Dimension of polynomial splines of mixed smoothness on T-meshes

Deepesh Toshniwal*, Nelly Villamizar

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
39 Downloads (Pure)


In this paper we study the dimension of splines of mixed smoothness on axis-aligned T-meshes. This is the setting when different orders of smoothness are required across the edges of the mesh. Given a spline space whose dimension is independent of its T-mesh's geometric embedding, we present constructive and sufficient conditions that ensure that the smoothness across a subset of the mesh edges can be reduced while maintaining stability of the dimension. The conditions have a simple geometric interpretation. Examples are presented to show the applicability of the results on both hierarchical and non-hierarchical T-meshes. For hierarchical T-meshes it is shown that mixed smoothness spline spaces that contain the space of PHT-splines (Deng et al., 2008) always have stable dimension.

Original languageEnglish
Article number101880
Pages (from-to)1-10
Number of pages10
JournalComputer Aided Geometric Design
Publication statusPublished - 2020


  • Dimension formula
  • Homological algebra
  • Mixed smoothness
  • Splines
  • T-meshes


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