The medial axis can be viewed as a compact representation for an arbitrary model; it is an essential geometric structure in many applications. A number of practical algorithms for its computation have been aimed at speeding ...

We use Cayley-Menger Determinants (CMDs) to obtain an intrinsic formulation of geometric constraints. First, we show that classical CMDs are very convenient to solve the Stewart platform problem. Second, issues like distances ...

Abstract A polynomial method is described for computing the shortest circuit with a prescribed homotopy on a surface. The surface is not described by a mesh but by a constellation: a set of sampling points. Points close ...

The present article proposes a method to signi cantly improve the construction and updating of 3D geological models used for oil and gas exploration. The proposed method takes advantage of the speci c structures which ...

Despite the growing interest in subdivision surfaces within the computer graphics and geometric processing communities, subdivision approaches have been receiving much less attention in solid modeling. This paper presents ...

We address the problem of updating non-manifold mixed-dimensional objects, described by three-dimensional simplicial complexes embedded in 3D Euclidean space. We consider two local update operations, edge collapse and ...

This paper presents a new and powerful heterogeneous solid modeling paradigm for representing, modeling, and rendering of multi-dimensional, physical attributes across any volumetric objects. The modeled solid can be of ...