On rationally supported surfaces

We analyze the class of surfaces which are equipped with rational support functions. Any rational support function can be decomposed into a symmetric (even) and an antisymmetric (odd) part. We analyze certain geometric properties of surfaces with odd and even rational support functions. In particular it is shown that odd rational support functions correspond to those rational surfaces which can be equipped with a linear field of normal vectors, which were discussed by Sampoli et al. (2006). As shown recently, this class of surfaces includes non–developable quadratic triangular Bézier surface patches (Lávička and Bastl, 2007; Peternell and Odehnal, 2007).