Locally RSD-Generated Parametrized G1-Spline Surfaces Interpolating First Order Data over 3D Triangular Meshes

Given a triangular mesh in R3 with a family of points associated to its vertices resp. a vectors associated to its edges, we construct interpolating parametrized polynomial G1-spline surfaces by means of the method of reduced side derivatives (RSD) with a locally generated G1-correction over mesh edges. In the case of polynomial RSD shape functions, we establish polynomial edge corrections by means of an algorithm with independent interest for finding optimal GCD cofactors with lowest degree for arbitrary families of polynomials.