Medial axis is known to be unstable for nonsmooth objects. For an open set O, we define the weak feature size, wfs, minimum distance between O and the critical points of the function distance to O.… (More)

Medial Axis Transform is sometimes used as an intermediate representation in algorithms for meshing or recognition of shapes from digitized data. This raises the question whether the Medial Axis… (More)

Given a point set that samples a shape, we formulate conditions under which the Rips complex of the point set at some scale reflects the homotopy type of the shape. For this, we associate with each… (More)

It is well known that the complexity of the Delaunay triangulation of N points in R 3, i.e. the number of its faces, can be O (N2). The case of points distributed on a surface is of great practical… (More)

In this work, one proves that under quite general assumptions one can deduce the topology of a bounded open set in Rn from a Hausdorff distance approximation of it. For this, one introduces the weak… (More)

Correctness of algorithms in computational geometry are usually proved using the unrealistic Real RAM machine model of computation with the undes:uable result that correct algorithms, when… (More)