The Role of Combined Quinary Refinement Scheme in Geometric Modeling

In this paper, we introduce a novel combined 5-point quinary refinement scheme that incorporates five parameters to enhance its adaptability and resilience. The development of the scheme stands on translating a 3-point approximating quinary refinement scheme to the new location 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 modest support with a C3 degree of smoothness that attains better shape control and flexibility. Additionally, we discuss the important characteristics like polynomial generation, reproduction, and approximation order. Moreover, we analyze that the proposed scheme exhibits complex behavior under specific parameter configuration. Further, we present some visual depictions based on polygons to verify the outcomes of the scheme. Lastly, to showcase the efficiency of the scheme, the comparison with the classical and recently proposed schemes is presented.