Mesh Preprocessing¶

preprocessing ¶

Test mesh creation and preparation for Eikonax solver runs.

Info

The creation of test meshes can be done with any other tool. The format of the required adjacency data for Eikonax is strict, however.

Functions:

Name	Description
`create_test_mesh`	Create a simple test mesh with Scipy's Delauny functionality.
`get_adjacent_vertex_data`	Preprocess mesh data for a vertex-centered evaluation.

eikonax.preprocessing.create_test_mesh ¶

create_test_mesh(mesh_bounds_x: Annotated[Iterable[float], Is[lambda x: len(x) == 2]], mesh_bounds_y: Annotated[Iterable[float], Is[lambda x: len(x) == 2]], num_points_x: Annotated[int, Is[lambda x: x >= 2]], num_points_y: Annotated[int, Is[lambda x: x >= 2]]) -> tuple[jtFloat[npt.NDArray, 'num_vertices dim'], jtInt[npt.NDArray, 'num_simplices 3']]

Create a simple test mesh with Scipy's Delaunay functionality.

This methods creates a simple square mesh with Scipy's Delaunay triangulation.

Parameters:

Name	Type	Description	Default
`mesh_bounds_x`	`Iterable[float, float]`	Mesh bounds for x-direction	required
`mesh_bounds_y`	`Iterable[float, float]`	Mesh bounds for y-direction	required
`num_points_x`	`int`	Number of vertices for x-direction	required
`num_points_y`	`int`	Number of vertices for y-direction	required

Raises:

Type	Description
`ValueError`	Checks that mesh bounds have correct dimension
`ValueError`	Checks that mesh bounds are provided correctly
`ValueError`	Checks that at least two mesh points are chosen

Returns:

Type	Description
`tuple[jtFloat[npt.NDArray, 'num_vertices dim'], jtInt[npt.NDArray, 'num_simplices 3']]`	tuple[npt.NDArray, npt.NDArray]: Array of vertex coordinates and array of simplex indices

eikonax.preprocessing.get_adjacent_vertex_data ¶

get_adjacent_vertex_data(simplices: jtInt[npt.NDArray, 'num_simplices 3'], num_vertices: Annotated[int, Is[lambda x: x > 0]]) -> jtInt[npt.NDArray, 'num_vertices max_num_adjacent_simplices 4']

Preprocess mesh data for a vertex-centered evaluation.

Standard mesh tools provide vertex coordinates and the vertex indices for each simplex. For the vertex-centered solution of the Eikonal equation, however, we need the adjacent simplices/vertices for each vertex. This method performs the necessary transformation.

Parameters:

Name	Type	Description	Default
`simplices`	`npt.NDArray`	Vertex indices for all simplices	required
`num_vertices`	`int`	Number of vertices in the mesh	required

Returns:

Type Description

jtInt[npt.NDArray, 'num_vertices max_num_adjacent_simplices 4']

npt.NDArray: Array containing for each vertex the vertex and simplex indices of all adjacent simplices. Dimension is (num_vertices, max_num_adjacent_simplices, 4), where the 4 entries contain the index of an adjacent simplex and the associated vertices. To ensure homogeneous arrays, all vertices have the same (maximum) number of adjacent simplices. Non-existing simplices are buffered with the value -1.