tessellation

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name: tessellation description: Use when meshing B-Rep faces or debugging tessellation output in crates/operations/src/tessellate/. Triggers: mesh cracks at shared face boundaries, boundary_edge_count > 0, non-manifold edges, a hole on a sphere/torus skinned over (mesh area too large), flipped triangle normals, adding or changing a face mesher, or choosing between CDT and a structured band mesher on a periodic surface (cylinder, cone, sphere, torus).

Tessellation: watertight meshing of B-Rep faces

When to use

You are producing or debugging a TriangleMesh from a solid: cracks between faces, boundary_edge_count(mesh) > 0, wrong mesh area or volume, flipped normals, or you are adding a mesher path. All CPU meshing lives in crates/operations/src/tessellate/. For verifying the overall solid (volume, Euler, validity) see the solid-verification skill; for booleans producing bad faces to mesh, see boolean-debugging; for keeping faces analytic in the first place, see analytic-preservation.

Quick reference

use brepkit_operations::tessellate::{
    tessellate_solid, is_watertight, boundary_edge_count, non_manifold_edge_count,
};

let mesh = tessellate_solid(&topo, solid, 0.1)?;
assert_eq!(boundary_edge_count(&mesh), 0);
assert!(is_watertight(&mesh));

is_watertight == boundary edges 0 AND non-manifold edges 0. Defined in crates/operations/src/tessellate/mesh_ops.rs, re-exported from tessellate/mod.rs. TriangleMesh { positions, normals, indices } is in tessellate/mod.rs. Deflection is the max chord sag; the default angular tolerance is brepkit_math::chord::DEFAULT_ANGULAR_TOL.

Locate the meshers and the dispatch:

rg -n 'pub\(super\) fn tessellate_' crates/operations/src/tessellate/nonplanar.rs
rg -n 'handled_notch|handled_band|tessellate_revolution_band_shared' crates/operations/src/tessellate/solid.rs

Expected mesher set (verify, do not assume): tessellate_revolution_band_shared, tessellate_torus_notch_band, tessellate_latitude_band_shared, tessellate_nonplanar_cdt, tessellate_nonplanar_snap. Full inventory and dispatch order: see reference.md, section "Mesher inventory".

Core doctrine: shared vertices by construction

Independently triangulated adjacent faces crack at their shared boundary. tessellate_solid samples every edge exactly once into a shared pool (edge_global_indices); every face's boundary triangles must reference those shared global ids. Two ways a face can fail this:

1. The snap path (tessellate_nonplanar_snap) meshes the face independently and reconciles rim vertices to the pool by 1e-6 proximity. When independent rim sampling and shared-edge sampling diverge by one segment (a radius/deflection dependent off-by-one), rim vertices land at different angles, miss the snap, and become near-coincident duplicates: a crack. This is issue #696 (drilled magnet hole); the rationale is in the doc comment of tessellate_revolution_band_shared in nonplanar.rs.
2. Free CDT on a periodic wall. Unwrapping u to a flat strip and welding u=0 to u=2pi still leaves the wall CDT free to disagree with a separately triangulated cap disc exactly at the cap-rim/seam corner. CDT cannot weld to a mesh it did not build. Same crack class as #696.

Rule: periodic-wall bands get STRUCTURED meshers that consume the shared rim vertex ids directly. Each structured mesher is deliberately narrow, checks its exact shape, and returns Ok(false) to defer to the fallback chain otherwise. When adding one, copy that contract: never guess, always defer.

CDT (tessellate_nonplanar_cdt) is correct for faces whose UV boundary is a genuine simple polygon: non-periodic patches, partial-revolution faces, faces with inner wires that do not wrap the seam.

Verify a change (procedure)

1. Build the shape, tessellate at two deflections (e.g. 0.1 and 0.5). Sampling-density bugs are deflection dependent; one value can pass by luck.
2. Check boundary_edge_count(&mesh) == 0 and non_manifold_edge_count(&mesh) == 0 at both. A small stable nonzero count (say 8) localized at seam/rim corners means a shared-vertex violation, not "almost done tuning". See reference.md, "Reading a nonzero boundary count".
3. Check orientation via signed volume: integrate the mesh (divergence theorem, as measure/volume.rs does) and compare against the analytic volume. Sign flip = global winding wrong; magnitude too large = a hole skinned over; too small = a face missing or inverted run.
4. All tessellation tests live in crates/operations/src/tessellate/tests.rs (included via mod tests; in tessellate/mod.rs); add one there that asserts bd=0 for your exact shape class.

Symptom to cause

Symptom	Likely cause	Where to look
Cracks at a hole rim or cap boundary	Snap path proximity miss (off-by-one rim sampling)	Did dispatch fall through to tessellate_nonplanar_snap? Instrument solid.rs dispatch
Mesh area/volume too LARGE on a bored sphere/torus	Constant-v band degenerated in UV, CDT skinned the hole	Should have hit tessellate_latitude_band_shared; check its early-return conditions
Stable small nonzero boundary count at seam corners	CDT wall vs separately meshed cap disagreement	Needs a structured shared-vertex mesher, not CDT tuning
Zero-extent face, empty triangulation on a closed edge	Endpoint-derived range on a closed edge (start == end)	edge_sampling.rs is_closed() handling; sample along the curve
Scattered flipped triangles inside one face, thin slivers	Per-triangle normal flipping on stitch triangles	Orient the whole run once: orient_triangle_run in nonplanar.rs
Whole face wound inward	Run-level flip decision wrong (degenerate largest triangle)	orient_triangle_run normal comparison at the centroid
Non-manifold edges after boolean	Upstream face topology (figure-eight wires), not the mesher	See boolean-debugging; also crates/heal/src/upgrade/split_self_intersecting_wires.rs

Degenerate-UV traps

• Constant-v bands give CDT nothing to bound. A sphere/torus band between two constant-v full-revolution loops projects each boundary to a zero-area back-and-forth segment in UV; CDT then fills the removed cap. The dispatch comment in solid.rs (search degenerates in UV) documents this. Structured band meshers exist because of it.
• Closed edges: start == end. Any quantity derived from a closed edge's endpoints (param range, winding, extent) collapses to zero. circle_param_range and sample_edge in edge_sampling.rs special-case edge.is_closed() to return the full period. Rule: whenever an edge can be closed, sample points along the curve; never derive from endpoints. The boolean engine learned the same lesson (face_boundary_all_degenerate in crates/algo/src/pave_filler/phase_ff.rs samples along curves).

Triangle orientation: orient runs, not triangles

Structured meshers emit a coherently wound run, then make ONE flip decision for the whole run via orient_triangle_run (nonplanar.rs): take the largest-area triangle (most reliable normal), compare its geometric normal to the surface outward normal at its centroid, flip the entire run if they disagree. Per-triangle flipping is unstable on the thin stitch triangles that bridge unevenly sampled rings; it flips neighbors inconsistently and breaks the 2-manifold. If you write a new stitching routine, emit raw, then orient the run.

Known-terminal case: crossing seam holes

A full-revolution periodic wall carrying two hole loops that CROSS each other (figure-eight, pinching at two points; the equal-radius perpendicular cylinder-union wall) is not triangulable by any current path. Two crossing hole loops are invalid hole topology for flat CDT, and the wall is periodic so flat-strip CDT cracks at the seam. Do not grind this blind. Bounded fixes only; details and what a real fix requires are in reference.md, "Crossing seam holes". Note split_self_intersecting_wires.rs in heal is a wire-topology cleanup and is NOT the missing geometric face split.

GPU path: keep faces analytic

CPU tessellation is not the only consumer of surface parameters. crates/render/src/compute_mesh.rs meshes cylinders on the GPU from packed analytic descriptors at screen-space LOD (CylinderDescriptor, screen_space_tess_factor). Cylinder only at time of writing; verify with rg -n 'Descriptor' crates/render/src/compute_mesh.rs before claiming more. Any operation that degrades an analytic face to NURBS or mesh kills this path for that face. See the analytic-preservation skill; audit degradations with cargo run --release --example approx_census -p brepkit-operations.

Anti-patterns

• Do NOT conclude "CDT just needs denser sampling" when boundary edges sit at seam or rim corners. That is a structural shared-vertex problem; density changes move the cracks, they do not close them.
• Do NOT snap vertices by proximity as a fix. Snapping is the disease (#696), not the cure.
• Do NOT widen a structured mesher's acceptance heuristically. If the shape check is not exact, return Ok(false) and let the chain fall through; a wrong structured mesh is worse than a snap-path crack.
• Do NOT fix winding per-triangle. Orient the run.
• Do NOT derive anything from a closed edge's endpoints.
• Do NOT tessellate inside L0-L2 crates to work around a hard face. Tessellation lives in operations (L3); core stays analytic (see CLAUDE.md, layer rules).
• Do NOT treat one passing deflection value as proof; sampling off-by-ones are deflection dependent.