On Defining Trigonometric Box Spline-Like Surface on Type-I Triangulation

Usually, a polynomial box spline surface is defined with the help of distributions, convolutions, Fourier transforms and recurrence relations. A better alternative to define the box spline surface is by subdivision method. In this paper, a trigonometric box spline surface on type-I triangulation is defined by introducing a new non-stationary subdivision scheme. This new subdivision scheme takes help of the previously defined non-stationary subdivision scheme in (Jena et al., A non-stationary subdivision scheme for generalizing trigonometric spline surfaces to arbitrary meshes, Computer Aided Geom. Design, 20, (2003), 61–77). The limit surface obtained by the repeated application of this new scheme to an initial regular triangular mesh, is a trigonometric box spline like surface. This can be considered as an initial attempt to define the trigonometric box spline surfaces by subdivision process. Besides, having a nice algorithm, the limit surface is compactly supported, satisfies the convex hull property and is uniformly continuous. We illustrate the performance of this scheme with some examples.