## 5 May 2000:

Fast Evaluation Of Tensor Product Hypersurfaces

Mac Casale, ICS, UC Irvine

The speaker, being under time pressure from upcoming exams,
retreats to the security of his roots in solid modeling - this
time, however, from the point of view of looking for lower bounds
and efficient, practical implementations of tensor products of
polynomials. The context is CAD/CAE, which has various
representations for solid objects. At issue is the efficient
evaluation of geometric objects known as tensor product surfaces
and hypersurfaces. A hypersurface is shown to be a tensor product
of polynomials, which can be written in various forms, depending on
choice of basis vectors in the linear space of polynomial
coefficients. This leads to the question of efficiency of
evaluating the tensor product form. We mention the industrial
context, followed by a review of lower bounds on polynomial
evaluation and show how these stack-up with traditional tensor
product evaluation methods. This is followed by some extensions.
The talk ends with a working session structured around four
different potential approaches.