Bounding hulls, such as convex hulls, have been shown to be useful in many
application areas. α-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 R3 of genus 0. Surfaces used are represented as NURBS (non-uniform
rational B-splines). The concept of concave hull is then extended for genus > 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