SpECTRE
v2023.10.11

Map from 3D unit right cylinder to a volume that connects a portion of a circle to a portion of a spherical surface. More...
#include <CylindricalFlatEndcap.hpp>
Public Member Functions  
CylindricalFlatEndcap (const std::array< double, 3 > ¢er_one, const std::array< double, 3 > ¢er_two, const std::array< double, 3 > &proj_center, double radius_one, double radius_two)  
CylindricalFlatEndcap (CylindricalFlatEndcap &&)=default  
CylindricalFlatEndcap (const CylindricalFlatEndcap &)=default  
CylindricalFlatEndcap &  operator= (const CylindricalFlatEndcap &)=default 
CylindricalFlatEndcap &  operator= (CylindricalFlatEndcap &&)=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) 
Static Public Member Functions  
static bool  is_identity () 
Static Public Attributes  
static constexpr size_t  dim = 3 
Friends  
bool  operator== (const CylindricalFlatEndcap &lhs, const CylindricalFlatEndcap &rhs) 
Map from 3D unit right cylinder to a volume that connects a portion of a circle to a portion of a spherical surface.
Consider a 2D circle in 3D space that is normal to the \(z\) axis and has (3D) center \(C_1\) and radius \(R_1\). Also consider a sphere with center \(C_2\), and radius \(R_2\). Also let there be a projection point \(P\).
CylindricalFlatEndcap maps a 3D unit right cylinder (with coordinates \((\bar{x},\bar{y},\bar{z})\) such that \(1\leq\bar{z}\leq 1\) and \(\bar{x}^2+\bar{y}^2 \leq 1\)) to the shaded area in the figure above (with coordinates \((x,y,z)\)). The "bottom" of the cylinder \(\bar{z}=1\) is mapped to the interior of the circle of radius \(R_1\). Curves of constant \((\bar{x},\bar{y})\) are mapped to portions of lines that pass through \(P\). Along each of these curves, \(\bar{z}=1\) is mapped to a point on the circle and \(\bar{z}=+1\) is mapped to a point on the sphere.
CylindricalFlatEndcap is intended to be composed with Wedge2D maps to construct a portion of a cylindrical domain for a binary system.
CylindricalFlatEndcap is described briefly in the Appendix of [32]. CylindricalFlatEndcap is used to construct the blocks labeled 'MA wedge' and 'MB wedge' in Figure 20 of that paper.
CylindricalFlatEndcap is implemented using FocallyLiftedMap
and FocallyLiftedInnerMaps::FlatEndcap
; see those classes for details.
The following restrictions are made so that the map is not singular or close to singular. It is possible to construct a valid map without these assumptions, but the assumptions simplify the code and avoid problematic edge cases, and the expected use cases obey these restrictions.
We demand that