A clean, robust 3D medial axis

Bastien Durix , Kathryn Leonard , Sylvie Chambon , Géraldine Morin (1, 2)

1 IRIT-REVA - Real Expression Artificial Life
2 IRIT - Institut de recherche en informatique de Toulouse

Computing the medial axis of a 3D surface mesh is challenging. Points on the discrete medial axis can be defined as interior Voronoï vertices of the surface mesh, but the resulting medial structure rarely has clean connectivity and consistent geometry. In this paper, we provide a medial axis computation based on the Voronoï diagram able to generate manifold medial sheets with coherent topology and geometry, generating consistent geometric structures similar to those in the continuous setting. Because of the correspondences between the surface mesh and resulting medial mesh, we also provide an efficient way to separate the shape into coherent regions associated to medial structures. This correspondence allows for a medial-axis-based filtration of surface structures to generate a Hausdorff ε-approximation of the surface points based on a simplified medial axis, thereby providing a robust medial representation with guaranteed surface approximation.

Mots clés: Skeleton; Structure; Mesh; Robust; Approximation guarantees

Domaines: Géométrie algorithmique [cs.CG]; Mathématique discrète [cs.DM]; Topologie géométrique [math.GT]

Bastien Durix, Kathryn Leonard, Sylvie Chambon, Géraldine Morin. A clean, robust 3D medial axis. 2023. ⟨hal-04262568v2⟩