The Role of Combined Quinary Refinement Scheme in Geometric Modeling

Abstract

 In this paper, we introduce a novel combined 5-point quinary refinement scheme that incorporates five parameters to enhance its adapt ability and resilience. The development of the scheme stands on translat ing a 3-point approximating quinary refinement scheme to the new loca tion by introducing the displacement vectors. We also demonstrate that the combined scheme generates numerous sub-schemes within a given set of parameters. The combined scheme has the modest support with   C3 degree of smoothness that attains better shape control and flexibil ity. Additionally, we discuss the important characteristic like polynomial generation, reproduction and approximation order. Moreover, we analyze that the proposed scheme exhibits complex behavior under specific pa rameter configuration. Further, we present some visual depiction based on polygons to verify the outcomes of the scheme. Lastly, to showcase the efficiency of the scheme the comparison with the classical and recentlyproposed schemes is presented