General Midpoint Subdivision

Understand

In this paper, we introduce two generalizations of midpoint subdivision and analyze the smoothness of the resulting subdivision surfaces at regular and extraordinary points.

• The smoothing operators used in midpoint and mid-edge subdivision connect the midpoints of adjacent faces or of adjacent edges, respectively.
• An arbitrary combination of these two operators and the refinement operator that splits each face with m vertices into m quadrilateral subfaces forms a general midpoint subdivision operator.
• We analyze the smoothness of the resulting subdivision surfaces by estimating the norm of a special second order difference scheme and by using established methods for analyzing midpoint subdivision.