＜正＞ In this paper we prove that there are no locally supported bivariate Gk-1spline functionsof degree k on cross-cut grid partitioned regions with no more than three lines meeting at acommon vertex.We also give explicit expressions of bivariate C~1 cubic B-spline with smallestlocal support on cross-cut triangular grid partitioned regions where each vertex is theintersection of three lines.Properly normalized,these B-splines are proved to be uniquelydetermined and form a partition of unity.Furthermore,the corresponding waxationdiminishing bivariate spline operators are proved to preserve all linear polynomials of twovariables.These facts enable us to give error estimates for approximation by bivariate C~1cubic splines for functions of class C,C~1 and C~2.
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