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 > &center_one, const std::array< double, 3 > &center_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)

Detailed Description

Map from 3D unit right cylinder to a volume that connects a portion of a circle to a portion of a spherical surface.

A cylinder maps to the shaded region.

Details

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 [33]. 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.

Restrictions on map parameters.

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

The plane containing the circle is below (i.e. at a smaller value of $z$ than) the sphere, by an amount at least 5% of the sphere radius $R_{2}$ but not more than 5 times the sphere radius $R_{2}$ .
$P$ is inside the sphere but not too close to its surface; specifically, we demand that $| P - C_{2} | \leq 0.95 R_{2}$ .
The ratio $R_{1} / R_{2}$ is between 10 and 1/10, inclusive.
The x and y components of $C_{2} - C_{1}$ both have magnitudes smaller than or equal to $R_{1} + R_{2}$ .

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

src/Domain/CoordinateMaps/CylindricalFlatEndcap.hpp

Public Member Functions

Static Public Member Functions

Static Public Attributes

Friends

Detailed Description

Details

Restrictions on map parameters.