Abstract: A area preserving transformation method is put forward for the parametrization of the polygonal primitivity, which uses the two part texture mapping. This method eliminates the aliasing of the convergency at the pole of the sphere and the discontinuity between the head and the end in the process of the mapping on the intermediate surface sphere by the natural parametrization. As a result, the texture mapping of the polygonal primitivity is realized,which is constructed by the nonparametric patches.