diff options
Diffstat (limited to 'extern/bullet2/src/LinearMath/btMatrix3x3.h')
-rw-r--r-- | extern/bullet2/src/LinearMath/btMatrix3x3.h | 85 |
1 files changed, 85 insertions, 0 deletions
diff --git a/extern/bullet2/src/LinearMath/btMatrix3x3.h b/extern/bullet2/src/LinearMath/btMatrix3x3.h index ca1a801402f..14aa4ae2348 100644 --- a/extern/bullet2/src/LinearMath/btMatrix3x3.h +++ b/extern/bullet2/src/LinearMath/btMatrix3x3.h @@ -284,6 +284,91 @@ class btMatrix3x3 { } + ///diagonalizes this matrix by the Jacobi method. rot stores the rotation + ///from the coordinate system in which the matrix is diagonal to the original + ///coordinate system, i.e., old_this = rot * new_this * rot^T. The iteration + ///stops when all off-diagonal elements are less than the threshold multiplied + ///by the sum of the absolute values of the diagonal, or when maxSteps have + ///been executed. Note that this matrix is assumed to be symmetric. + void diagonalize(btMatrix3x3& rot, btScalar threshold, int maxSteps) + { + rot.setIdentity(); + for (int step = maxSteps; step > 0; step--) + { + // find off-diagonal element [p][q] with largest magnitude + int p = 0; + int q = 1; + int r = 2; + btScalar max = btFabs(m_el[0][1]); + btScalar v = btFabs(m_el[0][2]); + if (v > max) + { + q = 2; + r = 1; + max = v; + } + v = btFabs(m_el[1][2]); + if (v > max) + { + p = 1; + q = 2; + r = 0; + max = v; + } + + btScalar t = threshold * (btFabs(m_el[0][0]) + btFabs(m_el[1][1]) + btFabs(m_el[2][2])); + if (max <= t) + { + if (max <= SIMD_EPSILON * t) + { + return; + } + step = 1; + } + + // compute Jacobi rotation J which leads to a zero for element [p][q] + btScalar mpq = m_el[p][q]; + btScalar theta = (m_el[q][q] - m_el[p][p]) / (2 * mpq); + btScalar theta2 = theta * theta; + btScalar cos; + btScalar sin; + if (theta2 * theta2 < btScalar(10 / SIMD_EPSILON)) + { + t = (theta >= 0) ? 1 / (theta + btSqrt(1 + theta2)) + : 1 / (theta - btSqrt(1 + theta2)); + cos = 1 / btSqrt(1 + t * t); + sin = cos * t; + } + else + { + // approximation for large theta-value, i.e., a nearly diagonal matrix + t = 1 / (theta * (2 + btScalar(0.5) / theta2)); + cos = 1 - btScalar(0.5) * t * t; + sin = cos * t; + } + + // apply rotation to matrix (this = J^T * this * J) + m_el[p][q] = m_el[q][p] = 0; + m_el[p][p] -= t * mpq; + m_el[q][q] += t * mpq; + btScalar mrp = m_el[r][p]; + btScalar mrq = m_el[r][q]; + m_el[r][p] = m_el[p][r] = cos * mrp - sin * mrq; + m_el[r][q] = m_el[q][r] = cos * mrq + sin * mrp; + + // apply rotation to rot (rot = rot * J) + for (int i = 0; i < 3; i++) + { + btVector3& row = rot[i]; + mrp = row[p]; + mrq = row[q]; + row[p] = cos * mrp - sin * mrq; + row[q] = cos * mrq + sin * mrp; + } + } + } + + protected: btScalar cofac(int r1, int c1, int r2, int c2) const |