Update Files

lib/haxebullet/bullet/LinearMath/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);
+  }
+}
+
+
+
+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);
+}
+