A Constructive Approach to Bivariate Hyperbolic Box Spline Functions - Jena, Hrushikesh (Armenian Journal of Mathematics, 2025)
This article is based on the construction procedure of bivariate hyperbolic box spline functions. Generally, box splines are considered as the multivariate generalizations of univariate B-splines. Both B-splines and box splines are refinable functions. Two different kinds of box splines like the polynomial box splines and the trigonometric box splines along with their usefulness are well studied in literature. However, another variant of box splines named as the class of hyperbolic box spline functions, has not gained much attention. This article focuses on the construction of bivariate hyperbolic box spline functions from univariate hyperbolic B-spline functions through directional convolution method. Also, the importance and usefulness of such functions are discussed.
Keywords: Hyperbolic B-Spline; Box Spline; Directional Convolution; Direction Matrix