The construction of a C1 interpolant to scattered data is considered in which the interpolant is positive everywhere if the original data are positive. This study is motivated by earlier work in which sufficient conditions are derived on Bezier points in order to ensure that surfaces comprising cubic Bezier triangular patches are always positive. In the current work, simpler and more relaxed conditions are derived on the Bezier points. The gradients at the data sites are then calculated to ensure that these conditions are satisfied. Each triangular patch of the interpolating surface is formed as a convex combination of three cubic Bezier triangular patches. Its construction is local. A number of examples are presented.