Symmetric four-directional bivariate pseudo-splines
For researchers in geometric modeling and subdivision surfaces, this work extends pseudo-spline theory to bivariate settings, but the algebraic approach may limit immediate practical impact.
The paper provides a formula for constructing symbols of symmetric four-directional bivariate pseudo-splines, which generalize uniform B-splines and interpolatory subdivision schemes to the bivariate case.
Univariate pseudo-splines are a generalization of uniform B-splines and interpolatory $2n$-point subdivision schemes. Each pseudo-spline is characterized as the subdivision scheme with least possible support among all schemes with specific degrees of polynomial generation and reproduction. In this paper we consider the problem of constructing the symbols of the bivariate counterpart and provide a formula for the symbols of a family of symmetric four-directional bivariate pseudo-splines. All methods employed are of purely algebraic nature.