Solid Geometry Representation Comparisons

The reference pawn is a region containing seven overlapping ellipsoids. Their union is non-trivial enough to exercise curved surfaces, overlapping interiors, and several component boundaries while remaining reliable across the conversions shown here. The sketch-and-revolve version independently follows the same nominal profile; it is not an exact conversion of the seven-piece CSG model.

Every shaded image uses the same orthographic view, 512x512 image size, material, and single-threaded renderer. The wireframe uses the same view and image size. The faceting and sampling settings are intentionally coarse enough to remain visible. A similar silhouette therefore does not mean that two database objects have the same structure or numerical boundary.

"Solid" in this table means that the stored object supplies usable inside/outside semantics for the pawn. An arbitrary B-rep or mesh is not automatically a solid: its boundary must be closed and consistently oriented. The point size used to render pnts makes each sample a small sphere, but those spheres do not reconstruct the pawn interior. A wireframe likewise does not become a solid merely because its curves appear closed in one view.

Analytic CSG is an implicit representation: intersections with ideal primitive surfaces are computed as needed rather than read from a stored boundary mesh. It is usually the most compact form here and makes edits such as changing the head radius or stem proportions direct. Its Boolean hierarchy also records why the shape was assembled.

sketch plus revolve is another procedural, parameterized description. It works especially well for an axisymmetric part, although a sketch with only line segments produces conical and cylindrical bands rather than the pawn’s original ellipsoidal surfaces. BRL-CAD supports primitive parameters, placement matrices, sketches, and sweeps; that should not be confused with a general constraint solver or an associative feature-history system.

A B-rep stores faces, trims, edges, vertices, and their topology explicitly. Rational NURBS can represent the source quadrics exactly as surfaces, but that does not make every CSG-to-B-rep conversion exact: intersections, trimming, topology classification, and repair use numerical tolerances. Keeping a tree of B-rep leaves isolates conversion to each primitive and retains high-level editing. Evaluating the tree yields a more self-contained boundary for exchange and face-level work, at the cost of that history. This snapshot’s evaluated result passes both brep …​ valid and brep …​ solid; conversion results should be checked rather than assumed to be closed.

All three images expose the same coarse tessellation. Their similar appearance hides an important distinction: the first still has seven editable operands, whereas the NMG and single BoT are evaluated results. NMG can represent polygonal faces and non-manifold adjacency; BoT faces are triangles only. Neither recreates analytic curvature when converted back. Finer tessellation reduces visible error but increases storage and processing cost.

The two voxel images are deliberately separate. The voxelize command emits ordinary box primitives and a combination, while vol reads scalar samples on a regular grid and derives a threshold boundary at ray-trace time. Both are volumetric approximations whose accuracy, memory, and feature size depend on cell spacing. A point cloud samples only the surface and has no connectivity; surface reconstruction requires additional assumptions and may invent or omit geometry.

This wireframe is a view-plane plot of MGED’s unevaluated display of the analytic CSG pawn; hidden lines are not removed. Wireframes are useful for selection, orientation, and seeing component curves, but they are ambiguous: curves alone do not say which side is material, which loops bound faces, or which surfaces enclose volume. Keep the solid that generated the display rather than treating the drawing as an equivalent conversion target.

A conversion command is not an equivalence guarantee. Before replacing source data, check at least these effects:

For parameter changes and repeated design work, prefer analytic primitives, sketch sweeps, and preserved combination trees. Prefer a validated B-rep when trimmed-surface topology or exchange requires it. Use NMG for topology-rich polygonal processing and BoT for triangle-oriented interchange or algorithms. Use voxels for occupancy operations and point clouds for measured or sampled data, not as silent substitutes for a watertight solid.

BRL-CAD also supports specialized forms such as DSP height fields, EBM extrusions, ARS surfaces, metaballs, and legacy poly and bspline objects. They are not shown as interchangeable pawn encodings: DSP and EBM are domain-specific, metaballs change the modeling method, and BoT and B-rep are the preferred general successors to the legacy polygon and spline forms.

The snapshot generator creates the database and runs these principal MGED operations (names shortened here only where noted):

The generator also runs g-voxel and expands its sparse occupied-cell report into the x-fastest byte array used by vol. It then renders every shaded object with rt -B -M -P1 and the saved view; MGED’s plot -2d, plot3-fb, and fb-png produce the wireframe image. See solid_geometry_comparison/generate_comparison.cmake and solid_geometry_comparison/create_pawn.tcl for the complete reproducible inputs.