Generating smooth surfaces of arbitrary topology is still a challenge. This paper considers the problem of creating a smooth parametric polynomial surface interpolating the vertices of an irregular triangular or quadrilateral mesh of arbitrary topological type. The surface is overall tangent plane continuous without any singular points and without any singular parameterizations. We particularly focus on design issues related to this spline model which offers several degrees of freedom. In particular, an exhaustive description of all available degrees of freedom is given and their geometric interpretation for shape design is specified. An extension of the model allows for additional normal vector interpolation and increases thus the number of design parameters. Finally several design issues are discussed and illustrated.

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