The motivation behind this research has been the idea of the capability of the computing device to dynamically reconfigure itself. The goal of this work is to measure the computational power of reconfigurable machines rather in an abstract manner by proposing a model the FPGAs abstract computing machines. Modeling FPGAs in terms of Automata Theory would give a base to answer more fundamental questions about the capabilities and possible answers. If a Finite State Machine (FSM) or a Turing Machine (TM) has the capability of reconfiguring its finite control, does this ability give the abstract computing device new computational power. In other words is a reconfigurable FSM, TM or a Cellular Automata more powerful than their corresponding non-configurable versions?

Surface fitting methods play an important role in many scientific fields as well as in computer aided geometric design. The problem treated here is that of constructing a smooth surface that interpolates data values associated with scattered nodes in the plane. The data is said to be convex if there exists a convex interpolant. The problem of convexity-preserving interpolation is to determine if the data is convex, and construct a convex interpolant if it exists.