HYPERGRAPH METHODS FOR VARIATIONAL GEOMETRY

DIMENSION DRIVEN CAD SYSTEMS HOLD GREAT PROMISE FOR ENHANCING PRODUCTIVITY AND COMPETITIVENESS OF THE EARLY CONCEPTUAL STAGES OF MECHANICAL ENGINEERING DESIGN. CURRENTSYSTEMS SUFFER ONE OF TWO SETS OF DEFICIENCIES. VARIATIONALGEOMETRY SYSTEMS SUFFER FROM SPEED PROBLEMS AND PROBLEMS CONTROLLING WHICH OF A NUMBER OF POSSIBLE SOLUTIONS THEIR GEOMETRY SOLUTION MECHANISM CONVERGES TO. CONSTRUCTIONAL OR"PARAMETRIC" SYSTEMS, WHILE FAST, HAVE A LESS INTUITIVE USER INTERFACE AND A LESS FLEXIBLE GEOMETRY REPRESENTATION. THE OBJECTIVE OF THE PROPOSED RESEARCH WILL BE TO DEVELOP A NEW GRAPH-THEORY BASED TECHNIQUE TO CONVERT A VARIATIONAL GEOMETRY DESCRIPTION TO A CONSTRUCTIONAL SYSTEM. PRELIMINARY RESEARCH IN 2-DIMENSIONS HAS INDICATED THE PROSPECT OF DRAMATICALLY INCREASING THE SPEED OF VARIATIONALGEOMETRY SOLUTION, AND THUS INCREASING THE RANGE OF PROBLEMSTO WHICH IT MAY BE APPLIED. SUCCESSFUL IMPLEMENTATION IN A MECHANICAL DESIGN PACKAGE WILL GREATLY EXPAND THE UTILITY OFCONCEPTUAL DESIGN SOFTWARE TO THE MECHANICAL ENGINEER.