Artifact analysis on triangular box-splines and subdivision surfaces defined by triangular polyhedra

Surface artifacts are features in a surface which cannot be avoided by movement of control points. They are present in B-splines, box splines and subdivision surfaces. We showed how the subdivision process can be used as a tool to analyse artifacts in surfaces defined by quadrilateral polyhedra (Sabin et al., 2005 and Augsdörfer et al., 2011).In this paper we are utilising the subdivision process to develop a generic expression which can be employed to determine the magnitude of artifacts in surfaces defined by any regular triangular polyhedra. We demonstrate the method by analysing box-splines and regular regions of subdivision surfaces based on triangular meshes: Loop subdivision, Butterfly subdivision and a novel interpolating scheme with two smoothing stages. We compare our results for surfaces defined by triangular polyhedra to those for surfaces defined by quadrilateral polyhedra.

Research highlights
► Surface artifacts are present in B-splines, box splines and subdivision surfaces.
► We present a generic expression to determine the magnitude of artifacts in surfaces.
► We demonstrate the method on surfaces based on triangular meshes.
► The artifact is affected by sampling, number of smoothing stages and their direction.
► We compare the results to surfaces based on quadrilateral meshes.