 
Summary: Accurate and Efficient Unions of Balls
Nina Amenta and Ravi Krishna Kolluri y
University of Texas at Austin
Abstract
Given a sample of points from the bound
ary of an object in IR 3 , we construct a rep
resentation of the object as a union of balls.
We use many fewer balls than previous con
structions, but our shape representation is
better. We bound the distance from the
surface of the union to the original object
surface, and show that when the sampling
is sufficiently dense the two are homeomor
phic. This implies a topological relation
ship between the true medial axis of the
object and both the medial axis, and the
ffshape, of the union of balls. We show
that the set of ball centers in our construc
tion converges to the true medial axis as
the sampling density increases.
