Some Classes of Surfaces Generated by Blending Interpolation on a Triangle with One Curved Side

The blending interpolation has many practical applications. Remind that blending interpolation is to interpolate a function at an infinite set of points: segments, curves, surfaces, etc. Thus, if one gives the contour of an object by such elements (segments, curves, surfaces) using a blending interpolation, we can generate a surface that contains the given contour. Hence, we can construct a surface (a blending function interpolant) which matches a given function and certain on its derivatives on the boundary of a plane domain (rectangle, triangle, etc. The aim of this paper is to construct some surfaces which satisfy some given condition on the boundary of a domain that can be decomposed in triangles with one curved side. We construct some new surfaces using some Lagrange, Hermite, Birkhoff and Nielson type operators.