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 inline Scalar
x()
const {
return this->derived().coeffs().coeff(0); }
63 inline Scalar
y()
const {
return this->derived().coeffs().coeff(1); }
65 inline Scalar
z()
const {
return this->derived().coeffs().coeff(2); }
67 inline Scalar
w()
const {
return this->derived().coeffs().coeff(3); }
70 inline Scalar&
x() {
return this->derived().coeffs().coeffRef(0); }
72 inline Scalar&
y() {
return this->derived().coeffs().coeffRef(1); }
74 inline Scalar&
z() {
return this->derived().coeffs().coeffRef(2); }
76 inline Scalar&
w() {
return this->derived().coeffs().coeffRef(3); }
85 inline const typename internal::traits<Derived>::Coefficients&
coeffs()
const {
return derived().coeffs(); }
88 inline typename internal::traits<Derived>::Coefficients&
coeffs() {
return derived().coeffs(); }
100 Derived& operator=(
const AngleAxisType& aa);
142 template<
typename Derived1,
typename Derived2>
160 template<
class OtherDerived>
162 {
return coeffs().isApprox(other.coeffs(), prec); }
172 template<
typename NewScalarType>
173 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> >
216 typedef Quaternion<_Scalar,_Options> PlainObject;
217 typedef _Scalar Scalar;
218 typedef Matrix<_Scalar,4,1,_Options> Coefficients;
220 Alignment = internal::traits<Coefficients>::Alignment,
226 template<
typename _Scalar,
int _Options>
227 class Quaternion :
public QuaternionBase<Quaternion<_Scalar,_Options> >
230 typedef QuaternionBase<Quaternion<_Scalar,_Options> > Base;
231 enum { NeedsAlignment = internal::traits<Quaternion>::Alignment>0 };
233 typedef _Scalar Scalar;
235 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(
Quaternion)
236 using Base::operator*=;
239 typedef typename Base::AngleAxisType AngleAxisType;
251 inline Quaternion(
const Scalar&
w,
const Scalar&
x,
const Scalar&
y,
const Scalar&
z) : m_coeffs(x, y, z, w){}
254 explicit inline Quaternion(
const Scalar* data) : m_coeffs(data) {}
260 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 template<
typename Derived1,
typename Derived2>
277 inline Coefficients& coeffs() {
return m_coeffs;}
278 inline const Coefficients& coeffs()
const {
return m_coeffs;}
280 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(NeedsAlignment)
283 Coefficients m_coeffs;
285 #ifndef EIGEN_PARSED_BY_DOXYGEN
286 static EIGEN_STRONG_INLINE
void _check_template_params()
288 EIGEN_STATIC_ASSERT( (_Options &
DontAlign) == _Options,
289 INVALID_MATRIX_TEMPLATE_PARAMETERS)
306 template<
typename _Scalar,
int _Options>
307 struct traits<Map<Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
314 template<
typename _Scalar,
int _Options>
315 struct traits<Map<const Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
317 typedef Map<const Matrix<_Scalar,4,1>, _Options> Coefficients;
318 typedef traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> > TraitsBase;
336 template<
typename _Scalar,
int _Options>
338 :
public QuaternionBase<Map<const Quaternion<_Scalar>, _Options> >
343 typedef _Scalar Scalar;
344 typedef typename internal::traits<Map>::Coefficients Coefficients;
345 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(
Map)
346 using Base::operator*=;
354 explicit EIGEN_STRONG_INLINE
Map(
const Scalar* coeffs) : m_coeffs(coeffs) {}
356 inline const Coefficients& coeffs()
const {
return m_coeffs;}
359 const Coefficients m_coeffs;
373 template<
typename _Scalar,
int _Options>
380 typedef _Scalar Scalar;
381 typedef typename internal::traits<Map>::Coefficients Coefficients;
382 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(
Map)
383 using Base::operator*=;
391 explicit EIGEN_STRONG_INLINE
Map(Scalar* coeffs) : m_coeffs(coeffs) {}
393 inline Coefficients& coeffs() {
return m_coeffs; }
394 inline const Coefficients& coeffs()
const {
return m_coeffs; }
397 Coefficients m_coeffs;
420 template<
int Arch,
class Derived1,
class Derived2,
typename Scalar,
int _Options>
struct quat_product
425 a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
426 a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
427 a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
428 a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
435 template <
class Derived>
436 template <
class OtherDerived>
437 EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar>
440 EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value),
441 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
442 return internal::quat_product<Architecture::Target, Derived, OtherDerived,
443 typename internal::traits<Derived>::Scalar,
444 EIGEN_PLAIN_ENUM_MIN(internal::traits<Derived>::Alignment, internal::traits<OtherDerived>::Alignment)>::run(*
this, other);
448 template <
class Derived>
449 template <
class OtherDerived>
452 derived() = derived() * other.derived();
463 template <
class Derived>
472 Vector3 uv = this->vec().cross(v);
474 return v + this->w() * uv + this->vec().cross(uv);
477 template<
class Derived>
480 coeffs() = other.coeffs();
484 template<
class Derived>
485 template<
class OtherDerived>
486 EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(
const QuaternionBase<OtherDerived>& other)
488 coeffs() = other.coeffs();
494 template<
class Derived>
499 Scalar ha = Scalar(0.5)*aa.angle();
501 this->vec() = sin(ha) * aa.axis();
511 template<
class Derived>
512 template<
class MatrixDerived>
515 EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),
516 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
517 internal::quaternionbase_assign_impl<MatrixDerived>::run(*
this, xpr.derived());
524 template<
class Derived>
534 const Scalar tx = Scalar(2)*this->x();
535 const Scalar ty = Scalar(2)*this->y();
536 const Scalar tz = Scalar(2)*this->z();
537 const Scalar twx = tx*this->w();
538 const Scalar twy = ty*this->w();
539 const Scalar twz = tz*this->w();
540 const Scalar txx = tx*this->x();
541 const Scalar txy = ty*this->x();
542 const Scalar txz = tz*this->x();
543 const Scalar tyy = ty*this->y();
544 const Scalar tyz = tz*this->y();
545 const Scalar tzz = tz*this->z();
547 res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);
548 res.coeffRef(0,1) = txy-twz;
549 res.coeffRef(0,2) = txz+twy;
550 res.coeffRef(1,0) = txy+twz;
551 res.coeffRef(1,1) = Scalar(1)-(txx+tzz);
552 res.coeffRef(1,2) = tyz-twx;
553 res.coeffRef(2,0) = txz-twy;
554 res.coeffRef(2,1) = tyz+twx;
555 res.coeffRef(2,2) = Scalar(1)-(txx+tyy);
570 template<
class Derived>
571 template<
typename Derived1,
typename Derived2>
577 Scalar c = v1.dot(v0);
589 c = numext::maxi(c,Scalar(-1));
592 Vector3 axis = svd.
matrixV().col(2);
594 Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
595 this->w() = sqrt(w2);
596 this->vec() = axis * sqrt(Scalar(1) - w2);
599 Vector3 axis = v0.cross(v1);
600 Scalar s = sqrt((Scalar(1)+c)*Scalar(2));
601 Scalar invs = Scalar(1)/s;
602 this->vec() = axis * invs;
603 this->w() = s * Scalar(0.5);
619 template<
typename Scalar,
int Options>
620 template<
typename Derived1,
typename Derived2>
624 quat.setFromTwoVectors(a, b);
635 template <
class Derived>
639 Scalar n2 = this->squaredNorm();
651 template<
int Arch,
class Derived,
typename Scalar,
int _Options>
struct quat_conj
665 template <
class Derived>
666 inline Quaternion<typename internal::traits<Derived>::Scalar>
669 return internal::quat_conj<Architecture::Target, Derived,
670 typename internal::traits<Derived>::Scalar,
671 internal::traits<Derived>::Alignment>::run(*
this);
678 template <
class Derived>
679 template <
class OtherDerived>
680 inline typename internal::traits<Derived>::Scalar
686 return Scalar(2) * atan2( d.vec().norm(), abs(d.w()) );
697 template <
class Derived>
698 template <
class OtherDerived>
706 Scalar d = this->dot(other);
707 Scalar absD = abs(d);
714 scale0 = Scalar(1) - t;
720 Scalar theta = acos(absD);
721 Scalar sinTheta = sin(theta);
723 scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;
724 scale1 = sin( ( t * theta) ) / sinTheta;
726 if(d<Scalar(0)) scale1 = -scale1;
734 template<
typename Other>
735 struct quaternionbase_assign_impl<Other,3,3>
737 typedef typename Other::Scalar Scalar;
743 Scalar t = mat.trace();
746 t = sqrt(t + Scalar(1.0));
747 q.w() = Scalar(0.5)*t;
749 q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
750 q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
751 q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
756 if (mat.coeff(1,1) > mat.coeff(0,0))
758 if (mat.coeff(2,2) > mat.coeff(i,i))
763 t = sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
764 q.coeffs().coeffRef(i) = Scalar(0.5) * t;
766 q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
767 q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
768 q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
774 template<
typename Other>
775 struct quaternionbase_assign_impl<Other,4,1>
777 typedef typename Other::Scalar Scalar;
778 template<
class Derived>
static inline void run(QuaternionBase<Derived>& q,
const Other& vec)
788 #endif // EIGEN_QUATERNION_H
Scalar x() const
Definition: Quaternion.h:61
Scalar dot(const QuaternionBase< OtherDerived > &other) const
Definition: Quaternion.h:134
Vector3 _transformVector(const Vector3 &v) const
Definition: Quaternion.h:465
Scalar y() const
Definition: Quaternion.h:63
Scalar norm() const
Definition: Quaternion.h:120
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:89
Matrix< Scalar, 3, 1 > Vector3
Definition: Quaternion.h:52
Quaternion< double > Quaterniond
Definition: Quaternion.h:299
const unsigned int LvalueBit
Definition: Constants.h:130
const VectorBlock< const Coefficients, 3 > vec() const
Definition: Quaternion.h:79
internal::cast_return_type< Derived, Quaternion< NewScalarType > >::type cast() const
Definition: Quaternion.h:173
const internal::traits< Derived >::Coefficients & coeffs() const
Definition: Quaternion.h:85
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:107
AngleAxis< Scalar > AngleAxisType
Definition: Quaternion.h:56
Scalar z() const
Definition: Quaternion.h:65
Quaternion()
Definition: Quaternion.h:242
Derived & operator*=(const QuaternionBase< OtherDerived > &q)
Definition: Quaternion.h:450
Definition: Constants.h:318
static Quaternion< Scalar > Identity()
Definition: Quaternion.h:106
Scalar squaredNorm() const
Definition: Quaternion.h:115
Map(const Scalar *coeffs)
Definition: Quaternion.h:354
void normalize()
Definition: Quaternion.h:124
Derived & setFromTwoVectors(const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
Definition: Quaternion.h:572
Expression of a fixed-size or dynamic-size sub-vector.
Definition: ForwardDeclarations.h:87
internal::traits< Derived >::Coefficients & coeffs()
Definition: Quaternion.h:88
Scalar & x()
Definition: Quaternion.h:70
Map(Scalar *coeffs)
Definition: Quaternion.h:391
bool isApprox(const QuaternionBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: Quaternion.h:161
const PlainObject normalized() const
Definition: Dot.h:114
const MatrixVType & matrixV() const
Definition: SVDBase.h:99
Quaternion(const Quaternion< OtherScalar, OtherOptions > &other)
Definition: Quaternion.h:271
Quaternion< Scalar > conjugate() const
Definition: Quaternion.h:667
Scalar & z()
Definition: Quaternion.h:74
Base class for quaternion expressions.
Definition: ForwardDeclarations.h:264
Quaternion< Scalar > inverse() const
Definition: Quaternion.h:636
Map< Quaternion< float >, 0 > QuaternionMapf
Definition: Quaternion.h:402
Definition: Eigen_Colamd.h:54
Quaternion(const AngleAxisType &aa)
Definition: Quaternion.h:260
The quaternion class used to represent 3D orientations and rotations.
Definition: ForwardDeclarations.h:270
Quaternion(const MatrixBase< Derived > &other)
Definition: Quaternion.h:267
Map< Quaternion< double >, 0 > QuaternionMapd
Definition: Quaternion.h:405
Two-sided Jacobi SVD decomposition of a rectangular matrix.
Definition: ForwardDeclarations.h:254
Scalar w() const
Definition: Quaternion.h:67
Matrix3 toRotationMatrix() const
Definition: Quaternion.h:526
Map< Quaternion< float >, Aligned > QuaternionMapAlignedf
Definition: Quaternion.h:408
QuaternionBase & setIdentity()
Definition: Quaternion.h:110
Scalar & w()
Definition: Quaternion.h:76
Quaternion< Scalar > normalized() const
Definition: Quaternion.h:127
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:379
Definition: Constants.h:227
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:266
Quaternion(const Scalar *data)
Definition: Quaternion.h:254
Quaternion< float > Quaternionf
Definition: Quaternion.h:296
Map< Quaternion< double >, Aligned > QuaternionMapAlignedd
Definition: Quaternion.h:411
Quaternion(const QuaternionBase< Derived > &other)
Definition: Quaternion.h:257