This research is in the design and implementation of symbolic, numeric and geometric algorithms for the creation, manipulation and visualization of polynomial (algebraic) curves, surfaces and splines. Such algorithms form the science base for diverse applications ranging from computer graphics game environments to computer aided geometric design for simulation based design prototyping. We take the view of abstract data types, that is, a data representation coupled together with the operations on them. In this framework, the choice of which representation of the polynomial curve or surface patch to use is determined by the desired optimality of the algorithms for the operations. This research on different representations of algebraic curves and surfaces for specific operations of global and local parameterization, visualization/finite element mesh generation and polynomial spline model construction.

This material is based upon work supported by the National Science Foundation under Grant No. 9732306

Any options, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.