HSS-progressive interpolation for Loop and Catmull–Clark Subdivision Surfaces

Abstract

Loop and Catmull–Clark subdivision schemes are the most popular and commonly employed approximation subdivision schemes. However, some features of the given mesh are lost in their refinement process. Thus, the subdivision surfaces of Loop and Catmull–Clark schemes does not interpolate the vertices of the given mesh and shrink in some cases. This paper proposed new progressive iterative approximation (PIA) formats based on Hermitian and skew-Hermitian splitting iteration technique (HSS). The proposed method named H-PIA and its weighted version called WH-PIA force the limit surface of Loop and Catmull–Clark subdivision schemes to interpolate the vertices of the given mesh. The approximate optimal weight of WH-PIA is given, and the convergence of H-PIA and WH-PIA are proved. Various test examples are provided to illustrate the efficiency and effectiveness of the proposed H-PIA and WH-PIA. Experimental results demonstrate that the rate of convergence of H-PIA and WH-PIA are faster than that of the PIA and weighted PIA (W-PIA), respectively.

Keywords

• Progressive-iterative approximation (PIA)
• Loop subdivision scheme (LSS)
• Catmull–Clark subdivision scheme (CSS)
• HSS iteration