Positivity Preserving Scattered Data Interpolation Using Ball Triangular Patches

The construction of a C1 interpolant to scattered data is considered in this paper in which the interpolant is positive every where if the original data are positive. This work is motivated by an earlier work of the second author, Piah et al. [8] where sufficient conditions are derived on B′ezier points to ensure that surfaces comprising cubic B′ezier triangular patches are always positive. In this paper, the corresponding simpler and more relaxed conditions are derived on the Ball points. The gradients at the data sites are then calculated to ensure that these positivity conditions aresatisfied. Each triangular patch of the interpolating surfaces is formed as a convex combination of three cubic Ball triangular patches. Its construction is local.