SpECTRE  v2021.12.06
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)
 Equiangular (const Equiangular &)=default
 Equiangular (Equiangular &&)=default
Equiangularoperator= (const Equiangular &)=default
Equiangularoperator= (Equiangular &&)=default
template<typename T >
std::array< tt::remove_cvref_wrap_t< T >, 1 > operator() (const std::array< T, 1 > &source_coords) const
std::optional< std::array< double, 1 > > inverse (const std::array< double, 1 > &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 >, 1, Frame::NoFramejacobian (const std::array< T, 1 > &source_coords) const
template<typename T >
tnsr::Ij< tt::remove_cvref_wrap_t< T >, 1, Frame::NoFrameinv_jacobian (const std::array< T, 1 > &source_coords) const
void pup (PUP::er &p)

Static Public Member Functions

static bool is_identity ()

Static Public Attributes

static constexpr size_t dim = 1


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

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}

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.

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