In this paper a new approach for a construction of polynomial surfaces with rational field of unit normals (PN surfaces) is presented. It is based on bivariate polynomials with quaternion coefficients. Relations between these coefficients are derived that allow one to construct PN surfaces of general odd and even degrees. For low degree PN surfaces the theoretical results are supplemented with algorithms and illustrated with numerical examples. Construction of polynomial PN surfaces based on bivariate polynomials with quaternion coefficients is presented.Particular polynomial PN surfaces of odd and even degrees are derived.Algorithms for low degree PN surfaces are given.Curvature properties are examined.Simple interpolation scheme is proposed.
['Jernej Kozak', 'Marjeta Krajnc', 'Vito Vitrih']
A quaternion approach to polynomial PN surfaces