Positivity preserving scattered data interpolation using quartic Ball triangular patches

Abstract

The construction of a C1 interpolant to scattered data is considered in which the interpolant is positive everywhere. A C1 positivity preserving interpolation scheme to scattered data using quartic Ball triangular patches is derived.. This work is motivated by an earlier work in which sufficient conditions are derived on Bézier points to ensure that surfaces comprising quartic Bézier triangular patches are always positive. In this paper, the corresponding simpler and more relaxed conditions are derived on the Ball points. The gradients at data sites are then calculated to ensure that these positivity conditions are satisfied. The scheme is local and it constructs C1 interpolating surface to scattered data by a convex combination with variable coefficient of quartic Ball triangular patches subject to constraint plane. The Ball ordinates are modified if necessary to ensure the positivity and C1 continuity of the triangular patches.