btPolarDecomposition.cpp

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#include "btPolarDecomposition.h"
#include "btMinMax.h"
 
namespace
{
btScalar abs_column_sum(const btMatrix3x3& a, int i)
{
        return btFabs(a[0][i]) + btFabs(a[1][i]) + btFabs(a[2][i]);
}
 
btScalar abs_row_sum(const btMatrix3x3& a, int i)
{
        return btFabs(a[i][0]) + btFabs(a[i][1]) + btFabs(a[i][2]);
}
 
btScalar p1_norm(const btMatrix3x3& a)
{
        const btScalar sum0 = abs_column_sum(a, 0);
        const btScalar sum1 = abs_column_sum(a, 1);
        const btScalar sum2 = abs_column_sum(a, 2);
        return btMax(btMax(sum0, sum1), sum2);
}
 
btScalar pinf_norm(const btMatrix3x3& a)
{
        const btScalar sum0 = abs_row_sum(a, 0);
        const btScalar sum1 = abs_row_sum(a, 1);
        const btScalar sum2 = abs_row_sum(a, 2);
        return btMax(btMax(sum0, sum1), sum2);
}
}  // namespace
 
btPolarDecomposition::btPolarDecomposition(btScalar tolerance, unsigned int maxIterations)
        : m_tolerance(tolerance), m_maxIterations(maxIterations)
{
}
 
unsigned int btPolarDecomposition::decompose(const btMatrix3x3& a, btMatrix3x3& u, btMatrix3x3& h) const
{
        // Use the 'u' and 'h' matrices for intermediate calculations
        u = a;
        h = a.inverse();
 
        for (unsigned int i = 0; i < m_maxIterations; ++i)
        {
                const btScalar h_1 = p1_norm(h);
                const btScalar h_inf = pinf_norm(h);
                const btScalar u_1 = p1_norm(u);
                const btScalar u_inf = pinf_norm(u);
 
                const btScalar h_norm = h_1 * h_inf;
                const btScalar u_norm = u_1 * u_inf;
 
                // The matrix is effectively singular so we cannot invert it
                if (btFuzzyZero(h_norm) || btFuzzyZero(u_norm))
                        break;
 
                const btScalar gamma = btPow(h_norm / u_norm, 0.25f);
                const btScalar inv_gamma = btScalar(1.0) / gamma;
 
                // Determine the delta to 'u'
                const btMatrix3x3 delta = (u * (gamma - btScalar(2.0)) + h.transpose() * inv_gamma) * btScalar(0.5);
 
                // Update the matrices
                u += delta;
                h = u.inverse();
 
                // Check for convergence
                if (p1_norm(delta) <= m_tolerance * u_1)
                {
                        h = u.transpose() * a;
                        h = (h + h.transpose()) * 0.5;
                        return i;
                }
        }
 
        // The algorithm has failed to converge to the specified tolerance, but we
        // want to make sure that the matrices returned are in the right form.
        h = u.transpose() * a;
        h = (h + h.transpose()) * 0.5;
 
        return m_maxIterations;
}
 
unsigned int btPolarDecomposition::maxIterations() const
{
        return m_maxIterations;
}
 
unsigned int polarDecompose(const btMatrix3x3& a, btMatrix3x3& u, btMatrix3x3& h)
{
        static btPolarDecomposition polar;
        return polar.decompose(a, u, h);
}