DeepAI AI Chat
Log In Sign Up

A new bound for smooth spline spaces

by   Hal Schenck, et al.
Iowa State University of Science and Technology
cornell university

For a planar simplicial complex Delta contained in R^2, Alfeld-Schumaker proved that the dimension of the space C^r_k(Delta) of planar splines of smoothness r and polynomial degree at most k on Delta is given by a polynomial P_Delta(r,k) when k >= 3r+1. Examples due to Morgan-Scott, Tohaneanu, and Yuan show that the equality dim C^r_k(Delta) = P_Delta(r,k) can fail when k = 2r or 2r+1. We prove that the equality dim C^r_k(Delta)= P_Delta(r,k) cannot hold in general for k <= (22r+7)/10.


page 1

page 2

page 3

page 4


C^s-smooth isogeometric spline spaces over planar multi-patch parameterizations

The design of globally C^s-smooth (s ≥ 1) isogeometric spline spaces ove...

Two Sample Test for Extrinsic Antimeans on Planar Kendall Shape Spaces with an Application to Medical Imaging

In this paper one develops nonparametric inference procedures for compar...

Critical Points for Two-view Triangulation

Two-view triangulation is a problem of minimizing a quadratic polynomial...

A lower bound for the dimension of tetrahedral splines in large degree

We derive a formula which is a lower bound on the dimension of trivariat...

Hereditary rigidity, separation and density In memory of Professor I.G. Rosenberg

We continue the investigation of systems of hereditarily rigid relations...