se3 Class Reference

Lie algebra of SE(3). More...

#include <LieGroup.h>

List of all members.

Public Member Functions
	se3 (int c)
	se3 (scalar c)
	se3 (scalar c0, scalar c1, scalar c2, scalar c3, scalar c4, scalar c5)
const se3 &	operator+ (void) const
se3	operator- (void) const
const se3 &	operator= (const se3 &)
const se3 &	operator= (const Vec3 &v)
const se3 &	operator= (scalar c)
const se3 &	operator+= (const se3 &)
const se3 &	operator+= (const Vec3 &v)
const se3 &	operator-= (const se3 &)
const se3 &	operator*= (scalar c)
se3	operator+ (const se3 &) const
se3	operator- (const se3 &) const
se3	operator* (scalar) const
scalar &	operator[] (int idx)
void	Ad (const SE3 &T, const se3 &V)
void	InvAd (const SE3 &T, const se3 &V)
void	ad (const se3 &V, const se3 &W)
Friends
ostream &	operator<< (ostream &, const se3 &)
se3	operator* (scalar, const se3 &)
scalar	operator* (const dse3 &F, const se3 &V)
scalar	operator* (const se3 &V, const dse3 &F)
SE3	Exp (const se3 &)
se3	Log (const SE3 &)
se3	Ad (const SE3 &T, const se3 &V)
se3	InvAd (const SE3 &T, const se3 &V)
Vec3	MinusLinearAd (const Vec3 &p, const se3 &V)
se3	ad (const se3 &X, const se3 &Y)
dse3	dad (const se3 &V, const dse3 &F)
scalar	SquareSum (const se3 &)
se3	Rotate (const SE3 &T, const se3 &S)
se3	InvRotate (const SE3 &T, const se3 &S)

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Detailed Description

se3 is a class for representing , the Lie algebra of . Geometrically it deals with generalized velocity. The first three elements correspond to angular velocity and the last three elements correspond to linear velocity.

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Constructor & Destructor Documentation

se3::se3

(

int

c

)

[explicit]

constructor : (c, c, c, c, c, c)

se3::se3

(

scalar

c

)

[explicit]

constructor : (c, c, c, c, c, c)

se3::se3	(	scalar	c0,
		scalar	c1,
		scalar	c2,
		scalar	c3,
		scalar	c4,
		scalar	c5
	)			[explicit]

constructor : (c0, c1, c2, c3, c4, c5)

---

Member Function Documentation

const se3 & se3::operator+

(

void

)

const

unary plus operator

se3 se3::operator-

(

void

)

const

unary minus operator

const se3 & se3::operator=

(

const se3 &

s

)

substitution operator

const se3 & se3::operator=

(

const Vec3 &

v

)

fast version of = se3(0, v)

const se3 & se3::operator=

(

scalar

c

)

substitution operator, fast version of = se3(c)

const se3 & se3::operator+=

(

const se3 &

s

)

+= operator

const se3 & se3::operator+=

(

const Vec3 &

v

)

fast version of += se3(0, v)

const se3 & se3::operator-=

(

const se3 &

s

)

-= operator

const se3 & se3::operator*=

(

scalar

c

)

= operator with scalar

se3 se3::operator+

(

const se3 &

s

)

const

addition operator

se3 se3::operator-

(

const se3 &

s

)

const

subtraction operator

se3 se3::operator*

(

scalar

d

)

const

scalar multiplication operator

scalar & se3::operator[]

(

int

idx

)

access to the idx th element.

void se3::Ad	(	const SE3 &	T,
		const se3 &	V
	)

set itself to be Ad(T, V).

void se3::InvAd	(	const SE3 &	T,
		const se3 &	V
	)

set itself to be Ad(Inv(T), V).

void se3::ad	(	const se3 &	V,
		const se3 &	W
	)

set itself to be ad(V, W).

---

Friends And Related Function Documentation

ostream& operator<<	(	ostream &	,
		const se3 &
	)			[friend]

standard output operator

se3 operator*	(	scalar	d,
		const se3 &	s
	)			[friend]

scalar multiplicaiton operator

scalar operator*	(	const dse3 &	F,
		const se3 &	V
	)			[friend]

inner product

Note:

,where .

scalar operator*	(	const se3 &	V,
		const dse3 &	F
	)			[friend]

inner product

SE3 Exp

(

const se3 &

S

)

[friend]

Exponential mapping

se3 Log

(

const SE3 &

T

)

[friend]

Log mapping

se3 Ad	(	const SE3 &	T,
		const se3 &	V
	)			[friend]

adjoint mapping

Note:

, where .

se3 InvAd	(	const SE3 &	T,
		const se3 &	V
	)			[friend]

fast version of Ad(Inv(T), V)

Vec3 MinusLinearAd	(	const Vec3 &	p,
		const se3 &	V
	)			[friend]

get a linear part of Ad(SE3(-p), V).

se3 ad	(	const se3 &	X,
		const se3 &	Y
	)			[friend]

adjoint mapping

Note:

, where .

dse3 dad	(	const se3 &	V,
		const dse3 &	F
	)			[friend]

dual adjoint mapping

Note:

, where .

scalar SquareSum

(

const se3 &

s

)

[friend]

get squared sum of all the elements

se3 Rotate	(	const SE3 &	T,
		const se3 &	S
	)			[friend]

fast version of se3(Rotate(T, Vec3(S[0], S[1], S[2])), Rotate(T, Vec3(S[3], S[4], S[5])))

se3 InvRotate	(	const SE3 &	T,
		const se3 &	S
	)			[friend]

fast version of se3(Rotate(Inv(T), Vec3(S[0], S[1], S[2])), Rotate(Inv(T), Vec3(S[3], S[4], S[5])))