🐛[BUG]: Several physicsnemo.mesh primitives load with reversed cell orientation #2135

Version

2.3.0a0 (commit 7e646b4)

On which installation method(s) does this occur?

Source

Describe the issue

Several primitives in physicsnemo.mesh.primitives wind their cells the opposite way from the rest of the library.

The convention elsewhere is clear:

• A cell of a Mesh[n, n] has a positive signed volume, det(v1 - v0, ..., vn - v0) > 0. validate(check_inverted_cells=True) flags every other cell as inverted.
• sphere_volume, cylinder_volume and lumpy_ball call orient_positive to enforce this.
• A closed Mesh[2, 3] has outward normals, as in sphere_icosahedral, sphere_uv, cube_surface, cylinder and lumpy_sphere.
• The cube_surface docstring states this convention: "counter-clockwise winding when viewed from outside".
• A triangle in the xy plane wound counterclockwise has normal +z, as basic.single_triangle_3d shows.

I loaded every primitive with its default arguments and measured the orientation. These disagree with the convention:

The torus signed volume should be +2π²Rr² = +1.777 for the defaults.

These primitives agree with the convention:

• basic: all
• planar: annulus_2d, circle_2d, equilateral_triangle, regular_polygon
• surfaces: cone, cube_surface, cylinder, cylinder_open, icosahedron_surface, octahedron_surface, sphere_icosahedral, sphere_uv, tetrahedron_surface
• volumes: cylinder_volume, tetrahedron_volume
• procedural: lumpy_ball, lumpy_sphere
• pyvista_datasets: hexbeam, ant, cow

Two related observations:

• curves.circle_2d and curves.ellipse_2d run counterclockwise. The 2D edge normal rotates the tangent counterclockwise, so their normals point inward.
• volumes.sphere_volume has 4 of 1164 cells with negative volume. Each has |V| < 1.5e-12, so these are slivers from delaunay_3d, not a winding error. PR Mesh: fix degenerate and overlapping cells in primitive generators #2129 replaces that construction.

Expected: every primitive follows the convention above. Actual: the primitives in the table load reversed. Tests and examples built on them see inverted cells, inward normals and negative curvature.

Minimum reproducible example

python - <<'EOF'
from physicsnemo.mesh.primitives import planar, surfaces, volumes

sq = planar.unit_square.load(subdivisions=1)
print("unit_square inverted:", sq.validate(check_inverted_cells=True)["n_inverted_cells"], "of", sq.n_cells)

cube = volumes.cube_volume.load(subdivisions=2)
print("cube_volume inverted:", cube.validate(check_inverted_cells=True)["n_inverted_cells"], "of", cube.n_cells)

for name in ["sphere_icosahedral", "torus"]:
    m = getattr(surfaces, name).load()
    print(name, "mean curvature:", round(m.mean_curvature_vertices.mean().item(), 3))
EOF

Relevant log output

unit_square inverted: 8 of 8
cube_volume inverted: 24 of 48
sphere_icosahedral mean curvature: 1.0
torus mean curvature: -1.588

Environment details

+ Environment location: Bare-metal, CPU only (CUDA_VISIBLE_DEVICES unset)
+ Python 3.13.8, torch 2.13.0+cu130, tensordict 0.15, warp 1.17.0