The (weighted) α-complex allows one to perform a multi-scale analysis of a collection of points (balls), in conjunction with a growth model encoded in Voronoi (power) diagrams. α-complexes are thus associated to affine Voronoi diagrams, and have been instrumental in surface reconstruction, geometric inference, as well as molecular modeling.
This work is concerned with the 3D λ-complex, namely the equivalent of the α-complex for an additively-multiplicatively weighted distance. Such a distance is associated with so-called compoundly weighted Voronoi diagrams, whose bissectors are degree four algebraic surfaces. We present the filtration associated with the λ-complex, together with the predicates required to compute it. Finally, we discuss an application to represent toleranced i.e. uncertain models in molecular modeling.
Joint work with Frédéric Cazals.
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