1 #ifndef POLARDECOMPOSITION_H 2 #define POLARDECOMPOSITION_H 3 4 #include "btMatrix3x3.h" 5 6 /** 7 * This class is used to compute the polar decomposition of a matrix. In 8 * general, the polar decomposition factorizes a matrix, A, into two parts: a 9 * unitary matrix (U) and a positive, semi-definite Hermitian matrix (H). 10 * However, in this particular implementation the original matrix, A, is 11 * required to be a square 3x3 matrix with real elements. This means that U will 12 * be an orthogonal matrix and H with be a positive-definite, symmetric matrix. 13 */ 14 class btPolarDecomposition 15 { 16 public: 17 18 19 /** 20 * Creates an instance with optional parameters. 21 * 22 * @param tolerance - the tolerance used to determine convergence of the 23 * algorithm 24 * @param maxIterations - the maximum number of iterations used to achieve 25 * convergence 26 */ 27 btPolarDecomposition(btScalar tolerance = btScalar(0.0001), 28 unsigned int maxIterations = 16); 29 30 /** 31 * Decomposes a matrix into orthogonal and symmetric, positive-definite 32 * parts. If the number of iterations returned by this function is equal to 33 * the maximum number of iterations, the algorithm has failed to converge. 34 * 35 * @param a - the original matrix 36 * @param u - the resulting orthogonal matrix 37 * @param h - the resulting symmetric matrix 38 * 39 * @return the number of iterations performed by the algorithm. 40 */ 41 unsigned int decompose(const btMatrix3x3& a, btMatrix3x3& u, btMatrix3x3& h) const; 42 43 /** 44 * Returns the maximum number of iterations that this algorithm will perform 45 * to achieve convergence. 46 * 47 * @return maximum number of iterations 48 */ 49 unsigned int maxIterations() const; 50 51 private: 52 btScalar m_tolerance; 53 unsigned int m_maxIterations; 54 }; 55 56 /** 57 * This functions decomposes the matrix 'a' into two parts: an orthogonal matrix 58 * 'u' and a symmetric, positive-definite matrix 'h'. If the number of 59 * iterations returned by this function is equal to 60 * btPolarDecomposition::DEFAULT_MAX_ITERATIONS, the algorithm has failed to 61 * converge. 62 * 63 * @param a - the original matrix 64 * @param u - the resulting orthogonal matrix 65 * @param h - the resulting symmetric matrix 66 * 67 * @return the number of iterations performed by the algorithm. 68 */ 69 unsigned int polarDecompose(const btMatrix3x3& a, btMatrix3x3& u, btMatrix3x3& h); 70 71 #endif // POLARDECOMPOSITION_H 72 73