 
Summary: The Medial Axis of a Union of Balls
Nina Amenta a;1 Ravi Krishna Kolluri a;1
a University of Texas, Computer Sciences Dept. , Austin, TX 78712, USA
Abstract
We present an algorithm for computing the exact interior medial axis of a union
of balls in IR d . Our algorithm combines the simple characterization of this medial
axis given by Attali and Montanvert with the combinatorial information provided
by Edelsbrunner's shape. This leads to a simple algorithm, which we have imple
mented for d = 3.
1 Introduction
There is considerable interest, in mesh generation, computer graphics, com
puter vision and medical imaging, in describing the shape of an object by its
medial axis. But computing the medial axis of a threedimensional object is
diĘcult in general; it can be done for polyhedra using exact arithmetic and
computational algebra [4].
Attali and Montanvert [1] showed that, in contrast, the medial axis of a three
dimensional union of balls has a simple structure. This is an important special
case, since any threedimensional shape can be approximated by a nite union
of balls; we recently showed [5] that given a certain welldened sample of
points P on an object surface, the union of a subset of the Voronoi balls
