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)
282 #ifdef EIGEN_QUATERNION_PLUGIN
283 # include EIGEN_QUATERNION_PLUGIN
287 Coefficients m_coeffs;
289 #ifndef EIGEN_PARSED_BY_DOXYGEN
290 static EIGEN_STRONG_INLINE
void _check_template_params()
292 EIGEN_STATIC_ASSERT( (_Options &
DontAlign) == _Options,
293 INVALID_MATRIX_TEMPLATE_PARAMETERS)
310 template<
typename _Scalar,
int _Options>
311 struct traits<Map<Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
318 template<
typename _Scalar,
int _Options>
319 struct traits<Map<const Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
321 typedef Map<const Matrix<_Scalar,4,1>, _Options> Coefficients;
322 typedef traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> > TraitsBase;
340 template<
typename _Scalar,
int _Options>
342 :
public QuaternionBase<Map<const Quaternion<_Scalar>, _Options> >
347 typedef _Scalar Scalar;
348 typedef typename internal::traits<Map>::Coefficients Coefficients;
349 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(
Map)
350 using Base::operator*=;
358 explicit EIGEN_STRONG_INLINE
Map(
const Scalar* coeffs) : m_coeffs(coeffs) {}
360 inline const Coefficients& coeffs()
const {
return m_coeffs;}
363 const Coefficients m_coeffs;
377 template<
typename _Scalar,
int _Options>
384 typedef _Scalar Scalar;
385 typedef typename internal::traits<Map>::Coefficients Coefficients;
386 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(
Map)
387 using Base::operator*=;
395 explicit EIGEN_STRONG_INLINE
Map(Scalar* coeffs) : m_coeffs(coeffs) {}
397 inline Coefficients& coeffs() {
return m_coeffs; }
398 inline const Coefficients& coeffs()
const {
return m_coeffs; }
401 Coefficients m_coeffs;
424 template<
int Arch,
class Derived1,
class Derived2,
typename Scalar,
int _Options>
struct quat_product
429 a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
430 a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
431 a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
432 a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
439 template <
class Derived>
440 template <
class OtherDerived>
441 EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar>
444 EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value),
445 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
446 return internal::quat_product<Architecture::Target, Derived, OtherDerived,
447 typename internal::traits<Derived>::Scalar,
448 EIGEN_PLAIN_ENUM_MIN(internal::traits<Derived>::Alignment, internal::traits<OtherDerived>::Alignment)>::run(*
this, other);
452 template <
class Derived>
453 template <
class OtherDerived>
456 derived() = derived() * other.derived();
467 template <
class Derived>
476 Vector3 uv = this->vec().cross(v);
478 return v + this->w() * uv + this->vec().cross(uv);
481 template<
class Derived>
484 coeffs() = other.coeffs();
488 template<
class Derived>
489 template<
class OtherDerived>
490 EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(
const QuaternionBase<OtherDerived>& other)
492 coeffs() = other.coeffs();
498 template<
class Derived>
503 Scalar ha = Scalar(0.5)*aa.
angle();
505 this->vec() = sin(ha) * aa.
axis();
515 template<
class Derived>
516 template<
class MatrixDerived>
519 EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),
520 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
521 internal::quaternionbase_assign_impl<MatrixDerived>::run(*
this, xpr.derived());
528 template<
class Derived>
538 const Scalar tx = Scalar(2)*this->x();
539 const Scalar ty = Scalar(2)*this->y();
540 const Scalar tz = Scalar(2)*this->z();
541 const Scalar twx = tx*this->w();
542 const Scalar twy = ty*this->w();
543 const Scalar twz = tz*this->w();
544 const Scalar txx = tx*this->x();
545 const Scalar txy = ty*this->x();
546 const Scalar txz = tz*this->x();
547 const Scalar tyy = ty*this->y();
548 const Scalar tyz = tz*this->y();
549 const Scalar tzz = tz*this->z();
551 res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);
552 res.coeffRef(0,1) = txy-twz;
553 res.coeffRef(0,2) = txz+twy;
554 res.coeffRef(1,0) = txy+twz;
555 res.coeffRef(1,1) = Scalar(1)-(txx+tzz);
556 res.coeffRef(1,2) = tyz-twx;
557 res.coeffRef(2,0) = txz-twy;
558 res.coeffRef(2,1) = tyz+twx;
559 res.coeffRef(2,2) = Scalar(1)-(txx+tyy);
574 template<
class Derived>
575 template<
typename Derived1,
typename Derived2>
581 Scalar c = v1.dot(v0);
593 c = numext::maxi(c,Scalar(-1));
596 Vector3 axis = svd.
matrixV().col(2);
598 Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
599 this->w() = sqrt(w2);
600 this->vec() = axis * sqrt(Scalar(1) - w2);
603 Vector3 axis = v0.cross(v1);
604 Scalar s = sqrt((Scalar(1)+c)*Scalar(2));
605 Scalar invs = Scalar(1)/s;
606 this->vec() = axis * invs;
607 this->w() = s * Scalar(0.5);
623 template<
typename Scalar,
int Options>
624 template<
typename Derived1,
typename Derived2>
628 quat.setFromTwoVectors(a, b);
639 template <
class Derived>
643 Scalar n2 = this->squaredNorm();
655 template<
int Arch,
class Derived,
typename Scalar,
int _Options>
struct quat_conj
669 template <
class Derived>
670 inline Quaternion<typename internal::traits<Derived>::Scalar>
673 return internal::quat_conj<Architecture::Target, Derived,
674 typename internal::traits<Derived>::Scalar,
675 internal::traits<Derived>::Alignment>::run(*
this);
682 template <
class Derived>
683 template <
class OtherDerived>
684 inline typename internal::traits<Derived>::Scalar
690 return Scalar(2) * atan2( d.vec().norm(), abs(d.w()) );
701 template <
class Derived>
702 template <
class OtherDerived>
710 Scalar d = this->dot(other);
711 Scalar absD = abs(d);
718 scale0 = Scalar(1) - t;
724 Scalar theta = acos(absD);
725 Scalar sinTheta = sin(theta);
727 scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;
728 scale1 = sin( ( t * theta) ) / sinTheta;
730 if(d<Scalar(0)) scale1 = -scale1;
738 template<
typename Other>
739 struct quaternionbase_assign_impl<Other,3,3>
741 typedef typename Other::Scalar Scalar;
744 const typename internal::nested_eval<Other,2>::type mat(a_mat);
748 Scalar t = mat.trace();
751 t = sqrt(t + Scalar(1.0));
752 q.w() = Scalar(0.5)*t;
754 q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
755 q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
756 q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
761 if (mat.coeff(1,1) > mat.coeff(0,0))
763 if (mat.coeff(2,2) > mat.coeff(i,i))
768 t = sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
769 q.coeffs().coeffRef(i) = Scalar(0.5) * t;
771 q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
772 q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
773 q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
779 template<
typename Other>
780 struct quaternionbase_assign_impl<Other,4,1>
782 typedef typename Other::Scalar Scalar;
783 template<
class Derived>
static inline void run(QuaternionBase<Derived>& q,
const Other& vec)
793 #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:469
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
Scalar angle() const
Definition: AngleAxis.h:89
Quaternion< double > Quaterniond
Definition: Quaternion.h:303
const unsigned int LvalueBit
Definition: Constants.h:138
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:454
static Quaternion< Scalar > Identity()
Definition: Quaternion.h:106
Scalar squaredNorm() const
Definition: Quaternion.h:115
Map(const Scalar *coeffs)
Definition: Quaternion.h:358
const Vector3 & axis() const
Definition: AngleAxis.h:94
void normalize()
Definition: Quaternion.h:124
Derived & setFromTwoVectors(const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
Definition: Quaternion.h:576
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:395
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:671
Scalar & z()
Definition: Quaternion.h:74
Base class for quaternion expressions.
Definition: ForwardDeclarations.h:265
Quaternion< Scalar > inverse() const
Definition: Quaternion.h:640
Map< Quaternion< float >, 0 > QuaternionMapf
Definition: Quaternion.h:406
Definition: Eigen_Colamd.h:54
Definition: Constants.h:326
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:409
Two-sided Jacobi SVD decomposition of a rectangular matrix.
Definition: ForwardDeclarations.h:255
Scalar w() const
Definition: Quaternion.h:67
Matrix3 toRotationMatrix() const
Definition: Quaternion.h:530
Map< Quaternion< float >, Aligned > QuaternionMapAlignedf
Definition: Quaternion.h:412
QuaternionBase & setIdentity()
Definition: Quaternion.h:110
Scalar & w()
Definition: Quaternion.h:76
Definition: Constants.h:235
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:387
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:267
Quaternion(const Scalar *data)
Definition: Quaternion.h:254
Quaternion< float > Quaternionf
Definition: Quaternion.h:300
Map< Quaternion< double >, Aligned > QuaternionMapAlignedd
Definition: Quaternion.h:415
Quaternion(const QuaternionBase< Derived > &other)
Definition: Quaternion.h:257