Spaces of generalized splines over T-meshes
For researchers in geometric modeling and approximation theory, this work extends spline theory to non-polynomial functions over T-meshes, but the results are theoretical and incremental.
The paper provides a dimension formula and a basis for non-polynomial spline spaces over T-meshes under certain conditions, and studies their approximation power.
We consider a class of non-polynomial spline spaces over T-meshes, that is, of spaces locally spanned both by polynomial and by suitably-chosen non-polynomial functions, which we will refer to as generalized splines over T-meshes. For such spaces, we provide, under certain conditions, a dimension formula and a basis based on the notion of minimal determining set. We explicitly examine some relevant cases, which enjoy a noteworthy behaviour with respect to differentiation and integration; finally, we also study the approximation power of the just constructed spline spaces.