Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!crdgw1!uunet!zephyr.ens.tek.com!orca.wv.tek.com!pogo!jd
From: jd@pogo.WV.TEK.COM (John Dalrymple)
Newsgroups: comp.graphics.visualization
Subject: Re: Marching Cubes
Summary: use 24 tetrahedra
Keywords: marching cubes, isosurface
Message-ID: <10820@pogo.WV.TEK.COM>
Date: 3 May 91 17:41:45 GMT
References: <1991Apr24.211855.11705@rice.edu> <1991Apr25.005705.16988@jarvis.csri.toronto.edu> <2551@lee.SEAS.UCLA.EDU> <5266@network.ucsd.edu> <1991Apr29.191415.23439@nas.nasa.gov>
Reply-To: jd@pogo.WV.TEK.COM (John Dalrymple)
Distribution: na
Organization: Tektronix, Inc., Wilsonville,  OR.
Lines: 33


If you have cycles to burn (:-) you may want to decompose a cube-like data
cell as follows:

	Average the spatial coordinates of the 4 vertices of each face to 
        yield an interior vertex on each face.  Average the data values
	at the face vertices and assign the result to this "face-interior
	vertex."

	Average the spatial coordinates of all 8 vertices of the cell
	to yield a vertex interior to the cell.  Average all 8 cell-vertex
        data values and assign the result to this "cell-interior vertex."

	Tessellate the cell into 24 tetrahedra by connecting the
	cell-interior vertex to all the other vertices, and by
	connecting each face-interior vertex to its corresponding face
	vertices.

Each tessellated face looks like this:

	*-----*
        |\   /|
        | \ / |
	|  #  |		* = original vertex
	| / \ |		# = averaged face-interior vertex
	|/   \|
        *-----*

This gives a better polyhedral approximation to the isosurface inside
the cell than does a tessellation into five tetrahedra, and is also
independent of the cell's position in the overall mesh.

JD