pub fn solid_euler(solid: &BrepSolid) -> EulerReportExpand description
Closedness and Euler parity: V − E + F − H over the reduced complex, and
whether the counts can belong to a closed orientable surface at all.
Pure topology — ids and use counts, never a coordinate — so like
solid_connectivity it is tolerance-free and cannot be noisy.
This does NOT verify the genus. A genus has no second derivation from the
same cell complex: genus = S − χ/2 IS the definition, so any recomputation
re-runs the same arithmetic. (The only independent route is geometric —
Gauss–Bonnet, ∮K dA plus the edge and vertex terms — which is a different
project.) What parity establishes without a second source is that a body
whose characteristic is odd is not a closed orientable surface at all.
The characteristic is a TOTAL over shells, which is necessary but not
sufficient: two shells each odd sum to even and pass. Per-shell parity needs
edges attributed to shells, which cross_shell_edges makes ambiguous
exactly when it would matter.