mrob::SE3 Class Reference

Inheritance diagram for mrob::SE3:

Public Member Functions
	SE3 (const Mat4 &T=Mat4::Identity())
	SE3 (const Mat61 &xi)
	SE3 (const SE3 &T)
	SE3 (const SO3 &R, const Mat31 &t)
	SE3 (const Mat3 &R, const Mat31 &t)
template<typename OtherDerived >
	SE3 (const Eigen::MatrixBase< OtherDerived > &rhs)
SE3 &	operator= (const SE3 &rhs)
SE3	operator* (const SE3 &rhs) const
SE3	mul (const SE3 &rhs) const
void	update_lhs (const Mat61 &dxi)
void	update_rhs (const Mat61 &dxi)
void	exp (const Mat4 &xi_hat)
Mat4	ln (void) const
Mat61	ln_vee () const
Mat31	transform (const Mat31 &p) const
MatX	transform_array (const MatX &P) const
SE3	inv (void) const
Mat6	adj () const
const Eigen::Ref< const Mat4 >	T () const
Mat4 &	ref2T ()
Mat3	R () const
Mat31	t () const
double	distance (const SE3 &rhs=SE3()) const
double	distance_rotation (const SE3 &rhs=SE3()) const
double	distance_trans (const SE3 &rhs=SE3()) const
void	regenerate ()
Mat41	transform_plane (const Mat41 &pi)
void	print (void) const
void	print_lie (void) const
std::string	toString () const
	Generates string representation of the object. More...

Protected Attributes
Mat4	T_

Constructor & Destructor Documentation

SE3() [1/6]

SE3::SE3

(

const Mat4 &

T = Mat4::Identity()

)

Constructor, requires the Transformation matrix 4x4

SE3() [2/6]

SE3::SE3

(

const Mat61 &

xi

)

Constructor, requires the Lie algebra xi^ se3 representing the rigid body transformation around the identity, by default generates T = exp(0^) = I

SE3() [3/6]

SE3::SE3

(

const SE3 &

T

)

Constructor, requires the Transformation in Se3

SE3() [4/6]

SE3::SE3	(	const SO3 &	R,
		const Mat31 &	t
	)

Constructor, requires the Rotation in SO3 and translation

SE3() [5/6]

SE3::SE3	(	const Mat3 &	R,
		const Mat31 &	t
	)

Constructor, requires the Rotation as a 3x3 matrix and translation

SE3() [6/6]

template<typename OtherDerived >

SE3::SE3

(

const Eigen::MatrixBase< OtherDerived > &

rhs

)

This constructor allows to construct from Eigen expressions Eigen suggestion: TopicCustomizingEigen.html

Member Function Documentation

adj()

Mat6 SE3::adj

(

)

const

Adjoint: T Exp(x) = Exp ( Adj_T x) T Adj_T = [R , 0] [t^R, R]

distance()

double SE3::distance

(

const SE3 &

rhs = SE3()

)

const

Provide the distance as a norm on the tangent space of the ln(T * T_rhs^{-1})

distance_rotation()

double SE3::distance_rotation

(

const SE3 &

rhs = SE3()

)

const

Provide the distance on the rotation in the tangent space of the ln(R * R_rhs^{-1})

distance_trans()

double SE3::distance_trans

(

const SE3 &

rhs = SE3()

)

const

Provide the distance of the translation part ||t - t'||

exp()

void SE3::exp

(

const Mat4 &

xi_hat

)

Exponential mapping of a skew symetric matrix in se3. exp(xi^) = [exp(w^) Vv], where exp(w^) is the so3_exp and V = I + c2*(w^) + c3*(w^)^2 , where o = norm(w), c2 = (1 - cos(o))/o^2, c3 = (o- sin(o) / o^3 t= Vv Exponential mapping of a skew symetric matrix in so3. The Rodrigues formula provides an exact solution to the Taylor expansion of exp(A) = I + A + c2*A^2 + ... exp(A) = I + c1*w^ + c2*(w^)^2, where o = norm(w), c1 =sin(o)/o and c2 = (1 - cos(o))/o^2

inv()

SE3 SE3::inv

(

void

)

const

Inverse: T^-1 = [R', -R't] [0 1]

ln()

Mat4 SE3::ln

(

void

)

const

Logarithm map, first we calculate ln(R) and then V^-1 = I - 1/2 w^ + 1/o^2(1 - A / 2B) (w^)^2 v = V^-1 t

ln_vee()

Mat61 SE3::ln_vee

(

)

const

Returns the vector xi R^6 which corresponds to the Lie algebra se3

mul()

SE3 SE3::mul

(

const SE3 &

rhs

)

const

Multiplication function, same as above, mainly for python

operator*()

SE3 SE3::operator*

(

const SE3 &

rhs

)

const

This method allows you to Multiply SE3 expressions

operator=()

SE3 & SE3::operator=

(

const SE3 &

rhs

)

This method allows you to assign Eigen expressions to SE3

R()

Mat3 SE3::R

(

)

const

R method returns a matrix 3x3 of the SO3 rotation corresponding to the subblock matrix

ref2T()

Mat4 & SE3::ref2T

(

)

ref2T returns a non-const reference to the matrix T to modify its content directly

regenerate()

void SE3::regenerate

(

)

Regenerate, does the following operation: T = Exp ( Ln(T) )

T()

const Eigen::Ref< const Mat4 > SE3::T

(

)

const

T method returns a matrix 4x4 of the SE3 transformation. Ref<> is more convinient than the matrix for the factor/nodes base class definitions and python bindings

t()

Mat31 SE3::t

(

)

const

t method returns translation

toString()

std::string SE3::toString

(

)

const

Generates string representation of the object.

Returns

std::string object to print

transform()

Mat31 SE3::transform

(

const Mat31 &

p

)

const

Transforms a point p = (x,y,z)' such as res = T*p. This function saves to transform to homogeneous coordinates.

transform_array()

MatX SE3::transform_array

(

const MatX &

P

)

const

Transforms an array of points P = {p_n} = (x,y,z)'_n such as res = T*p_n. The array is of the form Nx3 (usual convention from arrays) This function saves to transform to homogeneous coordinates.

update_lhs()

void SE3::update_lhs

(

const Mat61 &

dxi

)

This is our default way to update transformations, from the Left hand side of T Updates the current transformation with the incremental dxi se3 T'=exp(dxi^) * T

update_rhs()

void SE3::update_rhs

(

const Mat61 &

dxi

)

Updates the current transformation with the incremental dxi se3 T'= T * exp(dxi^)

---

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

• src/geometry/mrob/SE3.hpp
• src/geometry/SE3.cpp