A C1 triangular interpolant suitable for scattered data interpolation

We present here a method of constructing a triangle interpolant which interpolates position and partial derivatives specified at the three vertices of the triangle. The method employs the cubic Bezier triangular patch technique. The data given enable us to determine the appropriate Bezier control points so that adjacent patches meet with C1 continuity. However, the interior control point for the patch is replaced by three separate points, due to the implementation of three local schemes, each of which satisfies the boundary conditions on only one side of the triangle. Convex combination is used to blend these three local schemes.