Applied polar decomposition patch. Fixes Issue 621. Thanks to Christian for the report, Joshua for the fix, Dongsoo for checking the fix.

Applied picking cloth patch. Fixes Issue 646. Thanks to Dongsoo.
Applied patch Softbody updateConstraints. Fixes Issue 503. Thanks to Dave Bruce Phillips and Dongsoo.
Fix various warnigns under Mac OSX.

src/LinearMath/btPolarDecomposition.cpp

@@ -0,0 +1,99 @@
+#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);
+  }
+}
+
+const btScalar btPolarDecomposition::DEFAULT_TOLERANCE = btScalar(0.0001);
+const unsigned int btPolarDecomposition::DEFAULT_MAX_ITERATIONS = 16;
+
+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 = 1.0 / gamma;
+
+    // Determine the delta to 'u'
+    const btMatrix3x3 delta = (u * (gamma - 2.0) + h.transpose() * inv_gamma) * 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);
+}
+