diff options
Diffstat (limited to 'extern/bullet2/src/LinearMath/btMatrix3x3.h')
| -rw-r--r-- | extern/bullet2/src/LinearMath/btMatrix3x3.h | 96 |
1 files changed, 95 insertions, 1 deletions
diff --git a/extern/bullet2/src/LinearMath/btMatrix3x3.h b/extern/bullet2/src/LinearMath/btMatrix3x3.h index 94f53c3c0a5..14aa4ae2348 100644 --- a/extern/bullet2/src/LinearMath/btMatrix3x3.h +++ b/extern/bullet2/src/LinearMath/btMatrix3x3.h @@ -22,6 +22,9 @@ subject to the following restrictions: #include "btQuaternion.h" + +///The btMatrix3x3 class implements a 3x3 rotation matrix, to perform linear algebra in combination with btQuaternion, btTransform and btVector3. +///Make sure to only include a pure orthogonal matrix without scaling. class btMatrix3x3 { public: btMatrix3x3 () {} @@ -281,6 +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 @@ -356,7 +444,7 @@ class btMatrix3x3 { m_el[0].y() * m[0].z() + m_el[1].y() * m[1].z() + m_el[2].y() * m[2].z(), m_el[0].z() * m[0].x() + m_el[1].z() * m[1].x() + m_el[2].z() * m[2].x(), m_el[0].z() * m[0].y() + m_el[1].z() * m[1].y() + m_el[2].z() * m[2].y(), - m_el[0].z() * m[0].z() + m_el[1].z() * m[1].z() + m_el[2].z() * m[2].x()); + m_el[0].z() * m[0].z() + m_el[1].z() * m[1].z() + m_el[2].z() * m[2].z()); } SIMD_FORCE_INLINE btMatrix3x3 @@ -406,5 +494,11 @@ class btMatrix3x3 { } */ +SIMD_FORCE_INLINE bool operator==(const btMatrix3x3& m1, const btMatrix3x3& m2) +{ + return ( m1[0][0] == m2[0][0] && m1[1][0] == m2[1][0] && m1[2][0] == m2[2][0] && + m1[0][1] == m2[0][1] && m1[1][1] == m2[1][1] && m1[2][1] == m2[2][1] && + m1[0][2] == m2[0][2] && m1[1][2] == m2[1][2] && m1[2][2] == m2[2][2] ); +} #endif |