Seminars

Title: On the dimension and bases of planar T-Splines

Abstract:

Standard parametrisations of surfaces in CAGD are based on tensor product bspline functions, defined from a grid of nodes over a rectangular domain.
This representation is not well-adapted to local refinement, which is
particularly important in applications such as surface reconstruction or
isogeometric analysis.

To extend the representation of tensor-product splines while providing local refinement capabilities, some recent works have considered T-subdivisions. These are partitions of an axis-aligned box into smaller axis-aligned boxes.

In this talk, we will analyze the space of bivariate functions that are piecewise polynomial of bidegree (m,m') and class C^(r,r') over such a planar T-subdivision. We shall show how algebraic techniques yield a good control of its resolution, give a new formula for its dimension and explicit bases for small degree and regularity.