  Motivated by the fact that the medial axis transform is able to encode nearly
the complete shape, we propose to use as few medial balls as possible to
approximate the original enclosed volume by the boundary surface. We
progressively select new medial balls, in a top-down style, to enlarge the
region spanned by the existing medial balls. The key spirit of the selection
strategy is to encourage large medial balls while imposing given geometric
constraints. We further propose a speedup technique based on a provable
observation that the intersection of medial balls implies the adjacency of
power cells (in the sense of the power crust). We further elaborate the
selection rules in combination with two closely related applications. One
application is to develop an easy-to-use ball-stick modeling system that helps
non-professional users to quickly build a shape with only balls and wires, but
any penetration between two medial balls must be suppressed. The other
application is to generate porous structures with convex, compact (with a high
isoperimetric quotient) and shape-aware pores where two adjacent spherical
pores may have penetration as long as the mechanical rigidity can be well
preserved.
