11#ifndef EIGEN_QUATERNION_H
12#define EIGEN_QUATERNION_H
22template<
typename Other,
23 int OtherRows=Other::RowsAtCompileTime,
24 int OtherCols=Other::ColsAtCompileTime>
25struct quaternionbase_assign_impl;
34template<
class Derived>
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(); }
120 EIGEN_DEVICE_FUNC
inline Scalar
norm()
const {
return coeffs().norm(); }
142 template<
typename Derived1,
typename Derived2>
160 template<
class OtherDerived>
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
213template<
typename _Scalar,
int _Options>
214struct 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,
226template<
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;
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) {}
266 template<
typename Derived>
270 template<
typename OtherScalar,
int OtherOptions>
272 { m_coeffs = other.coeffs().template cast<Scalar>(); }
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> >
323 typedef Map<const Matrix<_Scalar,4,1>, _Options> Coefficients;
326 Flags = TraitsBase::Flags & ~LvalueBit
342template<
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;
379template<
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;
426template<
int Arch,
class Derived1,
class Derived2,
typename Scalar,
int _Options>
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()
441template <
class Derived>
442template <
class OtherDerived>
443EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar>
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,
450 EIGEN_PLAIN_ENUM_MIN(internal::traits<Derived>::Alignment, internal::traits<OtherDerived>::Alignment)>::run(*
this, other);
454template <
class Derived>
455template <
class OtherDerived>
458 derived() = derived() * other.derived();
469template <
class Derived>
478 Vector3 uv = this->vec().cross(v);
480 return v + this->w() * uv + this->vec().cross(uv);
483template<
class Derived>
486 coeffs() = other.
coeffs();
490template<
class Derived>
491template<
class OtherDerived>
492EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(
const QuaternionBase<OtherDerived>& other)
494 coeffs() = other.coeffs();
500template<
class Derived>
503 EIGEN_USING_STD_MATH(cos)
504 EIGEN_USING_STD_MATH(sin)
505 Scalar ha = Scalar(0.5)*aa.
angle();
507 this->vec() = sin(ha) * aa.
axis();
517template<
class Derived>
518template<
class MatrixDerived>
521 EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),
522 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
523 internal::quaternionbase_assign_impl<MatrixDerived>::run(*
this, xpr.
derived());
530template<
class Derived>
540 const Scalar tx = Scalar(2)*this->x();
541 const Scalar ty = Scalar(2)*this->y();
542 const Scalar tz = Scalar(2)*this->z();
543 const Scalar twx = tx*this->w();
544 const Scalar twy = ty*this->w();
545 const Scalar twz = tz*this->w();
546 const Scalar txx = tx*this->x();
547 const Scalar txy = ty*this->x();
548 const Scalar txz = tz*this->x();
549 const Scalar tyy = ty*this->y();
550 const Scalar tyz = tz*this->y();
551 const Scalar tzz = tz*this->z();
553 res.
coeffRef(0,0) = Scalar(1)-(tyy+tzz);
557 res.
coeffRef(1,1) = Scalar(1)-(txx+tzz);
561 res.
coeffRef(2,2) = Scalar(1)-(txx+tyy);
576template<
class Derived>
577template<
typename Derived1,
typename Derived2>
580 EIGEN_USING_STD_MATH(sqrt)
583 Scalar c = v1.dot(v0);
595 c = numext::maxi(c,Scalar(-1));
600 Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
601 this->w() = sqrt(w2);
602 this->vec() = axis * sqrt(Scalar(1) - w2);
606 Scalar s = sqrt((Scalar(1)+c)*Scalar(2));
607 Scalar invs = Scalar(1)/s;
608 this->vec() = axis * invs;
609 this->w() = s * Scalar(0.5);
618template<
typename Scalar,
int Options>
621 EIGEN_USING_STD_MATH(sqrt)
622 EIGEN_USING_STD_MATH(sin)
623 EIGEN_USING_STD_MATH(cos)
624 const Scalar u1 = internal::random<Scalar>(0, 1),
625 u2 = internal::random<Scalar>(0, 2*EIGEN_PI),
626 u3 = internal::random<Scalar>(0, 2*EIGEN_PI);
627 const Scalar a = sqrt(1 - u1),
629 return Quaternion (a * sin(u2), a * cos(u2), b * sin(u3), b * cos(u3));
643template<
typename Scalar,
int Options>
644template<
typename Derived1,
typename Derived2>
659template <
class Derived>
663 Scalar n2 = this->squaredNorm();
675template<
int Arch,
class Derived,
typename Scalar,
int _Options>
struct quat_conj
689template <
class Derived>
690EIGEN_DEVICE_FUNC
inline Quaternion<typename internal::traits<Derived>::Scalar>
693 return internal::quat_conj<Architecture::Target, Derived,
694 typename internal::traits<Derived>::Scalar,
695 internal::traits<Derived>::Alignment>::run(*
this);
702template <
class Derived>
703template <
class OtherDerived>
704EIGEN_DEVICE_FUNC
inline typename internal::traits<Derived>::Scalar
707 EIGEN_USING_STD_MATH(atan2)
709 return Scalar(2) * atan2( d.
vec().norm(), numext::abs(d.
w()) );
720template <
class Derived>
721template <
class OtherDerived>
725 EIGEN_USING_STD_MATH(
acos)
726 EIGEN_USING_STD_MATH(sin)
728 Scalar d = this->dot(other);
729 Scalar absD = numext::abs(d);
736 scale0 = Scalar(1) - t;
742 Scalar theta =
acos(absD);
743 Scalar sinTheta = sin(theta);
745 scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;
746 scale1 = sin( ( t * theta) ) / sinTheta;
748 if(d<Scalar(0)) scale1 = -scale1;
756template<
typename Other>
757struct quaternionbase_assign_impl<Other,3,3>
759 typedef typename Other::Scalar Scalar;
760 template<
class Derived> EIGEN_DEVICE_FUNC
static inline void run(
QuaternionBase<Derived>& q,
const Other& a_mat)
762 const typename internal::nested_eval<Other,2>::type mat(a_mat);
763 EIGEN_USING_STD_MATH(sqrt)
766 Scalar t = mat.trace();
769 t = sqrt(t + Scalar(1.0));
770 q.
w() = Scalar(0.5)*t;
772 q.
x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
773 q.
y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
774 q.
z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
779 if (mat.coeff(1,1) > mat.coeff(0,0))
781 if (mat.coeff(2,2) > mat.coeff(i,i))
786 t = sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
787 q.
coeffs().coeffRef(i) = Scalar(0.5) * t;
789 q.
w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
790 q.
coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
791 q.
coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
797template<
typename Other>
798struct quaternionbase_assign_impl<Other,4,1>
800 typedef typename Other::Scalar Scalar;
801 template<
class Derived> EIGEN_DEVICE_FUNC
static inline void run(QuaternionBase<Derived>& q,
const Other& vec)
Represents a 3D rotation as a rotation angle around an arbitrary 3D axis.
Definition: AngleAxis.h:50
Scalar angle() const
Definition: AngleAxis.h:91
const Vector3 & axis() const
Definition: AngleAxis.h:96
Derived & derived()
Definition: EigenBase.h:44
Two-sided Jacobi SVD decomposition of a rectangular matrix.
Definition: JacobiSVD.h:485
Map(Scalar *coeffs)
Definition: Quaternion.h:397
Map(const Scalar *coeffs)
Definition: Quaternion.h:360
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:90
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
const PlainObject normalized() const
Definition: Dot.h:118
The matrix class, also used for vectors and row-vectors.
Definition: Matrix.h:180
Scalar & coeffRef(Index rowId, Index colId)
Definition: PlainObjectBase.h:177
Base class for quaternion expressions.
Definition: Quaternion.h:36
Scalar y() const
Definition: Quaternion.h:63
Scalar squaredNorm() const
Definition: Quaternion.h:115
Scalar & y()
Definition: Quaternion.h:72
QuaternionBase & setIdentity()
Definition: Quaternion.h:110
Quaternion< Scalar > normalized() const
Definition: Quaternion.h:127
internal::traits< Derived >::Coefficients & coeffs()
Definition: Quaternion.h:88
internal::cast_return_type< Derived, Quaternion< NewScalarType > >::type cast() const
Definition: Quaternion.h:173
VectorBlock< Coefficients, 3 > vec()
Definition: Quaternion.h:82
const VectorBlock< const Coefficients, 3 > vec() const
Definition: Quaternion.h:79
static Quaternion< Scalar > Identity()
Definition: Quaternion.h:106
Scalar w() const
Definition: Quaternion.h:67
Quaternion< Scalar > conjugate() const
Definition: Quaternion.h:691
bool isApprox(const QuaternionBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: Quaternion.h:161
Scalar & z()
Definition: Quaternion.h:74
void normalize()
Definition: Quaternion.h:124
Derived & setFromTwoVectors(const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
Definition: Quaternion.h:578
Scalar & x()
Definition: Quaternion.h:70
Matrix3 toRotationMatrix() const
Definition: Quaternion.h:532
Matrix< Scalar, 3, 1 > Vector3
Definition: Quaternion.h:52
Scalar dot(const QuaternionBase< OtherDerived > &other) const
Definition: Quaternion.h:134
Derived & operator=(const AngleAxisType &aa)
Definition: Quaternion.h:501
Vector3 _transformVector(const Vector3 &v) const
Definition: Quaternion.h:471
Scalar norm() const
Definition: Quaternion.h:120
Quaternion< Scalar > inverse() const
Definition: Quaternion.h:660
Scalar z() const
Definition: Quaternion.h:65
Matrix< Scalar, 3, 3 > Matrix3
Definition: Quaternion.h:54
const internal::traits< Derived >::Coefficients & coeffs() const
Definition: Quaternion.h:85
AngleAxis< Scalar > AngleAxisType
Definition: Quaternion.h:56
Scalar x() const
Definition: Quaternion.h:61
Scalar & w()
Definition: Quaternion.h:76
Derived & operator*=(const QuaternionBase< OtherDerived > &q)
Definition: Quaternion.h:456
The quaternion class used to represent 3D orientations and rotations.
Definition: Quaternion.h:228
Quaternion(const QuaternionBase< Derived > &other)
Definition: Quaternion.h:257
static Quaternion UnitRandom()
Definition: Quaternion.h:619
Quaternion(const AngleAxisType &aa)
Definition: Quaternion.h:260
Quaternion(const Quaternion< OtherScalar, OtherOptions > &other)
Definition: Quaternion.h:271
Quaternion(const MatrixBase< Derived > &other)
Definition: Quaternion.h:267
Quaternion()
Definition: Quaternion.h:242
Quaternion(const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)
Definition: Quaternion.h:251
Quaternion(const Scalar *data)
Definition: Quaternion.h:254
Common base class for compact rotation representations.
Definition: RotationBase.h:30
friend RotationMatrixType operator*(const EigenBase< OtherDerived > &l, const Derived &r)
Definition: RotationBase.h:76
const MatrixVType & matrixV() const
Definition: SVDBase.h:99
Expression of a fixed-size or dynamic-size sub-vector.
Definition: VectorBlock.h:60
@ Aligned
Definition: Constants.h:235
@ DontAlign
Definition: Constants.h:326
@ AutoAlign
Definition: Constants.h:324
@ ComputeFullV
Definition: Constants.h:387
const unsigned int LvalueBit
Definition: Constants.h:139
Namespace containing all symbols from the Eigen library.
Definition: Core:287
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_acos_op< typename Derived::Scalar >, const Derived > acos(const Eigen::ArrayBase< Derived > &x)
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:151