Counting the dimension of splines of mixed smoothness: A general recipe, and its application to meshes of arbitrary topologies
Deepesh Toshniwal,
Michael DiPasquale
Abstract:In this paper we study the dimension of bivariate polynomial splines of mixed smoothness on polygonal meshes. Here, "mixed smoothness" refers to the choice of different orders of smoothness across different edges of the mesh. To study the dimension of spaces of such splines, we use tools from Homological Algebra. These tools were first applied to the study of splines by Billera (1988). Using them, estimation of the spline space dimension amounts to the study of the generalized Billera-Schenck-Stillman complex … Show more
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