>Can anyone recommend some references for "Meta-Sphere" or "Blobby Molecule"
>algorithms that create a tesselated 3-d geometry? (as opposed to scanline
>algorithms for direct rendering of these primitives)

	The surfaces of these blobby molecules are implicitly defined.
That is, they are defined by a single equation

	f(x, y, z) = 0

	I assume that you have seen Blinn's '82 paper on rendering these
directly.  It was printed in ACM transactions on Graphics, and pointed to
in that year's SIGGRAPH proceedings. 

	In the last couple of years several people have looked into using 
polygonal representations of implicit surfaces. Implicit surfaces
are becoming a little more popular because they are nice for defining
"blending surfaces". My advisor wrote his thesis on the form the implicit
blending surface needs to be in. Data that is in the form of spatially
arranged density data can also be viewed by picking a level set to be
the surface of interest. Lots of data is in this form: CT scan, NMR, 
some seismic data, etc. 

	Back to your initial question: what are some references on 
polygonalizing these things?

	Blinn, J., (1982)
	A Generalization of Algebraic Surface Drawing,
	ACM Transactions on Graphics, Vol. 1, Number 3, pp. 235-256.

	Wyvil, G.,McPheeters, C., and Wyvil, B., (1986)
	``Data structure for  soft objects",
	The Visual Computer,2:227-234.

	Lorenson, W., and Cline, H. (1987)
	``Marching Cubes: A High Resolution 3D Surface Construction Algorithm",
	Computer Graphics, Volume 21, No. 4, pp. 163-169.

	Duurst, M. J. (1988),
	"Additional Reference to Marching Cubes", 
	Computer Graphics, 
	Volume 22, No. 2, pp. 72,73.

	Bloomenthal, J., (1988) 
	Polygonalization of Implicit Surfaces,
	Computer Aided Geometric Design 5 (1988), pp. 341-355.
	(also Xerox Report CSL-87-2. and in SIGGRAPH course notes (87 & 88?))

	Hall, M., and Warren, J. (1988)
	"Adaptive Tessellation of Implicitly Defined Surfaces",
	(Submitted for publication  and Rice Technical report)
	*copies on e-mail request*


	As mentioned before, Blinn rendered these things directly. 
The brothers Wyvil have done a lot of work incorporating these objects
into their Graphicsland environment at U. Calgary. I see some
of their students posting in this group, if you have questions 
for them. Lorenson and Cline 
showed a table lookup algorithm that is quite nice. It does have 
(at least) one bug, a consequence of which is pointed out by Duurst,
but I have used it in a number of applications with pleasing results.
Bloomenthal presents an algorithmic approach with the added feature 
of being able to adaptively approximate the surface. That is, where
the surface is flat[ter], use fewer but larger polygons to approximate it.
His algorithm is tricky to implement correctly by his own admission. 
Joe Warren and I found a different method for adaptively polygonalizing
the surface that we think is easier to implement. 

Hope this helps. 

- mark

-----------------------------------------------------------

From: johnston@lbl-csam.arpa (Bill Johnston [csr])
Newsgroups: comp.graphics
Subject: Re: Blobbly Molecules - tessellating
Date: 16 Feb 89 19:47:29 GMT
Organization: Lawrence Berkeley Laboratory, Berkeley CA

The medical imaging folks have developed a very nice algorithm
called ``Marching Cubes'' for tessellating complex 3D surfaces:
  .ds [A W. Lorensen
  .as [A ", H. Cline
  .ds [T Marching Cubes: A High Resolution 3D Surface Construction Algorithm
  .ds [J Computer Graphics
  .ds [V 21
  .ds [N 4
  .ds [D 1987
  .ds [O (Proceedings ACM SIGGRAPH, 1987.)

This algorithm works locally, seeking to fit a surface through each
elemental cube (voxel) (as defined by the the grid intersections) that
intersects the surface. The result is a large number of small polygons
that completely cover the surface f=C.

For ``blobby molecules'' you might contour the electric field strength
using Marching Cubes to tessellate the surface |E|=C. We have made an
interesting movie of methane molecules trapped in a crystal lattice by
just tessellating the Van der Waal's radii about the collection of
atomic centers for methane.  We did nothing more complex than
tessellating a contour of the field f=x**2+y**2+z**2 about every atomic
center, and let the hidden surface processing worry about the
intersecting shperes. This, of course, does not give quite the blobbly
appearence of |E| = C taken over the whole molecule.

Be cautioned that the algorithm as presented at SIGGRAPH 87 has an
error that causes small holes to appear in the tessellation at some
saddle points on the surface. I talked to Bill Lorensen at SIGGRAPH
last year and he said that he was going to publish a correction in the
SIGGRAPH Quarterly. I don't know if he has done that yet, or not.

We have an implementation of this algorithm that we will make available
when we distribute our video movie making system software in a few months.
See:

  .ds [A W. E. Johnston
  .as [A ", D. E. Hall
  .as [A ", J. Huang
  .as [A ", M. Rible
  .as [A ", D. Robertson
  .ds [T Distributed Scientific Video Movie Making
  .ds [J Proceedings of the Supercomputing Conference
  .ds [D 1988
  .ds [O (The Computer Society of the IEEE.)


	Bill Johnston and David Robertson
	Lawrence Berkeley Laboratory
	(wejohnston@lbl.gov, ...ucbvax!lbl-csam.arpa!johnston)
	(dwrobertson@lbl.gov, ...ucbvax!lbl-csam.arpa!davidr)