Abstract: The present paper deals with the bivariate B-spline functions with integral definition on uniform type- Ⅰ triangulation and type-Ⅱ triangulation , and obtain the M-band refinement equations for any integer M(M ≥2). The result in this paper can sum up the subdivision of bivariate Box splines and bivariate B-splines with the minimal support. Furthermore , our method is simple and easy to be generalized.

Key words: bivariate B-spline, directional integration, refinement equation