Sampling and Interpolation

This module provides two categories of functionality:

Random point sampling

Generate random points distributed over the surface (or volume) of a mesh. Points are sampled using the Dirichlet distribution to produce uniform random barycentric coordinates within each cell. Sampling returns one point for every supplied cell index; repeated indices request multiple samples from a cell. Callers can draw those indices using cell areas/volumes when they need samples uniform over the full mesh measure.

Data interpolation at query points

Given a set of arbitrary query points, find which mesh cell contains each point (via BVH-accelerated search), compute barycentric coordinates, and interpolate point-level or cell-level data to the query locations.

Both capabilities are also accessible as methods on Mesh: sample_random_points_on_cells() and sample_data_at_points().

from physicsnemo.mesh.primitives.surfaces import sphere_icosahedral

mesh = sphere_icosahedral.load(subdivisions=3)

# Sample 10000 points uniformly over surface area. The method returns a
# tensor of coordinates, not a new Mesh.
import torch
cell_indices = torch.multinomial(
    mesh.cell_areas / mesh.cell_areas.sum(),
    num_samples=10000,
    replacement=True,
)
sampled_points = mesh.sample_random_points_on_cells(cell_indices)
print(sampled_points.shape)  # (10000, 3)

# Interpolate data at arbitrary query points
query_points = torch.randn(500, 3)
mesh.point_data["height"] = mesh.points[:, 2]
result = mesh.sample_data_at_points(query_points, data_source="points")

API Reference

Sampling operations for meshes.

This module provides functions for sampling points on meshes, including: - Random uniform point sampling on cells using Dirichlet distributions - Spatial data sampling at query points with interpolation - BVH-accelerated sampling for large meshes (via the bvh parameter)