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Reference documentation for deal.II version 9.3.3
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Functions | |
Rotation matrices | |
template<typename Number > | |
Tensor< 2, 2, Number > | rotation_matrix_2d (const Number &angle) |
template<typename Number > | |
Tensor< 2, 3, Number > | rotation_matrix_3d (const Point< 3, Number > &axis, const Number &angle) |
Transformation functions and tensors that are defined in terms of rotation angles and axes of rotation.
Tensor< 2, 2, Number > Physics::Transformations::Rotations::rotation_matrix_2d | ( | const Number & | angle | ) |
Return the rotation matrix for 2-d Euclidean space, namely
where is the rotation angle given in radians. In particular, this describes the counter-clockwise rotation of a vector relative to a fixed set of right-handed axes.
[in] | angle | The rotation angle (about the z-axis) in radians |
Tensor< 2, 3, Number > Physics::Transformations::Rotations::rotation_matrix_3d | ( | const Point< 3, Number > & | axis, |
const Number & | angle | ||
) |
Return the rotation matrix for 3-d Euclidean space. Most concisely stated using the Rodrigues' rotation formula, this function returns the equivalent of
where is the axial vector (an axial vector) and
is the rotation angle given in radians,
is the identity tensor and
is the skew symmetric tensor of
.
axis
of rotation. An alternative implementation is discussed at this link, but is inconsistent (sign-wise) with the Rodrigues' rotation formula as it describes the rotation of a coordinate system.[in] | axis | A unit vector that defines the axis of rotation |
[in] | angle | The rotation angle in radians |