Concave Hull of a Set of Freeform Closed Surfaces inR3

Bounding hulls, such as convex hulls, have been shown to be useful in many application areas. ?-hull, a generalization of convex hull, has been predominantly employed in reconstruction. Other hulls such as concave hull, which generates nonconvex polygons poly hull, r-shape and s-shape etc. have also been shown to be useful. Most algorithms for bounding hulls deal with point-set as input. Recently, we approached the question of bounding hull to a set of close planar freeform curves and proposed an algorithm for concave hull by defining it (definition was lacking even for a point-set). In this paper, we extend it to concave hull of a set of freeform closed surfaces in R 3 of genus 0. Surfaces used are represented as NURBS (non-uniform rational B-splines). The concept of concave hull is then extended for genus &gt
0 and showed that the hull will consists of lower dimensional elements and topological disks. Based on this observation, a conjecture is proposed for elements in the concave hull of freeform closed objects in n dimensions. � 2012 CAD Solutions, LLC.