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.

UnitTests/BulletUnitTests/TestCholeskyDecomposition.cpp

@@ -0,0 +1,68 @@
+#include "TestCholeskyDecomposition.h"
+#include "btCholeskyDecomposition.h"
+
+void TestCholeskyDecomposition::testZeroMatrix()
+{
+  const btMatrix3x3 A(0,0,0,0,0,0,0,0,0);
+  const int result = choleskyDecompose(A, L);
+
+  // The zero matrix is not positive definite so the decomposition does not
+  // exist.
+  CPPUNIT_ASSERT(result != 0);
+}
+
+void TestCholeskyDecomposition::testIdentityMatrix()
+{
+  const btMatrix3x3 A = I;
+  const int result = choleskyDecompose(A, L);
+
+  // The identity is a special case where the result should also be the
+  // identity.
+  CPPUNIT_ASSERT(result == 0);
+  CPPUNIT_ASSERT(equal(L, I));
+}
+
+void TestCholeskyDecomposition::testPositiveDefiniteMatrix()
+{
+  const btMatrix3x3 M(3,0,0,1,2,0,3,2,1);
+  const btMatrix3x3 A = M * M.transpose();
+  const int result = choleskyDecompose(A, L);
+
+  // By construction, the resulting decomposition of A should be equal to M
+  CPPUNIT_ASSERT(result == 0);
+  CPPUNIT_ASSERT(equal(L, M));
+  CPPUNIT_ASSERT(equal(A, L * L.transpose()));
+}
+
+void TestCholeskyDecomposition::testPositiveSemiDefiniteMatrix()
+{
+  const btMatrix3x3 M(3,0,0,1,0,0,3,2,1);
+  const btMatrix3x3 A = M * M.transpose();
+  const int result = choleskyDecompose(A, L);
+
+  // The matrix is semi definite, i.e. one of the eigenvalues is zero, so the
+  // Cholesky decomposition does not exist.
+  CPPUNIT_ASSERT(result != 0);
+}
+
+void TestCholeskyDecomposition::testNegativeDefiniteMatrix()
+{
+  const btMatrix3x3 M(3,0,0,1,2,0,3,2,1);
+  const btMatrix3x3 A = M * M.transpose() * (-1.0);
+  const int result = choleskyDecompose(A, L);
+
+  // The matrix is negative definite, i.e. all of the eigenvalues are negative,
+  // so the Cholesky decomposition does not exist.
+  CPPUNIT_ASSERT(result != 0);
+}
+
+bool TestCholeskyDecomposition::equal(const btMatrix3x3& A, const btMatrix3x3& B) const
+{
+  for (unsigned int i = 0; i < 3; ++i)
+    for (unsigned int j = 0; j < 3; ++j)
+      if (btFabs(A[i][j] - B[i][j]) > SIMD_EPSILON)
+        return false;
+
+  return true;
+}
+