🚀 go-pugleaf

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)