An improved refinement rule for multi-sided faces

Abstract Multi-sided faces arise in polyhedral modeling through introduction of features not aligned with the regular grid structure, e.g. when trimming off corners or merging primary shapes. A standard first step is to split the n -gon into n quadrilaterals that join at the n -gon’s centroid. A canonical example is the ‘face point rule’ of Catmull–Clark subdivision. We show that rules negatively impact shape – already in the single, first refinement step. A new alternative face (and edge) rule improves the shape of surfaces controlled by the refined mesh noticeably. The improved face rule has a moderately increased footprint compared to the Catmull–Clark rule but remains simple in that it is characterized by just one scalar weight for each n .