domain::CoordinateMaps::Rotation< 3 > Class Reference

Spatial rotation in three dimensions using Euler angles. More...

#include <Rotation.hpp>

Public Member Functions
	Rotation (double rotation_about_z, double rotation_about_rotated_y, double rotation_about_rotated_z)
	Constructor. More...
	Rotation (const Rotation &)=default
Rotation &	operator= (const Rotation &)=default
	Rotation (Rotation &&)=default
Rotation &	operator= (Rotation &&)=default
template<typename T >
std::array< tt::remove_cvref_wrap_t< T >, 3 >	operator() (const std::array< T, 3 > &source_coords) const
std::optional< std::array< double, 3 > >	inverse (const std::array< double, 3 > &target_coords) const
template<typename T >
tnsr::Ij< tt::remove_cvref_wrap_t< T >, 3, Frame::NoFrame >	jacobian (const std::array< T, 3 > &source_coords) const
template<typename T >
tnsr::Ij< tt::remove_cvref_wrap_t< T >, 3, Frame::NoFrame >	inv_jacobian (const std::array< T, 3 > &source_coords) const
void	pup (PUP::er &p)
bool	is_identity () const

Static Public Attributes
static constexpr size_t	dim = 3

Friends
bool	operator== (const Rotation< 3 > &lhs, const Rotation< 3 > &rhs)

Detailed Description

Spatial rotation in three dimensions using Euler angles.

Rotation angles should be specified in degrees. First rotation $\alpha$ is about z axis. Second rotation $\beta$ is about rotated y axis. Third rotation $\gamma$ is about rotated z axis. These rotations are of the $(\xi ,\eta ,\zeta )$ coordinate system with respect to the grid coordinates $(x,y,z)$.

The formula for the mapping is:

$$\begin{array}{rcl}x& =& \xi (\cos \gamma \cos \beta \cos \alpha -\sin \gamma \sin \alpha )+\eta (-\sin \gamma \cos \beta \cos \alpha -\cos \gamma \sin \alpha )+\zeta \sin \beta \cos \alpha \\ y& =& \xi (\cos \gamma \cos \beta \sin \alpha +\sin \gamma \cos \alpha )+\eta (-\sin \gamma \cos \beta \sin \alpha +\cos \gamma \cos \alpha )+\zeta \sin \beta \sin \alpha \\ z& =& -\xi \cos \gamma \sin \beta +\eta \sin \gamma \sin \beta +\zeta \cos \beta \end{array}$$

Constructor & Destructor Documentation

Rotation()

domain::CoordinateMaps::Rotation< 3 >::Rotation	(	double	rotation_about_z,
		double	rotation_about_rotated_y,
		double	rotation_about_rotated_z
	)

Constructor.

Parameters

rotation_about_z	the angle $\alpha$ (in radians).
rotation_about_rotated_y	the angle $\beta$ (in radians).
rotation_about_rotated_z	the angle $\gamma$ (in radians).

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The documentation for this class was generated from the following file:

• src/Domain/CoordinateMaps/Rotation.hpp