Remeshing#

Uniform remeshing via the ACVD (Approximate Centroidal Voronoi Diagram) clustering algorithm. Given a target number of clusters, the algorithm redistributes mesh vertices to produce a more uniform cell distribution.

The approach is dimension-agnostic and works for any simplicial manifold:

Weight vertices by incident cell areas
Initialize clusters via area-based region growing
Remove spatially isolated cluster regions
Reconstruct a simplified mesh from cluster adjacency

Note

The output mesh may contain a small percentage (~0.5-1%) of non-manifold edges, which is inherent to the face-mapping approach. Higher cluster counts relative to mesh resolution produce better manifold quality.

from physicsnemo.mesh.remeshing import remesh
from physicsnemo.mesh.primitives.surfaces import sphere_icosahedral

mesh = sphere_icosahedral.load(subdivisions=3)
remeshed = remesh(mesh, n_clusters=100)
print(remeshed.n_cells)  # approximately 200 triangles

API Reference#

Mesh remeshing and cell partitioning.

This module provides two complementary algorithms for mesh coarsening:

Cell partitioning (partition_cells()):: Assigns each cell of a fine mesh to its nearest seed point (by Euclidean centroid distance) and accumulates area, normal, and centroid per cluster. This is a single-step discrete approximation to the restricted Voronoi diagram on the surface. Pure PyTorch, no external dependencies.
ACVD remeshing (remesh()):: Iterative Approximate Centroidal Voronoi Diagram clustering that creates a new mesh topology with approximately uniform cell distribution. Requires the pyacvd package.

partition_cells is also a natural building block for a pure-PyTorch CVT (Lloyd’s algorithm iterates: partition -> move seeds to cluster centroids -> repeat).

Example

>>> from physicsnemo.mesh.primitives.surfaces import sphere_icosahedral
>>> mesh = sphere_icosahedral.load(subdivisions=3)
>>> # Remesh a triangle mesh to ~100 triangles
>>> remeshed = remesh(mesh, n_clusters=100)
>>> assert remeshed.n_cells > 0