Note: this is documentation for an old release. View the latest documentation at docs.fenicsproject.org/basix/v0.8.0/cpp/namespacebasix_1_1lattice.html

# Basix 0.5.1

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basix::lattice Namespace Reference

Lattices of points. More...

## Enumerations

enum  type {
type::equispaced = 0, type::gll = 1, type::chebyshev = 2, type::gl = 4,
type::chebyshev_plus_endpoints = 10, type::gl_plus_endpoints = 11
}
The type of point spacing to be used in a lattice. More...

enum  simplex_method { simplex_method::none = 0, simplex_method::warp = 1, simplex_method::isaac = 2, simplex_method::centroid = 3 }
The method used to generate points inside simplices. More...

## Functions

std::pair< std::vector< double >, std::array< std::size_t, 2 > > create (cell::type celltype, int n, lattice::type type, bool exterior, lattice::simplex_method simplex_method=lattice::simplex_method::none)
Create a lattice of points on a reference cell optionally including the outer surface points. More...

## Detailed Description

Lattices of points.

## ◆ simplex_method

 strong

The method used to generate points inside simplices.

Enumerator
none

Used when no method is needed, e.g. when making points on a quadrilateral, or when making equispaced points).

warp

Warping from Hesthaven and Warburton, Nodal Discontinuous Galerkin Methods, https://doi.org/10.1007/978-0-387-72067-8.

isaac

Points described in Isaac, Recursive, Parameter-Free, Explicitly Defined Interpolation Nodes for Simplices, https://doi.org/10.1137/20M1321802.

centroid

Place points at the centroids of the grid created by putting points on the edges, as described in Blyth and Pozrikidis, A Lobatto interpolation grid over the triangle, https://doi.org/10.1093/imamat/hxh077.

## ◆ type

 enum basix::lattice::type
strong

The type of point spacing to be used in a lattice.

Note
type::chebyshev_plus_endpoints and type::gl_plus_endpoints are only intended for internal use only.
Enumerator
equispaced

Equally spaced points

gll

Gauss-Lobatto-Legendre (GLL) points

chebyshev

Chebyshev points

gl

Gauss-Legendre (GL) points

chebyshev_plus_endpoints

Chebyshev points plus the endpoints of the interval

gl_plus_endpoints

Gauss-Legendre (GL) points plus the endpoints of the interval

## ◆ create()

 std::pair< std::vector< double >, std::array< std::size_t, 2 > > basix::lattice::create ( cell::type celltype, int n, lattice::type type, bool exterior, lattice::simplex_method simplex_method = lattice::simplex_method::none )

Create a lattice of points on a reference cell optionally including the outer surface points.

For a given celltype, this creates a set of points on a regular grid which covers the cell, eg for a quadrilateral, with n=2, the points are: [0,0], [0.5,0], [1,0], [0,0.5], [0.5,0.5], [1,0.5], [0,1], [0.5,1], [1,1]. If the parameter exterior is set to false, the points lying on the external boundary are omitted, in this case for a quadrilateral with n == 2, the points are: [0.5, 0.5]. The lattice type can be chosen as type::equispaced or type::gll. The type::gll lattice has points spaced along each edge at the Gauss-Lobatto-Legendre quadrature points. These are the same as type::equispaced when n < 3.

Parameters
 celltype The cell type n Size in each direction. There are n + 1 points along each edge of the cell type A lattice type exterior If set, includes outer boundaries simplex_method The method used to generate points on simplices
Returns
Set of points. Shape is (npoints, tdim) and storage is row-major