chuck@sunpix.UUCP ( Sun Visualization Products) (08/30/89)
A while ago someone (from Duke, I believe) posted a request for
help in interpolating sampled data values across a three-dimensional
surface represented as a polygonal mesh. I just came across a
reference that will help him, but I have since lost the original
message, hence the post. Mayhap others may find it useful.
In the latest issue of IEEE PAMI (Vol 11, No. 9, Sept. 1989) on
pp. 1001-1005 there is an algorithm for computing geodesic (i.e.,
minimal) distances on a three-dimensional polyhedral surface.
Once you have a routine to do this, computing a color (or voltage,
or whatever) at any point on the surface is straightforward. The
algorithm's "computational complexity per se is not favorable".
It in fact appears to be exponential, but with the relatively small
number of polygons involved in both the author's and the original
requestors applications (order of magnitude 1000) it is not
prohibitive.
The title and authors:
Computing Minimal Distances on Polyhedral Surfaces
by Estarose Wolfson and Eric Schwartz
Hope this is helpful.
P.S. There is an amusing misprint in the summary which points out the
need for care in notational script: "This run took about 2 hours and
used 12 ubytes of memory". Now there's a space-efficient algorithm!
Chuck Mosher
Visualization Products, Sun Microsystems
cmosher@sun.com