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;
47 Flags = Eigen::internal::traits<Derived>::Flags
61 EIGEN_DEVICE_FUNC
inline Scalar
x()
const {
return this->derived().coeffs().coeff(0); }
63 EIGEN_DEVICE_FUNC
inline Scalar
y()
const {
return this->derived().coeffs().coeff(1); }
65 EIGEN_DEVICE_FUNC
inline Scalar
z()
const {
return this->derived().coeffs().coeff(2); }
67 EIGEN_DEVICE_FUNC
inline Scalar
w()
const {
return this->derived().coeffs().coeff(3); }
70 EIGEN_DEVICE_FUNC
inline Scalar&
x() {
return this->derived().coeffs().coeffRef(0); }
72 EIGEN_DEVICE_FUNC
inline Scalar&
y() {
return this->derived().coeffs().coeffRef(1); }
74 EIGEN_DEVICE_FUNC
inline Scalar&
z() {
return this->derived().coeffs().coeffRef(2); }
76 EIGEN_DEVICE_FUNC
inline Scalar&
w() {
return this->derived().coeffs().coeffRef(3); }
85 EIGEN_DEVICE_FUNC
inline const typename internal::traits<Derived>::Coefficients&
coeffs()
const {
return derived().coeffs(); }
88 EIGEN_DEVICE_FUNC
inline typename internal::traits<Derived>::Coefficients&
coeffs() {
return derived().coeffs(); }
100 EIGEN_DEVICE_FUNC Derived& operator=(
const AngleAxisType& aa);
115 EIGEN_DEVICE_FUNC
inline Scalar
squaredNorm()
const {
return coeffs().squaredNorm(); }
120 EIGEN_DEVICE_FUNC
inline Scalar
norm()
const {
return coeffs().norm(); }
124 EIGEN_DEVICE_FUNC
inline void normalize() { coeffs().normalize(); }
139 EIGEN_DEVICE_FUNC Matrix3 toRotationMatrix()
const;
142 template<
typename Derived1,
typename Derived2>
160 template<
class OtherDerived>
162 {
return coeffs().isApprox(other.coeffs(), prec); }
165 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Vector3 _transformVector(
const Vector3& v)
const;
172 template<
typename NewScalarType>
173 EIGEN_DEVICE_FUNC
inline typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type
cast()
const 175 return typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type(derived());
178 #ifdef EIGEN_QUATERNIONBASE_PLUGIN 179 # include EIGEN_QUATERNIONBASE_PLUGIN 213 template<
typename _Scalar,
int _Options>
214 struct traits<Quaternion<_Scalar,_Options> >
217 typedef _Scalar Scalar;
220 Alignment = internal::traits<Coefficients>::Alignment,
226 template<
typename _Scalar,
int _Options>
231 enum { NeedsAlignment = internal::traits<Quaternion>::Alignment>0 };
233 typedef _Scalar Scalar;
235 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(
Quaternion)
236 using Base::operator*=;
238 typedef typename internal::traits<Quaternion>::Coefficients Coefficients;
239 typedef typename Base::AngleAxisType AngleAxisType;
251 EIGEN_DEVICE_FUNC
inline Quaternion(
const Scalar& w,
const Scalar& x,
const Scalar& y,
const Scalar& z) : m_coeffs(x, y, z, w){}
254 EIGEN_DEVICE_FUNC
explicit inline Quaternion(
const Scalar* data) : m_coeffs(data) {}
260 EIGEN_DEVICE_FUNC
explicit inline Quaternion(
const AngleAxisType& aa) { *
this = aa; }
266 template<
typename Derived>
270 template<
typename OtherScalar,
int OtherOptions>
272 { m_coeffs = other.coeffs().template cast<Scalar>(); }
274 EIGEN_DEVICE_FUNC
static Quaternion UnitRandom();
276 template<
typename Derived1,
typename Derived2>
279 EIGEN_DEVICE_FUNC
inline Coefficients& coeffs() {
return m_coeffs;}
280 EIGEN_DEVICE_FUNC
inline const Coefficients& coeffs()
const {
return m_coeffs;}
282 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(
bool(NeedsAlignment))
284 #ifdef EIGEN_QUATERNION_PLUGIN 285 # include EIGEN_QUATERNION_PLUGIN 289 Coefficients m_coeffs;
291 #ifndef EIGEN_PARSED_BY_DOXYGEN 292 static EIGEN_STRONG_INLINE
void _check_template_params()
294 EIGEN_STATIC_ASSERT( (_Options &
DontAlign) == _Options,
295 INVALID_MATRIX_TEMPLATE_PARAMETERS)
312 template<
typename _Scalar,
int _Options>
313 struct traits<Map<Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
320 template<
typename _Scalar,
int _Options>
321 struct traits<Map<const Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
324 typedef traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> > TraitsBase;
342 template<
typename _Scalar,
int _Options>
344 :
public QuaternionBase<Map<const Quaternion<_Scalar>, _Options> >
349 typedef _Scalar Scalar;
350 typedef typename internal::traits<Map>::Coefficients Coefficients;
351 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(
Map)
352 using Base::operator*=;
360 EIGEN_DEVICE_FUNC
explicit EIGEN_STRONG_INLINE
Map(
const Scalar* coeffs) : m_coeffs(coeffs) {}
362 EIGEN_DEVICE_FUNC
inline const Coefficients& coeffs()
const {
return m_coeffs;}
365 const Coefficients m_coeffs;
379 template<
typename _Scalar,
int _Options>
386 typedef _Scalar Scalar;
387 typedef typename internal::traits<Map>::Coefficients Coefficients;
388 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(
Map)
389 using Base::operator*=;
397 EIGEN_DEVICE_FUNC
explicit EIGEN_STRONG_INLINE
Map(Scalar* coeffs) : m_coeffs(coeffs) {}
399 EIGEN_DEVICE_FUNC
inline Coefficients& coeffs() {
return m_coeffs; }
400 EIGEN_DEVICE_FUNC
inline const Coefficients& coeffs()
const {
return m_coeffs; }
403 Coefficients m_coeffs;
426 template<
int Arch,
class Derived1,
class Derived2,
typename Scalar>
struct quat_product
431 a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
432 a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
433 a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
434 a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
441 template <
class Derived>
442 template <
class OtherDerived>
446 EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value),
447 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
448 return internal::quat_product<Architecture::Target, Derived, OtherDerived,
449 typename internal::traits<Derived>::Scalar>::run(*
this, other);
453 template <
class Derived>
454 template <
class OtherDerived>
457 derived() = derived() * other.derived();
468 template <
class Derived>
477 Vector3 uv = this->vec().cross(v);
479 return v + this->w() * uv + this->vec().cross(uv);
482 template<
class Derived>
485 coeffs() = other.coeffs();
489 template<
class Derived>
490 template<
class OtherDerived>
493 coeffs() = other.coeffs();
499 template<
class Derived>
502 EIGEN_USING_STD_MATH(
cos)
503 EIGEN_USING_STD_MATH(
sin)
504 Scalar ha = Scalar(0.5)*aa.
angle();
506 this->vec() =
sin(ha) * aa.
axis();
516 template<
class Derived>
517 template<
class MatrixDerived>
520 EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),
521 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
522 internal::quaternionbase_assign_impl<MatrixDerived>::run(*
this, xpr.
derived());
529 template<
class Derived>
539 const Scalar tx = Scalar(2)*this->x();
540 const Scalar ty = Scalar(2)*this->y();
541 const Scalar tz = Scalar(2)*this->z();
542 const Scalar twx = tx*this->w();
543 const Scalar twy = ty*this->w();
544 const Scalar twz = tz*this->w();
545 const Scalar txx = tx*this->x();
546 const Scalar txy = ty*this->x();
547 const Scalar txz = tz*this->x();
548 const Scalar tyy = ty*this->y();
549 const Scalar tyz = tz*this->y();
550 const Scalar tzz = tz*this->z();
552 res.
coeffRef(0,0) = Scalar(1)-(tyy+tzz);
556 res.
coeffRef(1,1) = Scalar(1)-(txx+tzz);
560 res.
coeffRef(2,2) = Scalar(1)-(txx+tyy);
575 template<
class Derived>
576 template<
typename Derived1,
typename Derived2>
579 EIGEN_USING_STD_MATH(
sqrt)
582 Scalar c = v1.dot(v0);
594 c = numext::maxi(c,Scalar(-1));
597 Vector3 axis = svd.
matrixV().col(2);
599 Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
600 this->w() =
sqrt(w2);
601 this->vec() = axis *
sqrt(Scalar(1) - w2);
604 Vector3 axis = v0.cross(v1);
605 Scalar s =
sqrt((Scalar(1)+c)*Scalar(2));
606 Scalar invs = Scalar(1)/s;
607 this->vec() = axis * invs;
608 this->w() = s * Scalar(0.5);
617 template<
typename Scalar,
int Options>
620 EIGEN_USING_STD_MATH(
sqrt)
621 EIGEN_USING_STD_MATH(
sin)
622 EIGEN_USING_STD_MATH(
cos)
623 const Scalar u1 = internal::random<Scalar>(0, 1),
624 u2 = internal::random<Scalar>(0, 2*EIGEN_PI),
625 u3 = internal::random<Scalar>(0, 2*EIGEN_PI);
626 const Scalar a =
sqrt(1 - u1),
642 template<
typename Scalar,
int Options>
643 template<
typename Derived1,
typename Derived2>
658 template <
class Derived>
662 Scalar n2 = this->squaredNorm();
674 template<
int Arch,
class Derived,
typename Scalar>
struct quat_conj
688 template <
class Derived>
692 return internal::quat_conj<Architecture::Target, Derived,
693 typename internal::traits<Derived>::Scalar>::run(*
this);
700 template <
class Derived>
701 template <
class OtherDerived>
702 EIGEN_DEVICE_FUNC
inline typename internal::traits<Derived>::Scalar
705 EIGEN_USING_STD_MATH(atan2)
707 return Scalar(2) * atan2( d.
vec().norm(), numext::abs(d.
w()) );
718 template <
class Derived>
719 template <
class OtherDerived>
723 EIGEN_USING_STD_MATH(
acos)
724 EIGEN_USING_STD_MATH(
sin)
726 Scalar d = this->dot(other);
727 Scalar absD = numext::abs(d);
734 scale0 = Scalar(1) - t;
740 Scalar theta =
acos(absD);
741 Scalar sinTheta =
sin(theta);
743 scale0 =
sin( ( Scalar(1) - t ) * theta) / sinTheta;
744 scale1 =
sin( ( t * theta) ) / sinTheta;
746 if(d<Scalar(0)) scale1 = -scale1;
754 template<
typename Other>
755 struct quaternionbase_assign_impl<Other,3,3>
757 typedef typename Other::Scalar Scalar;
758 template<
class Derived> EIGEN_DEVICE_FUNC
static inline void run(
QuaternionBase<Derived>& q,
const Other& a_mat)
760 const typename internal::nested_eval<Other,2>::type mat(a_mat);
761 EIGEN_USING_STD_MATH(
sqrt)
764 Scalar t = mat.trace();
767 t =
sqrt(t + Scalar(1.0));
768 q.w() = Scalar(0.5)*t;
770 q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
771 q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
772 q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
777 if (mat.coeff(1,1) > mat.coeff(0,0))
779 if (mat.coeff(2,2) > mat.coeff(i,i))
784 t =
sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
785 q.coeffs().coeffRef(i) = Scalar(0.5) * t;
787 q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
788 q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
789 q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
795 template<
typename Other>
796 struct quaternionbase_assign_impl<Other,4,1>
798 typedef typename Other::Scalar Scalar;
809 #endif // EIGEN_QUATERNION_H Scalar z() const
Definition: Quaternion.h:65
const Vector3 & axis() const
Definition: AngleAxis.h:96
Definition: Constants.h:326
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:88
Matrix< Scalar, 3, 1 > Vector3
Definition: Quaternion.h:52
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:161
Scalar angle() const
Definition: AngleAxis.h:91
Quaternion< double > Quaterniond
Definition: Quaternion.h:305
const unsigned int LvalueBit
Definition: Constants.h:139
Scalar dot(const QuaternionBase< OtherDerived > &other) const
Definition: Quaternion.h:134
Namespace containing all symbols from the Eigen library.
Definition: Core:287
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:150
const PlainObject normalized() const
Definition: Dot.h:121
Scalar norm() const
Definition: Quaternion.h:120
internal::cast_return_type< Derived, Quaternion< NewScalarType > >::type cast() const
Definition: Quaternion.h:173
AngleAxis< Scalar > AngleAxisType
Definition: Quaternion.h:56
Derived & derived()
Definition: EigenBase.h:45
Quaternion()
Definition: Quaternion.h:242
Scalar x() const
Definition: Quaternion.h:61
Derived & operator*=(const QuaternionBase< OtherDerived > &q)
Definition: Quaternion.h:455
static Quaternion< Scalar > Identity()
Definition: Quaternion.h:106
Map(const Scalar *coeffs)
Definition: Quaternion.h:360
void normalize()
Definition: Quaternion.h:124
Derived & setFromTwoVectors(const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
Definition: Quaternion.h:577
Scalar & coeffRef(Index rowId, Index colId)
Definition: PlainObjectBase.h:183
Expression of a fixed-size or dynamic-size sub-vector.
Definition: ForwardDeclarations.h:87
Scalar squaredNorm() const
Definition: Quaternion.h:115
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:88
const VectorBlock< const Coefficients, 3 > vec() const
Definition: Quaternion.h:79
static Quaternion UnitRandom()
Definition: Quaternion.h:618
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
Scalar & x()
Definition: Quaternion.h:70
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
Map(Scalar *coeffs)
Definition: Quaternion.h:397
Definition: Constants.h:235
Quaternion(const Quaternion< OtherScalar, OtherOptions > &other)
Definition: Quaternion.h:271
Quaternion< Scalar > normalized() const
Definition: Quaternion.h:127
Scalar & z()
Definition: Quaternion.h:74
Base class for quaternion expressions.
Definition: ForwardDeclarations.h:268
Quaternion< Scalar > inverse() const
Definition: Quaternion.h:659
Map< Quaternion< float >, 0 > QuaternionMapf
Definition: Quaternion.h:408
Definition: Eigen_Colamd.h:50
Quaternion(const AngleAxisType &aa)
Definition: Quaternion.h:260
The quaternion class used to represent 3D orientations and rotations.
Definition: ForwardDeclarations.h:273
Quaternion(const MatrixBase< Derived > &other)
Definition: Quaternion.h:267
Map< Quaternion< double >, 0 > QuaternionMapd
Definition: Quaternion.h:411
Two-sided Jacobi SVD decomposition of a rectangular matrix.
Definition: ForwardDeclarations.h:258
Map< Quaternion< float >, Aligned > QuaternionMapAlignedf
Definition: Quaternion.h:414
QuaternionBase & setIdentity()
Definition: Quaternion.h:110
Scalar & w()
Definition: Quaternion.h:76
Quaternion< Scalar > conjugate() const
Definition: Quaternion.h:690
const MatrixVType & matrixV() const
Definition: SVDBase.h:99
Scalar y() const
Definition: Quaternion.h:63
Scalar & y()
Definition: Quaternion.h:72
Matrix< Scalar, 3, 3 > Matrix3
Definition: Quaternion.h:54
VectorBlock< Coefficients, 3 > vec()
Definition: Quaternion.h:82
Definition: Constants.h:387
Vector3 _transformVector(const Vector3 &v) const
Definition: Quaternion.h:470
Quaternion(const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)
Definition: Quaternion.h:251
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:531
Quaternion(const Scalar *data)
Definition: Quaternion.h:254
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sin_op< typename Derived::Scalar >, const Derived > sin(const Eigen::ArrayBase< Derived > &x)
Scalar w() const
Definition: Quaternion.h:67
const internal::traits< Derived >::Coefficients & coeffs() const
Definition: Quaternion.h:85
Quaternion< float > Quaternionf
Definition: Quaternion.h:302
Map< Quaternion< double >, Aligned > QuaternionMapAlignedd
Definition: Quaternion.h:417
Quaternion(const QuaternionBase< Derived > &other)
Definition: Quaternion.h:257