English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Polynomial splines are ubiquitous in the fields of computer aided geometricdesign and computational analysis. Splines on T-meshes, especially, have thepotential to be incredibly versatile since local mesh adaptivity enablesefficient modeling and approximation of local features. Meaningful use of suchsplines for modeling and approximation requires the construction of a suitablespanning set of linearly independent splines, and a theoretical understandingof the spline space dimension can be a useful tool when assessing possibleapproaches for building such splines. Here, we provide such a tool. Focusing onT-meshes, we study the dimension of the space of bivariate polynomial splines,and we discuss the general setting where local mesh adaptivity is combined withlocal polynomial degree adaptivity. The latter allows for the flexibility ofchoosing non-uniform bi-degrees for the splines, i.e., different bi-degrees ondifferent faces of the T-mesh. In particular, approaching the problem usingtools from homo-logical algebra, we generalize the framework and the discoursepresented by Mourrain (2014) for uniform bi-degree splines. We derivecombinatorial lower and upper bounds on the spline space dimension andsubsequently outline sufficient conditions for the bounds to coincide.

Polynomial spline spaces of non-uniform bi-degree on T-meshes: Combinatorial bounds on the dimension