1 #include "btPolarDecomposition.h"
2 #include "btMinMax.h"
3
4 namespace
5 {
abs_column_sum(const btMatrix3x3 & a,int i)6 btScalar abs_column_sum(const btMatrix3x3& a, int i)
7 {
8 return btFabs(a[0][i]) + btFabs(a[1][i]) + btFabs(a[2][i]);
9 }
10
abs_row_sum(const btMatrix3x3 & a,int i)11 btScalar abs_row_sum(const btMatrix3x3& a, int i)
12 {
13 return btFabs(a[i][0]) + btFabs(a[i][1]) + btFabs(a[i][2]);
14 }
15
p1_norm(const btMatrix3x3 & a)16 btScalar p1_norm(const btMatrix3x3& a)
17 {
18 const btScalar sum0 = abs_column_sum(a, 0);
19 const btScalar sum1 = abs_column_sum(a, 1);
20 const btScalar sum2 = abs_column_sum(a, 2);
21 return btMax(btMax(sum0, sum1), sum2);
22 }
23
pinf_norm(const btMatrix3x3 & a)24 btScalar pinf_norm(const btMatrix3x3& a)
25 {
26 const btScalar sum0 = abs_row_sum(a, 0);
27 const btScalar sum1 = abs_row_sum(a, 1);
28 const btScalar sum2 = abs_row_sum(a, 2);
29 return btMax(btMax(sum0, sum1), sum2);
30 }
31 } // namespace
32
btPolarDecomposition(btScalar tolerance,unsigned int maxIterations)33 btPolarDecomposition::btPolarDecomposition(btScalar tolerance, unsigned int maxIterations)
34 : m_tolerance(tolerance), m_maxIterations(maxIterations)
35 {
36 }
37
decompose(const btMatrix3x3 & a,btMatrix3x3 & u,btMatrix3x3 & h) const38 unsigned int btPolarDecomposition::decompose(const btMatrix3x3& a, btMatrix3x3& u, btMatrix3x3& h) const
39 {
40 // Use the 'u' and 'h' matrices for intermediate calculations
41 u = a;
42 h = a.inverse();
43
44 for (unsigned int i = 0; i < m_maxIterations; ++i)
45 {
46 const btScalar h_1 = p1_norm(h);
47 const btScalar h_inf = pinf_norm(h);
48 const btScalar u_1 = p1_norm(u);
49 const btScalar u_inf = pinf_norm(u);
50
51 const btScalar h_norm = h_1 * h_inf;
52 const btScalar u_norm = u_1 * u_inf;
53
54 // The matrix is effectively singular so we cannot invert it
55 if (btFuzzyZero(h_norm) || btFuzzyZero(u_norm))
56 break;
57
58 const btScalar gamma = btPow(h_norm / u_norm, 0.25f);
59 const btScalar inv_gamma = btScalar(1.0) / gamma;
60
61 // Determine the delta to 'u'
62 const btMatrix3x3 delta = (u * (gamma - btScalar(2.0)) + h.transpose() * inv_gamma) * btScalar(0.5);
63
64 // Update the matrices
65 u += delta;
66 h = u.inverse();
67
68 // Check for convergence
69 if (p1_norm(delta) <= m_tolerance * u_1)
70 {
71 h = u.transpose() * a;
72 h = (h + h.transpose()) * 0.5;
73 return i;
74 }
75 }
76
77 // The algorithm has failed to converge to the specified tolerance, but we
78 // want to make sure that the matrices returned are in the right form.
79 h = u.transpose() * a;
80 h = (h + h.transpose()) * 0.5;
81
82 return m_maxIterations;
83 }
84
maxIterations() const85 unsigned int btPolarDecomposition::maxIterations() const
86 {
87 return m_maxIterations;
88 }
89
polarDecompose(const btMatrix3x3 & a,btMatrix3x3 & u,btMatrix3x3 & h)90 unsigned int polarDecompose(const btMatrix3x3& a, btMatrix3x3& u, btMatrix3x3& h)
91 {
92 static btPolarDecomposition polar;
93 return polar.decompose(a, u, h);
94 }
95