 
Summary: OnePass Delaunay Filtering for
Homeomorphic 3D Surface Reconstruction
TR9908
Nina Amenta \Lambda Sunghee Choi y
April 12, 1999
Abstract
We give a simple algorithm for surface reconstruction from a set
of point samples in R 3 , using only one threedimensional Voronoi dia
gram computation. We also give a fairly simple proof that the recon
struction is topologically correct when the input is a sufficiently dense
sample from a smooth surface.
1 Introduction
We give an algorithm for fitting a surface triangulation to a set S of point
samples in three dimensional space. We assume no additional information
besides the threedimensional coordinates of the points. Practical variants of
this problem, in which more information might be given, arise in computer
graphics, reverse engineering, medical imaging and computer vision.
Like many previous algorithms, our approach is to select some subset of the
Delaunay triangles of S as the surface triangulation. This is a natural idea,
\Lambda Computer Sciences, University of Texas, Austin, TX 78712. Supported by NSF grant
