Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!sdd.hp.com!hplabs!nataraja
From: nataraja@hplabs.hpl.hp.com (Balas Natarajan)
Newsgroups: comp.graphics
Subject: marching cubes, holes
Keywords: topology
Message-ID: <6016@hplabsb.hplabs.hpl.hp.com>
Date: 30 Apr 91 19:29:26 GMT
Organization: HPLabs, Palo Alto, CA 94304
Lines: 26

in regard to marching cubes and holes;

there are two possible methods of fixing the holes.

method (1): use an ad hoc but consistent treatment of the ambiguities.
this eliminates the holes, but can result in topologies that are
different from the topology of the true isosurface of the trilinear
interpolant of the data.  an unfortunate side effect of the latter
is that refining the data can cause drastic changes in topology.

method (2): analyze the true topology of the isosurface of the
trilinear interpolant and report this topology.
this eliminates the holes, and the refinement problem.
the challenge here is to still report a small number of polygons
for each voxel, unlike the  method of "dividing cubes";

i have implementations of both methods.  in method (1) i use a slight
and "greedy" modification of the marching cubes case table.
method (2) involves a topological analysis of the trilinear
interpolant in each voxel.
my implementation of method (2) runs about 10% slower than marching cubes on
the sample data i checked it on.

--bkn
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