Mesh to B-Rep (STL to STEP)

The conversion triangle has three edges that throw information away in a controlled way — implicit→mesh, B-Rep→mesh, mesh→implicit are all discretisations. This is the fourth direction, and it is a different kind of problem because it puts information back: a triangle mesh re-recognised as a parametric BrepSolid of analytic faces. A drilled plate comes back as about seven faces — six planes and one cylindrical bore — not five thousand planar facets wearing a .step extension.

MeshToBrep.Reconstruct is that fourth edge. It segments the triangles into regions across sharp creases, fits a plane / cylinder / sphere to each region with the residual reported, recovers each region boundary as the exact intersection of the two fitted surfaces (so the faces actually close), and welds the trimmed faces into a BrepSolid that must pass Validate().

// A drilled plate, tessellated to a triangle mesh — as if it had arrived as an STL with no
// surface information at all, just facets.
var plate = SolidFactory.MakeBox(new Aabb((0, 0, 0), (40, 30, 10)));
var bore = SolidFactory.MakeCylinder(4, 20).Transformed(Matrix4d.CreateTranslation((20, 15, -5)));
var mesh = BRepTessellator.Tessellate(BrepBoolean.Difference(plate, bore), segmentsPerCircle: 64);

// Re-recognise the analytic surfaces. The report names each region's fitted type and how
// well it fit; RegionCount is the headline metric — seven faces, not the mesh's facets.
var result = MeshToBrep.Reconstruct(mesh);

var scene = new Scene();
scene.Add(new Part("reconstructed", Shape.From(result.Solid!)));

Run it in your browser

The report is the honest half. result.Report.RegionCount is 7; every region is a Plane except the one Cylinder, and each ReconstructedRegion.Residual is the worst distance from a mesh vertex to its fitted surface — machine-epsilon-small here, because a tessellation of exact geometry has its vertices lying on the surface.

The test that separates a real fit from its impostor

A cylinder tessellated at 32, 64, 128 or 256 segments is an inscribed n-gon, and its vertices lie exactly on the cylinder. A least-squares fit through points on a circle recovers the true radius at every density — not the inscribed radius r·cos(π/n), which a chord-length fit would report and which is off by 0.024 at 32 segments. That distinction — exact radius versus inscribed radius — is what tells a reconstruction apart from a plausible impostor, so it is the first thing the tests pin.

Scope, stated

v1 is the tessellated-CAD case: the input is a tessellation of exact geometry, so a fit’s residual is the chord error and nothing else. Reverse-engineering a 3D scan (noise, outliers, missing regions) is a different product and is not attempted — a region whose best plane / cylinder / sphere fit exceeds the tolerance is reported Unfitted by name rather than forced onto a surface it is not.

Refused by name, each for a stated reason:

• an open or non-manifold mesh (run MeshRepair.AutoRepair first — closing holes invents surface, so it is not done silently);
• cone, torus and freeform regions (a NURBS surface fitter is the genuinely new numerical work and is future work);
• a seamless closed surface with no boundary edge — a whole sphere is one face with no edge, and a seamed single-face solid is out of v1 scope (the fit is still reported).