherScalar, OtherOptions > &other)
Definition: Quaternion.h:276
Quaternion< Scalar > normalized() const
Definition: Quaternion.h:132
CoeffReturnType x() const
Definition: Quaternion.h:66
Base class for quaternion expressions.
Definition: ForwardDeclarations.h:268
Quaternion< Scalar > inverse() const
Definition: Quaternion.h:664
CoeffReturnType y() const
Definition: Quaternion.h:68
Map< Quaternion< float >, 0 > QuaternionMapf
Definition: Quaternion.h:413
Definition: Eigen_Colamd.h:50
Quaternion(const AngleAxisType &aa)
Definition: Quaternion.h:265
The quaternion class used to represent 3D orientations and rotations.
Definition: ForwardDeclarations.h:273
Quaternion(const MatrixBase< Derived > &other)
Definition: Quaternion.h:272
Map< Quaternion< double >, 0 > QuaternionMapd
Definition: Quaternion.h:416
Two-sided Jacobi SVD decomposition of a rectangular matrix.
Definition: ForwardDeclarations.h:258
Map< Quaternion< float >, Aligned > QuaternionMapAlignedf
Definition: Quaternion.h:419
QuaternionBase & setIdentity()
Definition: Quaternion.h:115
Quaternion< Scalar > conjugate() const
Definition: Quaternion.h:695
const MatrixVType & matrixV() const
Definition: SVDBase.h:99
Matrix< Scalar, 3, 3 > Matrix3
Definition: Quaternion.h:59
VectorBlock< Coefficients, 3 > vec()
Definition: Quaternion.h:87
Definition: Constants.h:387
Vector3 _transformVector(const Vector3 &v) const
Definition: Quaternion.h:475
Quaternion(const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)
Definition: Quaternion.h:256
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
Represents a 3D rotation as a rotation angle around an arbitrary 3D axis.
Definition: ForwardDeclarations.h:270
Matrix3 toRotationMatrix() const
Definition: Quaternion.h:536
Quaternion(const Scalar *data)
Definition: Quaternion.h:259
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sin_op< typename Derived::Scalar >, const Derived > sin(const Eigen::ArrayBase< Derived > &x)
const internal::traits< Derived >::Coefficients & coeffs() const
Definition: Quaternion.h:90
Quaternion< float > Quaternionf
Definition: Quaternion.h:307
Map< Quaternion< double >, Aligned > QuaternionMapAlignedd
Definition: Quaternion.h:422
Quaternion(const QuaternionBase< Derived > &other)
Definition: Quaternion.h:262