Scaffolding skeletons using spherical Voronoi diagrams: feasibility, regularity and symmetry

Alvaro Javier Fuentes Suárez 1 Evelyne Hubert 1
1 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , National and Kapodistrian University of Athens
Abstract : Given a skeleton made of line segments we describe how to obtain a coarse quad mesh of a surface that encloses tightly the skeleton and follows its structure-the scaffold. We formalize as an Integer Linear Program the problem of constructing an optimal scaffold that minimizes the total number of quads on the mesh. We prove the feasibility of the Integer Linear Program for any skeleton. In particular we can generate these scaffolds for skeletons with cycles. We additionally show how to obtain regular scaffolds, i.e. with the same number of quad patches around each line segment, and symmetric scaffolds that respect the symmetries of the skeleton. An application to polygonization of skeleton-based implicit surfaces is also presented.
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Alvaro Javier Fuentes Suárez, Evelyne Hubert. Scaffolding skeletons using spherical Voronoi diagrams: feasibility, regularity and symmetry. Computer-Aided Design, Elsevier, 2018, 102, pp.83 - 93. ⟨10.1016/j.cad.2018.04.016⟩. ⟨hal-01774909⟩

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