Two C1-methods to generate Bézier surfaces from the boundary

Two methods to generate tensor-product Bézier surface patches from their boundary curves and with tangent conditions along them are presented. The first one is based on the tetraharmonic equation: we show the existence and uniqueness of the solution of ∆4−→x = 0 with prescribed boundary and adjacent to the boundary control points of a n× n Bézier surface. The second one is based on the nonhomogeneous biharmonic equation ∆2−→x = p, where p could be understood as a vectorial load adapted to the C1-boundary conditions.