Storage implementation of SE3 Lie group. More...

#include <se3.hpp>

Inheritance diagram for SE3< _Scalar >:

[legend]

Public Member Functions
template<typename SO3Derived , typename T3Derived >
	SE3 (const SO3Base< SO3Derived > &so3, const Eigen::MatrixBase< T3Derived > &r3)
	Construct from SO3 and translation.

	SE3 (const Eigen::Transform< Scalar, 3, Eigen::Isometry > &t)
	Construct from Eigen transform.

Public Member Functions inherited from SE3Base< SE3< _Scalar > >
Map< SO3< Scalar > >	so3 ()
	Access SO(3) part.

Map< const SO3< Scalar > >	so3 () const
	Const access SO(3) part.

Eigen::Map< Eigen::Vector3< Scalar > >	r3 ()
	Access R3 part.

Eigen::Map< const Eigen::Vector3< Scalar > >	r3 () const
	Const access R3 part.

Eigen::Transform< Scalar, 3, Eigen::Isometry >	isometry () const
	Return as 3D Eigen transform.

Eigen::Vector3< Scalar >	operator* (const Eigen::MatrixBase< EigenDerived > &v) const
	Tranformation action on 3D vector.

Eigen::Matrix< Scalar, 3, 6 >	dr_action (const Eigen::MatrixBase< EigenDerived > &v) const
	Jacobian of rotation action w.r.t. group.

SE2< Scalar >	project_se2 () const
	Project to SE2.

Public Member Functions inherited from LieGroupBase< Derived >
template<bool = true> requires (is_mutable)
auto &	coeffs () const
	Access underlying storages.

const auto &	coeffs () const
	Const access underlying storages.

template<bool = true> requires (is_mutable)
auto *	data () const
	Access raw pointer.

const auto *	data () const
	Const access raw pointer.

template<typename OtherDerived > requires (is_mutable && std::is_same_v<Impl, typename liebase_info<OtherDerived>::Impl>)
Derived &	operator= (const LieGroupBase< OtherDerived > &o) noexcept

Eigen::Index	dof () const noexcept
	Dynamic size (degrees of freedom).

void	setIdentity () noexcept
	Set to group identity element.

void	setRandom () noexcept
	Set to a random element.

Matrix	matrix () const noexcept
	Return as matrix Lie group element in \( \mathbb{R}^{\mathtt{dim} \times \mathtt{dim}} \).

template<typename OtherDerived > requires (std::is_same_v<Impl, typename liebase_info<OtherDerived>::Impl>)
bool	isApprox (const LieGroupBase< OtherDerived > &o, const Scalar &eps=Eigen::NumTraits< Scalar >::dummy_precision()) const noexcept
	Check if (approximately) equal to other element `o`.

template<typename NewScalar >
CastT< NewScalar >	cast () const noexcept
	Cast to different scalar type.

template<typename OtherDerived > requires (std::is_same_v<Impl, typename liebase_info<OtherDerived>::Impl>)
PlainObject	operator* (const LieGroupBase< OtherDerived > &o) const noexcept
	Group binary composition operation.

template<typename OtherDerived > requires (is_mutable && std::is_same_v<Impl, typename liebase_info<OtherDerived>::Impl>)
Derived &	operator*= (const LieGroupBase< OtherDerived > &o) noexcept
	Inplace group binary composition operation.

PlainObject	inverse () const noexcept
	Group inverse operation.

Tangent	log () const noexcept
	Lie group logarithm.

TangentMap	Ad () const noexcept
	Lie group adjoint.

template<typename TangentDerived >
PlainObject	operator+ (const Eigen::MatrixBase< TangentDerived > &a) const noexcept
	Right-plus.

template<typename TangentDerived > requires (is_mutable)
Derived &	operator+= (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Inplace right-plus: \( \mathbf{x} \leftarrow \mathbf{x} \circ \exp(\mathbf{a}) \).

template<typename OtherDerived > requires (std::is_same_v<Impl, typename liebase_info<OtherDerived>::Impl>)
Tangent	operator- (const LieGroupBase< OtherDerived > &xo) const noexcept
	Right-minus.

Additional Inherited Members
Public Types inherited from LieGroupBase< Derived >
using	Scalar = typename traits::Scalar
	Scalar type.

using	Matrix = Eigen::Matrix< Scalar, Dim, Dim >
	Lie group matrix type.

using	Tangent = Eigen::Matrix< Scalar, Dof, 1 >
	Lie group parameterized tangent type.

using	TangentMap = Eigen::Matrix< Scalar, Dof, Dof >
	Matrix representing map between tangent elements.

using	Hessian = Eigen::Matrix< Scalar, Dof, Dof *Dof >
	Plain return type with different scalar.

template<typename NewScalar >
using	CastT = typename traits::template PlainObject< NewScalar >
	Plain return type with different scalar.

using	PlainObject = CastT< Scalar >
	Plain return type.

Static Public Member Functions inherited from LieGroupBase< Derived >
static PlainObject	Identity () noexcept
	Construct the identity element.

static PlainObject	Random () noexcept
	Construct a random element.

template<typename TangentDerived >
static PlainObject	exp (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Lie group exponential map.

template<typename TangentDerived >
static Matrix	hat (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Lie algebra hat map.

template<typename MatrixDerived >
static Tangent	vee (const Eigen::MatrixBase< MatrixDerived > &A) noexcept
	Lie alebra vee map.

template<typename TangentDerived >
static TangentMap	ad (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Lie algebra adjoint.

template<typename TangentDerived1 , typename TangentDerived2 >
static Tangent	lie_bracket (const Eigen::MatrixBase< TangentDerived1 > &a, const Eigen::MatrixBase< TangentDerived2 > &b) noexcept
	Lie algebra bracket.

template<typename TangentDerived >
static TangentMap	dr_exp (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Right jacobian of the exponential map.

template<typename TangentDerived >
static TangentMap	dr_expinv (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Inverse of right jacobian of the exponential map.

template<typename TangentDerived >
static TangentMap	dl_exp (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Left jacobian of the exponential map.

template<typename TangentDerived >
static TangentMap	dl_expinv (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Inverse of left jacobian of the exponential map.

template<typename TangentDerived >
static Hessian	d2r_exp (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Right Hessian of the exponential map.

template<typename TangentDerived >
static Hessian	d2r_expinv (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Right Hessian of the log map.

template<typename TangentDerived >
static Hessian	d2l_exp (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Left Hessian of the exponential map.

template<typename TangentDerived >
static Hessian	d2l_expinv (const Eigen::MatrixBase< TangentDerived > &a) noexcept
	Left Hessian of the log map.

Public Attributes inherited from SE3Base< SE3< _Scalar > >
	SMOOTH_INHERIT_TYPEDEFS

Static Public Attributes inherited from LieGroupBase< Derived >
static constexpr int	RepSize = Impl::RepSize
	Number of scalars in internal representation.

static constexpr int	Dof = Impl::Dof
	Degrees of freedom of manifold (equal to tangent space dimension).

static constexpr int	Dim = Impl::Dim
	Side of Lie group matrix representation.

static constexpr bool	IsCommutative = Impl::IsCommutative
	Commutativity of group. A commutative group has a zero Lie bracket.

Protected Types inherited from LieGroupBase< Derived >
using	traits = liebase_info< Derived >
	CRTP traits.

using	Impl = typename traits::Impl
	Group-specific Lie group implementation.

Static Protected Attributes inherited from LieGroupBase< Derived >
static constexpr bool	is_mutable = traits::is_mutable
	True if underlying storage supports modification.

Detailed Description

template<typename _Scalar>
class SE3< _Scalar >

Storage implementation of SE3 Lie group.

See also: SE3Base for memory layout.

Definition at line 170 of file se3.hpp.

Constructor & Destructor Documentation

◆ SE3() [1/2]

template<typename _Scalar >

template<typename SO3Derived , typename T3Derived >

SE3< _Scalar >::SE3	(	const SO3Base< SO3Derived > &	so3,
		const Eigen::MatrixBase< T3Derived > &	r3
	)

inline

Construct from SO3 and translation.

Parameters

so3	orientation component.
r3	translation component.

Definition at line 184 of file se3.hpp.

◆ SE3() [2/2]

template<typename _Scalar >

SE3< _Scalar >::SE3 ( const Eigen::Transform< Scalar, 3, Eigen::Isometry > & t )

inlineexplicit

Construct from Eigen transform.

Definition at line 193 of file se3.hpp.

The documentation for this class was generated from the following file:

include/smooth/se3.hpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ SE3() [1/2]

◆ SE3() [2/2]