Filling N Sided Holes With Trimmed B Spline Surfaces Based on Energy Minimization Method

Abstract

Using a trimmed rectangular BSpline surface to fill an nsided hole is a much desired operation in computer aided design (CAD), but few papers have addressed this issue. Based on an energyminimization or variational BSpline technique, the paper presents the technique of using one single trimmed rectangular BSpline surface to fill an nsided hole. The method is efficient and robust, and takes a fraction of a second to fill nsided holes with highquality waterproof BSpline surfaces under complex constraints. As the foundation of filling nsided holes, the paper also presents the framework and addresses the key issues on variational BSpline technique. Without any precalculation, the variational BSpline technique discussed in this paper can solve virtually any BSpline surface with up to 20,000 control points in real time, which is much more efficient and powerful than previous work in the variational BSpline field. Moreover, the result is accurate and satisfies CAD systems' highprecision requirements.