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 }
32
33 const btScalar btPolarDecomposition::DEFAULT_TOLERANCE = btScalar(0.0001);
34 const unsigned int btPolarDecomposition::DEFAULT_MAX_ITERATIONS = 16;
35
btPolarDecomposition(btScalar tolerance,unsigned int maxIterations)36 btPolarDecomposition::btPolarDecomposition(btScalar tolerance, unsigned int maxIterations)
37 : m_tolerance(tolerance)
38 , m_maxIterations(maxIterations)
39 {
40 }
41
decompose(const btMatrix3x3 & a,btMatrix3x3 & u,btMatrix3x3 & h) const42 unsigned int btPolarDecomposition::decompose(const btMatrix3x3& a, btMatrix3x3& u, btMatrix3x3& h) const
43 {
44 // Use the 'u' and 'h' matrices for intermediate calculations
45 u = a;
46 h = a.inverse();
47
48 for (unsigned int i = 0; i < m_maxIterations; ++i)
49 {
50 const btScalar h_1 = p1_norm(h);
51 const btScalar h_inf = pinf_norm(h);
52 const btScalar u_1 = p1_norm(u);
53 const btScalar u_inf = pinf_norm(u);
54
55 const btScalar h_norm = h_1 * h_inf;
56 const btScalar u_norm = u_1 * u_inf;
57
58 // The matrix is effectively singular so we cannot invert it
59 if (btFuzzyZero(h_norm) || btFuzzyZero(u_norm))
60 break;
61
62 const btScalar gamma = btPow(h_norm / u_norm, 0.25f);
63 const btScalar inv_gamma = btScalar(1.0) / gamma;
64
65 // Determine the delta to 'u'
66 const btMatrix3x3 delta = (u * (gamma - btScalar(2.0)) + h.transpose() * inv_gamma) * btScalar(0.5);
67
68 // Update the matrices
69 u += delta;
70 h = u.inverse();
71
72 // Check for convergence
73 if (p1_norm(delta) <= m_tolerance * u_1)
74 {
75 h = u.transpose() * a;
76 h = (h + h.transpose()) * 0.5;
77 return i;
78 }
79 }
80
81 // The algorithm has failed to converge to the specified tolerance, but we
82 // want to make sure that the matrices returned are in the right form.
83 h = u.transpose() * a;
84 h = (h + h.transpose()) * 0.5;
85
86 return m_maxIterations;
87 }
88
maxIterations() const89 unsigned int btPolarDecomposition::maxIterations() const
90 {
91 return m_maxIterations;
92 }
93
polarDecompose(const btMatrix3x3 & a,btMatrix3x3 & u,btMatrix3x3 & h)94 unsigned int polarDecompose(const btMatrix3x3& a, btMatrix3x3& u, btMatrix3x3& h)
95 {
96 static btPolarDecomposition polar;
97 return polar.decompose(a, u, h);
98 }
99
100