Geometry#

Fundamental geometric primitives shared across the codebase. These functions compute quantities that underlie both the discrete calculus operators and the curvature computations:

  • Interior angles of each cell at each vertex

  • Circumcenters of each cell (used by DEC for the dual mesh)

  • Dual volumes (Voronoi areas/volumes around vertices and edges)

  • Cotangent weights (the standard FEM/DEC edge weighting)

Most users will not call these functions directly. They are most commonly invoked internally by the calculus and curvature modules, and their results are cached on the :class:~physicsnemo.mesh.mesh.Mesh object. The API exposes them for advanced use cases such as custom discrete exterior calculus (DEC) operators or specialized finite element method (FEM) assembly.

from physicsnemo.mesh.geometry import (
    compute_vertex_angles,
    compute_circumcenters,
    compute_dual_volumes_0,
    compute_cotan_weights_fem,
)
from physicsnemo.mesh.primitives.surfaces import sphere_icosahedral

mesh = sphere_icosahedral.load(subdivisions=2)

angles = compute_vertex_angles(mesh)           # (n_cells, n_manifold_dims + 1)
circumcenters = compute_circumcenters(mesh)    # (n_cells, n_spatial_dims)
dual_areas = compute_dual_volumes_0(mesh)      # (n_points,)
cotan_w = compute_cotan_weights_fem(mesh)      # (n_edges,)

API Reference#

Geometric primitives and computations for simplicial meshes.

This module contains fundamental geometric operations that are shared across the codebase, including: - Interior angle computation for n-simplices - Dual mesh (Voronoi/circumcentric) computations - Circumcenter calculations - Support volume computations (for DEC) - Geometric utility functions

These are used by both DEC operators (calculus module) and differential geometry computations (curvature module).

On this page