This project concerns 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. The project has an abstract data type orientation. 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. Research will therefore be done on different representations of algebraic curve and surface splines for specific operations of display, finite element mesh generation and polynomial spline model construction. Piecewise polynomial or rational functions or surfaces of some fixed degree d and continuously differentiable up to some order r are known as algebraic splines or finite elements. While it is possible to model a general closed surface of arbitrary genus as a single algebraic surface patch, the geometry of such a global surface is difficult to specify, interactively control, and display. This research will covers both implicit and parametric algebraic surface splines (algebraic patches and non-uniform rational B-spline patches).
