Neighbors and Adjacency#

This module computes topological adjacency relationships between mesh elements. Rather than using spatial proximity, it indicates the mesh connectivity for which points/cells are connected to which other points/cells.

Four adjacency types are supported:

  • Point-to-points: which vertices share an edge (graph neighbors)

  • Point-to-cells: which cells contain a given vertex (the vertex star)

  • Cell-to-cells: which cells share a facet

  • Cell-to-points: which vertices belong to a given cell

All adjacency relationships are returned as Adjacency objects, which encode ragged arrays using an (indices, offsets) pair. This is the same sparse format used by PyTorch Geometric’s edge_index and is efficient for GPU computation. For debugging or interoperability, call .to_list() to convert to a Python list of lists.

from physicsnemo.mesh.primitives.surfaces import sphere_icosahedral

mesh = sphere_icosahedral.load(subdivisions=2)

# Compute adjacency (also available as Mesh methods)
p2p = mesh.get_point_to_points_adjacency()
c2c = mesh.get_cell_to_cells_adjacency()

# Inspect the ragged structure
print(p2p.indices.shape)   # (total_neighbor_pairs,)
print(p2p.offsets.shape)   # (n_points + 1,)

# Convert to list-of-lists for inspection
neighbors_of_vertex_0 = p2p.to_list()[0]

API Reference#

Neighbor and adjacency computation for simplicial meshes.

This module provides GPU-compatible functions for computing various adjacency relationships in simplicial meshes, including point-to-cells, point-to-points, and cell-to-cells adjacency.

All adjacency relationships are returned as Adjacency tensorclass objects using offset-indices encoding for efficient representation of ragged arrays.

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