Triangular √7 and quadrilateral √5 subdivision schemes: Regular case

This paper is devoted to the study of triangular √7 and quadrilateral √5 surface subdivisions. Both approximation and interpolatory subdivision schemes are considered, with illustrative examples of both scalar-valued and matrix-valued √7 and √5 subdivision masks that satisfy the sum rule of sufficiently high orders. In particular, “optimal” Sobolev smoothness is determined and Hölder smoothness estimates are presented. © 2007 Elsevier Inc. All rights reserved.