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 Tensor< 1, 3, Number > &axis, 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
[in] | angle | The rotation angle (about the z-axis) in radians |
Tensor< 2, 3, Number > Physics::Transformations::Rotations::rotation_matrix_3d | ( | const Tensor< 1, 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
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 |
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
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 |