Removing Polar Rendering Artifacts in Subdivision Surfaces

There is a belief that subdivision schemes require the subdominant eigenvalue, λ , to be the same around extraordinary vertices as in the regular regions of the mesh [Barthe and Kobbelt, 2004, Zulti et al., 2006, Ni and Nasri, 2006]. This belief is owing to the polar rendering artifacts which occur around extraordinary points when λ is significantly larger than in the regular regions [Sabin and Barthe, 2003]. By constraining the tuning of subdivision schemes to solutions which fulfill this condition we may prevent ourselves from finding the optimal limit surface [Zorin and Schröder, 2000, pp 95–97]. We show that the perceived problem is purely a rendering artifact and that it does not reflect the quality of the underlying limit surface. Using the bounded curvature Catmull-Clark scheme [Augsdörfer et al., 2006] as an example, we describe three practical methods by which this rendering artifact can be removed, thereby allowing us to tune subdivision schemes using any appropriate values of λ .