TriangleManifold

TriangleManifold classifies points against a closed, consistently oriented triangulated (TRI3) surface mesh in 3-D. Given a prepared 2-D surface mesh it validates that the mesh forms a closed 2-manifold, builds a lightweight yz-plane acceleration grid, and answers point-in-solid queries.

Containment is resolved in three stages:

1. a cheap global bounding-box rejection;

2. near-surface detection via a pre-built point locator (points within surface_tolerance of the surface are treated as on the surface);

3. odd/even parity counting along a fixed +x ray, with an automatic fallback to a solid-angle accumulation test when the ray grazes a triangle edge or vertex.

The class exposes contains(), which returns true for interior and on-surface points, and sideness(), which returns SurfaceSide::INSIDE, ::OUTSIDE, or ::ON. On-surface points are detected before parity counting, so sideness() and contains() agree (contains() == sideness() != OUTSIDE).

This engine backs the fixed_x_ray method of PointInPolyhedronCheckUO (via PointContainmentClassifier). It supports only 3-D TRI3 surfaces. The referenced mesh must be serialized and must outlive the object; any geometric transforms should be applied to the mesh before construction.