domain::CoordinateMaps::EquatorialCompression Class Reference

Redistributes gridpoints on the sphere. More...

#include <EquatorialCompression.hpp>

Public Member Functions
	EquatorialCompression (double aspect_ratio, size_t index_pole_axis=2)
	EquatorialCompression (EquatorialCompression &&)=default
	EquatorialCompression (const EquatorialCompression &)=default
EquatorialCompression &	operator= (const EquatorialCompression &)=default
EquatorialCompression &	operator= (EquatorialCompression &&)=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
	The inverse function is only callable with doubles because the inverse might fail if called for a point out of range, and it is unclear what should happen if the inverse were to succeed for some points in a DataVector but fail for other points.
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 EquatorialCompression &lhs, const EquatorialCompression &rhs)

Detailed Description

Redistributes gridpoints on the sphere.

A sphere with an `aspect_ratio` of 3.

Details

A mapping from the sphere to itself which redistributes points towards (or away from) a user-specifed axis, indicated by index_pole_axis_. Once the axis is selected, the map is determined by a single parameter, the aspect_ratio $\alpha$, which is the ratio of the distance perpendicular to the polar axis to the distance along the polar axis for a given point. This parameter name was chosen because points with $\tan \theta =1$ get mapped to points with $\tan {\theta }^{\prime }=\alpha$. In general, gridpoints located at an angle $\theta$ from the pole are mapped to a new angle ${\theta }^{\prime }$ satisfying $\tan {\theta }^{\prime }=\alpha \tan \theta$.

For an aspect_ratio greater than one, the gridpoints are mapped towards the equator, leading to an equatorially compressed grid. For an aspect_ratio less than one, the gridpoints are mapped towards the poles. Note that the aspect ratio must be positive.

Suppose the polar axis were the z-axis, given by index_pole_axis_ == 2. We can then define the auxiliary variables $r:=\sqrt{x^2+y^2+z^2}$ and $\rho :=\sqrt{x^2+y^2+{\alpha }^{-2}{z}^2}$.

The map corresponding to this transformation in cartesian coordinates is then given by:

$${\overrightarrow{x}}^{\prime }(x,y,z)=\frac{r}{\rho }\left[\begin{array}{c}x\\ y\\ {\alpha }^{-1}z\end{array}\right].$$

The mappings for polar axes along the x and y axes are similarly obtained.

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

• src/Domain/CoordinateMaps/EquatorialCompression.hpp