Lattices of points. More...
Enumerations  
enum  type { equispaced = 0, gll = 1, chebyshev = 2, gl = 4, chebyshev_plus_endpoints = 10, gl_plus_endpoints = 11 } 
enum  simplex_method { none = 0, warp = 1, isaac = 2, centroid = 3 } 
Functions  
xt::xtensor< double, 2 >  create (cell::type celltype, int n, lattice::type type, bool exterior, lattice::simplex_method simplex_method=lattice::simplex_method::none) 
Lattices of points.

strong 
The method used to generate points inside simplices.
lattice::simplex_method::none can be used when no method is needed (eg when making points on a quadrilateral, or when making equispaced points).
lattice::simplex_method::warp will use the warping defined in Hesthaven and Warburton, Nodal Discontinuous Galerkin Methods, 2008, pp 175180 (https://doi.org/10.1007/9780387720678).
lattice::simplex_method::isaac will use the method described in Isaac, Recursive, ParameterFree, Explicitly Defined Interpolation Nodes for Simplices, 2020 (https://doi.org/10.1137/20M1321802).
lattice::simplex_method::centroid will 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, 2001 (https://doi.org/10.1093/imamat/hxh077).

strong 
The type of point spacing to be used in a lattice.
lattice::type::equispaced represents equally spaced points on an interval and a regularly spaced set of points on other shapes.
lattice::type::gll represents the GLL (GaussLobattoLegendre) points.
lattice::type::chebyshev represents the Chebyshev points.
lattice::type::gl represents the GL (GaussLegendre) points.
lattice::type::chebyshev_plus_endpoints represents the Chebyshev points plus the endpoints of the interval. lattice::type::gl_plus_endpoints represents the Chebyshev points plus the endpoints of the interval. These points are only intended for internal use.
xt::xtensor< double, 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 "equispaced" or "gll". The "gll" lattice has points spaced along each edge at the GaussLobattoLegendre quadrature points. These are the same as "equispaced" when n<3.
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 