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