A hybrid subdivision surface scheme - Hong, Zipeng (2015)
The J-Spline scheme was developed by Maillot and Stam to allow users the flexibility to generate limit curves which trades off between the smoothness of an approximating scheme and the adherence to the control curve of an interpolating scheme. Rossignac and Schaefer then modified the scheme such that the generated limit shapes enjoys levels of smoothness which are on par or superior to that of limit shapes generated by the approximating and interpolating schemes involved. The aim of this paper is to design the ButterLoop scheme, an adaptation of Rossignac and Schaefer's version of the J-Spline scheme on triangular meshes which involves the Loop and Butterfly subdivision schemes and interpolation parameter λ, then determine the values of λ which produce the smoothest limit surfaces based on some sample meshes as well as whether the smoothness of these limit surfaces is comparable or even superior to that of Loop subdivision. The test is performed by generating limit surfaces of 3 sample meshes for -5 ≤ λ ≤ 5 and evaluating their smoothness using the Gaussian and Mean curvature estimations. The results of the experiment indicate that 0 ≤ λ ≤ 0.8 for generating limit surfaces with the greatest quality of smoothness. Furthermore, these limit surfaces are shown to have better quality of smoothness that those produced by Loop Subdivision. This study could be improved by experimenting on a larger sample size and adapting the ButterLoop scheme to work on open meshes.