In this work, we study the cellular decomposition of S induced by a filling pair curves v and w, \(Dec_{v,w}(S) = {\setminus } (v \cup w)\), its connection to distance function d(v, w) in curve graph closed orientable surface genus g. Building on work Leasure, efficient geodesics were introduced first author joint with Margalit Menasco 2016, giving an algorithm that begins non-separating determ...

The objective of this paper is to study and construct matrix-valued templates for interpolatory curve subdivision. Since our investigation of this problem was motivated by the need of such subdivision stencils as boundary templates for interpolatory surface subdivision, we provide both spline and non-spline templates that are necessarily symmetric, due to the lack of direction-orientation in ca...