Principal Patches - A New Class of Surface Patch Based on Differential Geometry

Abstract

This paper describes a new class of surface patch for use in computational geometry, where fairness is built in at the design stage by using ideas from differential geometry. Principal patches are patches whose sides are lines of curvature, and can be created by making the boundary curves obey two conditions called the frame and position matching equations. It is shown that surface continuity is automatically achieved when composite surfaces are formed. Particular cases are discussed, especially Dupin's cyclide patches based on circular arc sides. Some advantages of Dupin's cyclides over conventional, bicubic patches are described. Finally it is shown how the use of principal patches leads to a natural, geometric need for non -four -sided patches.