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#ifndef POLARDECOMPOSITION_H
#define POLARDECOMPOSITION_H
#include "btMatrix3x3.h"
/**
* 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.
*/
class btPolarDecomposition
{
public:
static const btScalar DEFAULT_TOLERANCE;
static const unsigned int DEFAULT_MAX_ITERATIONS;
/**
* Creates an instance with optional parameters.
*
* @param tolerance - the tolerance used to determine convergence of the
* algorithm
* @param maxIterations - the maximum number of iterations used to achieve
* convergence
*/
btPolarDecomposition(btScalar tolerance = DEFAULT_TOLERANCE,
unsigned int maxIterations = DEFAULT_MAX_ITERATIONS);
/**
* 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.
*
* @param a - the original matrix
* @param u - the resulting orthogonal matrix
* @param h - the resulting symmetric matrix
*
* @return the number of iterations performed by the algorithm.
*/
unsigned int decompose(const btMatrix3x3& a, btMatrix3x3& u, btMatrix3x3& h) const;
/**
* Returns the maximum number of iterations that this algorithm will perform
* to achieve convergence.
*
* @return maximum number of iterations
*/
unsigned int maxIterations() const;
private:
btScalar m_tolerance;
unsigned int m_maxIterations;
};
/**
* This functions decomposes the matrix 'a' into two parts: an orthogonal matrix
* 'u' and a symmetric, positive-definite matrix 'h'. If the number of
* iterations returned by this function is equal to
* btPolarDecomposition::DEFAULT_MAX_ITERATIONS, the algorithm has failed to
* converge.
*
* @param a - the original matrix
* @param u - the resulting orthogonal matrix
* @param h - the resulting symmetric matrix
*
* @return the number of iterations performed by the algorithm.
*/
unsigned int polarDecompose(const btMatrix3x3& a, btMatrix3x3& u, btMatrix3x3& h);
#endif // POLARDECOMPOSITION_H
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