Run the Cauchy-Crofton ray-sampling estimator on an already-prepared raytrace instance. The caller owns rtip and must call rt_free_rti after this function returns.
- Parameters
-
| out_surf_area | Receives the estimated surface area (mm^2). |
| out_volume | Receives the estimated volume (mm^3). |
| out_aabb_min | Optional sampled AABB minimum; pair with out_aabb_max. |
| out_aabb_max | Optional sampled AABB maximum; pair with out_aabb_min. |
| out_obb | Optional sampled OBB in ARB8 point ordering. |
| out_points | Optional sampled surface points allocated with bu_malloc; the caller must free the returned array. |
| out_point_count | Number of returned points; pair with out_points. |
| rtip | Prepared raytrace instance (rt_prep_parallel must have been called first). |
| params | Stopping criteria. NULL or all-zero -> 2 000-ray default. |
| bbox_min | Optional focused sampling bbox minimum. Pass NULL to derive the sampling sphere from prepared soltab extents. |
| bbox_max | Optional focused sampling bbox maximum. Pass NULL to derive the sampling sphere from prepared soltab extents. At least one output must be requested. All output pointers are optional except that the AABB pair and point-array/count pair must be supplied together. Bounds and points are derived from the same converged sample set used for the surface-area estimate. |
- Returns
- The total number of ray-surface crossings accumulated during sampling (>= 0) on success; -1 on bad arguments or a requested bound fit failure. A return value of 0 means no geometry was intersected by the sampler.
Near-tolerance sliver geometry: CSG vs BoT divergence
The Cauchy-Crofton formula is mathematically exact for any well-defined solid, but its numerical result depends critically on how the underlying raytracer reports intersections. Two representations of what is intended to be the same geometry can yield radically different – and both internally consistent – surface-area estimates when the geometry contains a sub-tolerance sliver.
Anatomy of the sliver
Consider a window-frame region modelled as a base box minus a slightly smaller cutout box (the r.wind6 pattern in havoc.g). If the subtractor's face protrudes less than BN_TOL_DIST (0.0005 mm) past the base face, a thin sliver of near-zero thickness is present in the raw CSG description. The sliver has two large faces (the Z-faces of the cutout interior, each ~41 600 mm² for a 160 × 260 mm cutout) and a negligible edge band.
CSG raytracer behavior (boolweave filtering)
The BRL-CAD CSG Boolean evaluator (boolweave) discards any solid segment whose thickness is below BN_TOL_DIST. For a ray fired perpendicular to the sliver faces the two-segment chord through the sliver is 0.000340 mm thick – shorter than BN_TOL_DIST – so boolweave merges the entry and exit events and reports a MISS through that region.
For oblique rays, however, the apparent thickness grows with the secant of the angle from normal: chord = d / cos(θ). Once θ exceeds approximately 47° (for a 0.000340 mm gap and a 0.0005 mm tolerance) the sliver segment survives boolweave filtering and contributes two crossing events. Since the Crofton bounding sphere uniformly samples all directions, roughly 68% of solid angles subtend the sliver at angles steep enough to be counted. The result is that the CSG SA estimate converges to a value that is ~74% higher than the ideal clean-frame SA – not because sampling is insufficient, but because the CSG raytracer is correctly reflecting its own view of the geometry: the sliver is visible from the majority of directions but hidden from near-perpendicular directions. Denser sampling does not reduce this bias; experiments with up to 2 000 000 rays confirm that the CSG estimate is stable at ~89 900 mm² (vs an ideal of 51 520 mm²) within the first 500 000 rays and does not drift further regardless of sample count.
BoT raytracer behavior (per-triangle hits)
A triangle mesh (BoT) has no boolweave layer. Every ray that intersects a triangle face produces a hit event regardless of how thin the resulting segment is. A BoT tessellated from the raw CSG without any sliver correction therefore exposes both large sliver faces to the full Crofton hemisphere, converging to ~130 400 mm² – approximately the ideal frame SA plus both full sliver faces (51 520 + 2 × 41 600 ≈ 134 720 mm²).
Perturbed BoT (correct result)
The facetize command's variant-planning / perturb pass enlarges the subtractor just enough to eliminate the sub-tolerance sliver before Manifold performs its Boolean evaluation. The resulting BoT has no phantom interior faces and its Crofton SA converges to ~51 750 mm² – within 0.5% of the analytic ideal – typically in fewer than 64 000 rays (<0.1 s).
Summary table (measured, 200 × 300 × 8 mm frame,
gap = 0.000340 mm < BN_TOL_DIST = 0.0005 mm)
| Representation | Converged SA (mm²) | vs ideal | Stable by |
| CSG (raw, unperturbed) | ~89 900 | +74.5% | ~500k rays |
| BoT (perturbed) | ~51 750 | +0.5% | ~64k rays |
| BoT (no perturb) | ~130 400 | +153% | ~32k rays |
Design implication
The Crofton estimator is accurate and well-converged in all three cases; the divergence is caused by the geometry, not by sampling noise. When comparing a CSG Crofton SA against a BoT Crofton SA as a facetize quality check, geometry with sub-tolerance slivers will always produce a mismatch no matter how many rays are fired. For such geometry the volume estimate (which is insensitive to sliver SA: sliver volume is ~14 mm³ out of 147 200 mm³, or 0.01%) is a far more reliable cross-check metric.
1.9.8