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From: yamo@nas.nasa.gov (Michael Yamasaki)
Newsgroups: comp.graphics.visualization
Subject: Re: Marching Cubes
Keywords: marching cubes, isosurface
Message-ID: <1991Apr29.191415.23439@nas.nasa.gov>
Date: 29 Apr 91 19:14:15 GMT
References: <1991Apr24.211855.11705@rice.edu> <1991Apr25.005705.16988@jarvis.csri.toronto.edu> <2551@lee.SEAS.UCLA.EDU> <5266@network.ucsd.edu>
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In article <5266@network.ucsd.edu> slamont@network.ucsd.edu (Steve Lamont) writes:
>
>The problem with tetrahedra is effectively the same as the problem with cubes,
>they can both produce surfaces with holes in them.  If you play around with
>the tetrahedral algorithm, you'll see what I mean.
>

Uh, gee, I've played around with them quite a bit and still haven't run
into that ambiguous case. And since there are only 2 real cases...

         +            +
        /|\          /|\
       - | -        + | -
        \|/          \|/
         -            -

There is a bit of a trick to decomposing the cubes into tetrahedra properly
to avoid holes.  If you are decomposing the cubes into 5 tetrahedra there 
are two possible outcomes (mirror symmetry).  These two decompositions 
should alternate such that each laterally adjacent cube is a mirror image. 
In this way the edges of the tetrahedra "line up".  Otherwise the 
edges cross and different values are used for the interpolations. In 
which case the surfaces are riddled with holes.

Adjacent cubes should be like this:

         ---------            _______
        /        /|\        /|\      
       /        / | \      / | \      
      /________/  |  \    /  |  \      
      \        \  |  /    \  |  /      
       \        \ | /      \ | /      
        \________\|/        \|/______      

Not like this:

         ---------            _______
        /        /|\        / \      
       /        / | \      /   \      
      /________/  |  \    /_____\      
      \        \  |  /    \     /      
       \        \ | /      \   /      
        \________\|/        \ /______      


I would imagine there is a similar pattern for decomposing the cubes into
6 tetrahedra though I haven't worked with this method.


                                       -Yamo-
                                 yamo@wk209.nas.nasa.gov
                                yamo@amelia.nas.nasa.gov
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