A combined approximating and interpolating subdivision scheme with C2 continuity

• DOI: 10.1016/j.aml.2012.05.012
• Publication Date: 2012-06-05T10:35:39Z
• Authors: Jun Pan; Shujin Lin; Xiaonan Luo
• Keywords: Polygon (computer graphics); Smoothness; Subdivision surface

AbstractIn this paper a combined approximating and interpolating subdivision scheme is presented. The relationship between approximating subdivision and interpolating subdivision is derived by directly performing operations on geometric rules. The behavior of the limit curve produced by our combined subdivision scheme is analyzed by the Laurent polynomial and attains C2 degree of smoothness. Furthermore, a non-uniform combined subdivision with shape control parameters is introduced, which allows a different tension value for every edge of the original control polygon.