Technical notes

Some parts of Rockable rest on methods that need more than a reference page: derivations, choices made in the implementation, validation and known limits. They are documented in technical notes, written like short articles, with their references to the literature. Each note is a PDF built from the LaTeX sources kept in this folder of the repository (sphinxdoc/source/notes/<note>/, built with make).

Watertight skin meshes of three-dimensional R-shapes

Exact distance, visualisation and mass properties — V. Richefeu, October 2026.

Download the note (PDF)

A sphero-polyhedron is stored as a skeleton and a radius, so its surface is never built, and the viewers draw it with overlapping spheres, tubes and plates, which fails with transparency and cannot be exported. The note documents the tools that build the surface explicitly:

• the exact signed distance to an R-shape (the distance to the skeleton minus the radius) and its analytic gradient, with the three rules that give its sign (clean manifold, imported face soup, open surface) — class ShapeSDF;

• the watertight skin mesh, by marching cubes and Newton projection onto the exact surface, driven by a single sag tolerance — buildShapeMesh;

• the coplanar merge that removes the extra triangles of the flat faces without moving the surface — simplifyCoplanar;

• the volume, centre of mass and inertia by the divergence theorem on the mesh, compared with the Monte-Carlo estimate of Shape::massProperties;

• the command-line mesher shape2mesh and the .rmsh file read by see and shapeSurvey (see also Converters), the validation tests in test/ShapeSDF, and stress tests on difficult skeletons, with the cases where the mesher fails.

Note

In the library, the mesh gives the volume and the area of a shape. The centre of mass and the inertia computed from the mesh are described in the note but are not yet used by Shape::massProperties, which still relies on the Monte-Carlo integration (keyword MCnstep of the shape file).