Bullet Collision Detection & Physics Library: btPolarDecomposition.cpp Source File

Bullet Collision Detection & Physics Library

btPolarDecomposition.cpp
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1 #include "btPolarDecomposition.h"
2 #include "btMinMax.h"
3
4 namespace
5 {
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
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
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
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
33 btPolarDecomposition::btPolarDecomposition(btScalar tolerance, unsigned int maxIterations)
34 : m_tolerance(tolerance), m_maxIterations(maxIterations)
35 {
36 }
37
38 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
85 unsigned int btPolarDecomposition::maxIterations() const
86 {
87 return m_maxIterations;
88 }
89
90 unsigned int polarDecompose(const btMatrix3x3& a, btMatrix3x3& u, btMatrix3x3& h)
91 {
92 static btPolarDecomposition polar;
93 return polar.decompose(a, u, h);
94 }
btPolarDecomposition::m_tolerance
btScalar m_tolerance
Definition: btPolarDecomposition.h:50
btPolarDecomposition::decompose
unsigned int decompose(const btMatrix3x3 &a, btMatrix3x3 &u, btMatrix3x3 &h) const
Decomposes a matrix into orthogonal and symmetric, positive-definite parts.
Definition: btPolarDecomposition.cpp:38
btPolarDecomposition::maxIterations
unsigned int maxIterations() const
Returns the maximum number of iterations that this algorithm will perform to achieve convergence...
Definition: btPolarDecomposition.cpp:85
btPolarDecomposition::btPolarDecomposition
btPolarDecomposition(btScalar tolerance=btScalar(0.0001), unsigned int maxIterations=16)
Creates an instance with optional parameters.
Definition: btPolarDecomposition.cpp:33
btMatrix3x3::transpose
btMatrix3x3 transpose() const
Return the transpose of the matrix.
Definition: btMatrix3x3.h:1026
btMinMax.h
btPow
btScalar btPow(btScalar x, btScalar y)
Definition: btScalar.h:501
polarDecompose
unsigned int polarDecompose(const btMatrix3x3 &a, btMatrix3x3 &u, btMatrix3x3 &h)
This functions decomposes the matrix &#39;a&#39; into two parts: an orthogonal matrix &#39;u&#39; and a symmetric...
Definition: btPolarDecomposition.cpp:90
btFuzzyZero
bool btFuzzyZero(btScalar x)
Definition: btScalar.h:552
btMax
const T & btMax(const T &a, const T &b)
Definition: btMinMax.h:27
btPolarDecomposition::m_maxIterations
unsigned int m_maxIterations
Definition: btPolarDecomposition.h:51
btMatrix3x3
The btMatrix3x3 class implements a 3x3 rotation matrix, to perform linear algebra in combination with...
Definition: btMatrix3x3.h:46
btPolarDecomposition.h
btMatrix3x3::inverse
btMatrix3x3 inverse() const
Return the inverse of the matrix.
Definition: btMatrix3x3.h:1070
btPolarDecomposition
This class is used to compute the polar decomposition of a matrix.
Definition: btPolarDecomposition.h:14
maxIterations
int maxIterations
Definition: btQuantizedBvh.cpp:349
btScalar
float btScalar
The btScalar type abstracts floating point numbers, to easily switch between double and single floati...
Definition: btScalar.h:294
btFabs
btScalar btFabs(btScalar x)
Definition: btScalar.h:477