C1- and C2-continuous spline-interpolation of a regular triangular net of points

Abstract The investigations focus on the construction of a C k -continuous ( k =0,1,2) interpolating spline-surface for a given data set consisting of points P ijk arranged in a regular triangular net and corresponding barycentric parameter triples ( u i , v j , w k ). We try to generalize an algorithm by A.W. Overhauser who solved the analogous problem for the case of a univariate data set. As a straightforward generalization does not work out we adapt the Overhauser-construction . We use some blending of basic surfaces with uniquely determined basic functions. This yields a spline-surface with a polynomial parametric representation which display C 1 - or C 2 -continuity along the common curve of two adjacent sub-patches. Local control of the emerging spline surface is provided which means moving one data point P changes only some of the sub-patches around P and does not affect regions lying far away.