TooN::SL< N, Precision > Class Template Reference

represents an element from the group SL(n), the NxN matrices M with det(M) = 1. More...

#include <sl.h>

Public Member Functions
	SL ()
	default constructor, creates identity element
template<int S, typename P , typename B >
	SL (const Vector< S, P, B > &v)
	exp constructor, creates element through exponentiation of Lie algebra vector. see SL::exp.
template<int R, int C, typename P , typename A >
	SL (const Matrix< R, C, P, A > &M)
	copy constructor from a matrix, coerces matrix to be of determinant = 1
const Matrix< N, N, Precision > &	get_matrix () const
	returns the represented matrix
SL	inverse () const
	returns the inverse using LU
template<typename P >
SL< N, typename Internal::MultiplyType< Precision, P >::type >	operator* (const SL< N, P > &rhs) const
	multiplies to SLs together by multiplying the underlying matrices
template<typename P >
SL	operator*= (const SL< N, P > &rhs)
	right multiplies this SL with another one
Vector< N *N-1, Precision >	ln () const
template<int S, typename P , typename B >
SL< N, Precision >	exp (const Vector< S, P, B > &v)

Static Public Member Functions
template<int S, typename P , typename B >
static SL	exp (const Vector< S, P, B > &)
	exponentiates a vector in the Lie algebra to compute the corresponding element More...
static Matrix< N, N, Precision >	generator (int)
	returns one generator of the group. More...

Static Public Attributes
static const int	size = N
	size of the matrices represented by SL<N>
static const int	dim = N*N - 1
	dimension of the vector space represented by SL<N>

Friends
std::istream &	operator>> (std::istream &, SL &)

Detailed Description

template<int N, typename Precision = DefaultPrecision>
class TooN::SL< N, Precision >

represents an element from the group SL(n), the NxN matrices M with det(M) = 1.

This can be used to conveniently estimate homographies on n-1 dimentional spaces. The implementation uses the matrix exponential function exp for exponentiation from an element in the Lie algebra and LU to compute an inverse.

The Lie algebra are the NxN matrices M with trace(M) = 0. The N*N-1 generators used to represent this vector space are the following:

• diag(...,1,-1,...), n-1 along the diagonal
• symmetric generators for every pair of off-diagonal elements
• anti-symmetric generators for every pair of off-diagonal elements This choice represents the fact that SL(n) can be interpreted as the product of all symmetric matrices with det() = 1 times SO(n).

Member Function Documentation

exp()

template<int N, typename Precision = DefaultPrecision>

template<int S, typename P , typename B >

static SL TooN::SL< N, Precision >::exp ( const Vector< S, P, B > &  )

inlinestatic

exponentiates a vector in the Lie algebra to compute the corresponding element

• v a vector of dimension SL::dim

generator()

template<int N, typename Precision >

Matrix< N, N, Precision > TooN::SL< N, Precision >::generator ( int  i )

inlinestatic

returns one generator of the group.

see SL for a detailed description of the generators used.

• i number of the generator between 0 and SL::dim -1 inclusive

---

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

• TooN/sl.h