vrsyrotiuk@water.waterloo.edu (Violet Syrotiuk) (04/03/89)
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES
JOINT COMPUTER GRAPHICS/MAPLE SEMINAR
- Friday, April 7, 1989
Dr. Louis J. Billera, of Rutgers University, will speak
on ``Groebner Basis Techniques for Multivariate
Splines''.
TIME: 1:30 PM
ROOM: DC 1304
ABSTRACT
We describe how Groebner basis techniques of
computational algebra can be applied to compute
dimensions and bases for spaces of smooth multivariate
splines over general polyhedral subdivisions in d
dimensional space.
Making use of the inherent algebraic structure of the
problem, we describe how the sequence of dimensions (as
we vary the degrees of the polynomials) can be
described by a simple rational generating function, and
we describe in what sense this generating function
remains invariant as we vary the embedding of the
subdivision.
We then show how this generating function can be
effectively computed using Groebner basis techniques.
These techniques are generally available on many
computer algebra systems. With a bit more work,
similar methods can be used to produce bases for spline
spaces of any desired degree.
Finally, we describe some limited experience with these
methods on small examples, using general-purpose
software. On a particular 3-dimensional example, this
experience suggests the potential of a significant
improvement over results reported by others.
--
Violet R. Syrotiuk | vrsyrotiuk@water.uucp
Computer Science Dept. | watmath!water!vrsyrotiuk
University of Waterloo | vrsyrotiuk@water.uwaterloo.ca
Waterloo, ON N2L 3G1 | vrsyrotiuk@water.waterloo.edu (or .cdn)