domain::CoordinateMaps::Equiangular Class Reference

Non-linear map from \(\xi \in [A, B]\rightarrow x \in [a, b]\). More...

#include <Equiangular.hpp>

Public Member Functions
	Equiangular (double A, double B, double a, double b) noexcept
	Equiangular (const Equiangular &)=default
	Equiangular (Equiangular &&) noexcept=default
Equiangular &	operator= (const Equiangular &)=default
Equiangular &	operator= (Equiangular &&)=default
template<typename T >
std::array< tt::remove_cvref_wrap_t< T >, 1 >	operator() (const std::array< T, 1 > &source_coords) const noexcept
std::optional< std::array< double, 1 > >	inverse (const std::array< double, 1 > &target_coords) const noexcept
	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 >, 1, Frame::NoFrame >	jacobian (const std::array< T, 1 > &source_coords) const noexcept
template<typename T >
tnsr::Ij< tt::remove_cvref_wrap_t< T >, 1, Frame::NoFrame >	inv_jacobian (const std::array< T, 1 > &source_coords) const noexcept
void	pup (PUP::er &p) noexcept

Static Public Member Functions
static bool	is_identity () noexcept

Static Public Attributes
static constexpr size_t	dim = 1

Friends
bool	operator== (const Equiangular &lhs, const Equiangular &rhs) noexcept

Detailed Description

Non-linear map from \(\xi \in [A, B]\rightarrow x \in [a, b]\).

The formula for the mapping is:

\begin{align} x &= \frac{a}{2} \left(1-\mathrm{tan}\left( \frac{\pi(2\xi-B-A)}{4(B-A)}\right)\right) + \frac{b}{2} \left(1+\mathrm{tan}\left( \frac{\pi(2\xi-B-A)}{4(B-A)}\right)\right)\\ \xi &= \frac{A}{2} \left(1-\frac{4}{\pi}\mathrm{arctan}\left( \frac{2x-a-b}{b-a}\right)\right)+ \frac{B}{2} \left(1+\frac{4}{\pi}\mathrm{arctan}\left( \frac{2x-a-b}{b-a}\right)\right) \end{align}

Note

The intermediate step in which a tangent map is applied can be more clearly understood if we define the coordinates:

\begin{align} \xi_{logical} &:= \frac{2\xi-B-A}{B-A} \in [-1, 1]\\ \Xi &:= \mathrm{tan}\left(\frac{\pi\xi_{logical}}{4}\right) \in [-1, 1] \end{align}

This map is intended to be used with the Wedge map when equiangular coordinates are chosen for those maps. For more information on this choice of coordinates, see the documentation for Wedge.