Boundaries and Topology

This module provides three groups of functionality:

Boundary detection

Identify which vertices, edges, or cells lie on the boundary of a mesh. A boundary facet is one that appears in exactly one cell (interior facets are shared by two cells).

Facet extraction

Extract the (n-1)-dimensional sub-simplices (facets) from an n-dimensional mesh. For a triangle mesh, facets are edges; for a tetrahedral mesh, facets are triangles. The extraction pipeline deduplicates facets and can aggregate per-cell data onto the resulting facet mesh.

Topology checking

Test whether a mesh is watertight (no boundary facets) or manifold (every facet is shared by at most two cells).

These are also accessible as methods on Mesh: get_boundary_mesh(), get_facet_mesh(), is_watertight(), is_manifold().

from physicsnemo.mesh.primitives.surfaces import sphere_icosahedral

mesh = sphere_icosahedral.load(subdivisions=2)

# Topology checks
print(mesh.is_watertight())  # True for a closed sphere
print(mesh.is_manifold())    # True

# Extract boundary (empty for a closed mesh)
boundary = mesh.get_boundary_mesh()

# Extract all edges (facets of a triangle mesh)
edge_mesh = mesh.get_facet_mesh()

API Reference

Boundary detection and facet extraction for simplicial meshes.

This module provides: 1. Boundary detection: identify vertices, edges, and cells on mesh boundaries 2. Facet extraction: extract lower-dimensional simplices from cells 3. Topology checking: validate watertight and manifold properties