This class is used to compute the polar decomposition of a matrix. More...

#include <btPolarDecomposition.h>

Public Member Functions
	btPolarDecomposition (btScalar tolerance=btScalar(0.0001), unsigned int maxIterations=16)
	Creates an instance with optional parameters.

unsigned int	decompose (const btMatrix3x3 &a, btMatrix3x3 &u, btMatrix3x3 &h) const
	Decomposes a matrix into orthogonal and symmetric, positive-definite parts.

unsigned int	maxIterations () const
	Returns the maximum number of iterations that this algorithm will perform to achieve convergence.

Private Attributes
btScalar	m_tolerance

unsigned int	m_maxIterations

Detailed Description

This class is used to compute the polar decomposition of a matrix.

In general, the polar decomposition factorizes a matrix, A, into two parts: a unitary matrix (U) and a positive, semi-definite Hermitian matrix (H). However, in this particular implementation the original matrix, A, is required to be a square 3x3 matrix with real elements. This means that U will be an orthogonal matrix and H with be a positive-definite, symmetric matrix.

Definition at line 14 of file btPolarDecomposition.h.

Constructor & Destructor Documentation

◆ btPolarDecomposition()

btPolarDecomposition::btPolarDecomposition	(	btScalar	tolerance = `btScalar(0.0001)`,
		unsigned int	maxIterations = `16`
	)

Creates an instance with optional parameters.

Parameters

tolerance	- the tolerance used to determine convergence of the algorithm
maxIterations	- the maximum number of iterations used to achieve convergence

Definition at line 33 of file btPolarDecomposition.cpp.

Member Function Documentation

◆ decompose()

unsigned int btPolarDecomposition::decompose	(	const btMatrix3x3 &	a,
		btMatrix3x3 &	u,
		btMatrix3x3 &	h
	)		const

Decomposes a matrix into orthogonal and symmetric, positive-definite parts.

If the number of iterations returned by this function is equal to the maximum number of iterations, the algorithm has failed to converge.

Parameters

a	- the original matrix
u	- the resulting orthogonal matrix
h	- the resulting symmetric matrix

Returns: the number of iterations performed by the algorithm.

Definition at line 38 of file btPolarDecomposition.cpp.

◆ maxIterations()

unsigned int btPolarDecomposition::maxIterations ( ) const

Returns the maximum number of iterations that this algorithm will perform to achieve convergence.

Returns: maximum number of iterations

Definition at line 85 of file btPolarDecomposition.cpp.

Member Data Documentation

◆ m_maxIterations

unsigned int btPolarDecomposition::m_maxIterations

private

Definition at line 51 of file btPolarDecomposition.h.

◆ m_tolerance

btScalar btPolarDecomposition::m_tolerance