Seeder

The key functionalities of the seeder module include:

• Generation of seed points within a specified box regularly or using quasi-random methods.

• Filtering seed points based on signed distance functions.

• Calculation of integration points and weights for standard geometric elements such as lines, triangles, and tetrahedrons in specific configurations.

• Tensor product Gauß-Quadrature

Generation of nodes

regular_in_psdf(psdf, min, max, spacing[, atol])	Generates regular seed points within a box and filters them using psdf.
regular_in_box(min, max, spacing)	Generates regular seed points within a specified box.
quasi_random_in_psdf(psdf, min, max, ...[, ...])	Generates quasi-random seed points and filters them using psdf.
quasi_random_in_box(min, max, n_seeds, mode)	Generates quasi-random seed points within a specified box using the given mode.
gauss_points_in_psdf(psdf, min, max, ...[, ...])	Quadrature in background cells.
estimate_size(min, max, fill_ratio)	Estimates the region size based on the fill ratio.
just_in_psdf(psdf, x_seeds, n_seeds, atol[, ...])	Filters seed points based on a positive smooth distance function (psdf).

Numerical integration

tensor_product_two_coordinate_arrays(xi, yi)	Computes the tensor product of two coordinate arrays.
tensor_product_rule(roots_1d, weights_1d, dim)	Generates integration points and weights for tensor product quadrature rules.
gauss_legendre_1d(order)	Returns positions and weights for Gauss-Legendre quadrature for the interval [0,1]
gauss_legendre_nd(dimension, order)	Returns positions and weights for Gauss-Legendre quadrature in higher dimensions based on tensor product rules
gauss_lobatto_1d(order)	Returns positions and weights for Gauss-Lobatto quadrature for the interval [0,1]
gauss_lobatto_nd(dimension, order)	Returns positions and weights for Gauss-Lobatto quadrature in higher dimensions based on tensor product rules
int_pts_ref_tri(order)	Returns tuple with integration point coordinates and weights on a reference triangle, accurate up to polynomial order
int_pts_ref_tet(order)	Returns tuple with integration point coordinates and weights on a reference tetrahedron accurate up to polynomial order
int_pts_line(x_i, order)	Linear mapping of integration points on reference line to integration points on one physical line
int_pts_tri(x_i, order)	Linear mapping of integration points in reference triangle to integration points in one physical triangle
int_pts_tet(x_i, order)	Linear mapping of integration points in reference tetrahedron to integration points in one physical tetrahedron
int_pts_in_line_mesh(x_nodes, elem, order)	Given a mesh of lines, it linearly maps integration points from a reference line onto the actual lines
int_pts_in_tri_mesh(x_nodes, elem, order)	Given a mesh of triangles, it linearly maps integration points from a reference triangle into the actual triangles
int_pts_in_tet_mesh(x_nodes, elem, order)	Given a mesh of tetrahedrons, it linearly maps integration points from a reference tetrahedron into the actual tetrahedrons