Some new formulations of smoothness conditions and conformality conditions for bivariate splines

This paper is concerned with a study of some new formulations of smoothness conditions and conformality conditions for multivariate splines in terms of B-net representation. In bivariate setting, a group of new parameters of bivariate cubic polynomials over a planar simplex is introduced, and smoothness conditions and conformality conditions of bivariate cubic C1 splines are simplified.