 
Summary: Eurographics Symposium on Geometry Processing 2009
Marc Alexa and Michael Kazhdan
(Guest Editors)
Volume 28 (2009), Number 5
Recovering Structure from rSampled Objects
O. Aichholzer
, F. Aurenhammer
, B. Kornberger
, S. Plantinga§
, G. Rote¶
, A. Sturm¶
, G. Vegter§
Abstract
For a surface F in 3space that is represented by a set S of sample points, we construct a coarse approximating
polytope P that uses a subset of S as its vertices and preserves the topology of F. In contrast to surface reconstruc
tion we do not use all the sample points, but we try to use as few points as possible. Such a polytope P is useful as
a `seed polytope' for starting an incremental refinement procedure to generate better and better approximations
of F based on interpolating subdivision surfaces or e.g. Bézier patches.
Our algorithm starts from an rsample S of F. Based on S, a set of surface covering balls with maximal radii
is calculated such that the topology is retained. From the weighted shape of a proper subset of these highly
