Adaptive medial-axis approximation for sphere-tree construction

Abstract

Hierarchical object representations play an important role in performing efficient collision handling. Many different geometric primitives have been used to construct these representations, which allow areas of interaction to be localized quickly. For time-critical algorithms, there are distinct advantages to using hierarchies of spheres, known as sphere-trees, for object representation. This paper presents a novel algorithm for the construction of sphere-trees. The algorithm presented approximates objects, both convex and non-convex, with a higher degree of fit than existing algorithms. In the lower levels of the representations, there is almost an order of magnitude decrease in the number of spheres required to represent the objects to a given accuracy.

Numerical analysis of contact electrification of non-spherical particles in a rotating drum

“…The irregular particle shape can lead to various dynamic behaviours and alter the charging process during powder handling processes. In the current study, to investigate the effect of the particle shape on contact electrification, the particle shape is approximated using a sphere-tree multi-sphere method [24,25]. For instance, the geometry of the particle can be 6 represented by a 3D object.…”

“…Then the surface of the particle is meshed into triangular elements and the particle is represented using a polyhedron (Figure 1). The sphere-tree construction toolkit (http://isg.cs.tcd.ie/spheretree/) developed by Bradshow and O'Sullivan [25] is then used to construct the particle (multi-sphere) with a selection of primary spheres of various sizes to approximate the shape of the meshed particle.…”

“…The medial axis approximation method is used to generate the multi-sphere assembled by primary spheres [25]. First, the surface of the polyhedron is sampled with a number of seeds as shown in Figure 1.…”

“…A merge optimization method can also be used to control and reduce the number of primary spheres [25]. In this method, each pair of neighbouring spheres are merged and approximated by a new parent sphere that should contain the same set of surface seeds covered by the child neighbouring pair.…”

Inner sphere trees for proximity and penetration queries

“…Previous algorithms for building ordinary sphere trees, like the medial axis approach [BO04], [Hub95] work well if the spheres constitute a covering of the object and have similar size, but in our scenario we use disjoint inner spheres that exhibit a large variation in size. Other approaches based on the k-center problem work only for sets of points and do not support spheres.…”