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 ...

The notion of e-sample, as introduced by Amenta and Bern, has proven to be a key concept in the theory of sampled surfaces. Of particular interest is the fact that, if E is an e-sample of a smooth surface S for a suf ciently ...

We present a method for dealing with degenerate situations in an exact boundary evaluation system. We describe the possible degeneracies that can arise and how to detect them. We then present a numeric perturbation method ...

Shape skeletonization (i.e., medial axis extraction) is powerful in many visual computing applications, such as pattern recognition, object segmentation, registration, and animation. This is because medial axis (or skeleton) ...

In this paper we describe the design of B-spline surface models by means of curves and tangency conditions. The intended application is the conceptual constraint-driven design of surfaces from hand-sketched curves. The ...

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 ...

Plumber is a specialized shape classi cation method for detecting tubular features of 3D objects represented by a triangle mesh. The Plumber algorithm segments a surface into connected components that are either body parts ...

In this paper, we present the first nontrivial theoretical bound on the quality of the 3D solids generated by any contour interpolation method. Given two arbitrary parallel contour slices with n vertices in 3D, let a be ...

We present a method for scattered data approximation with subdivision surfaces which actually uses the true representation of the limit surface as a linear combination of smooth basis functions associated with the control ...

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 ...