The author presents a method for generating a surface on a region bounded by a polygon with arbitrary number of sides, which may also possess “holes”, i.e. inner boundary sides. The generation of the proposed surface is done by blending suitable functions defined on the sides of the region and boundary conditions along the edges. The outcoming surface is such that \(C^ 1\)-continuity to adjacent patches is guaranteed. In a final discussion, the method is compared with the use of composite 4- sided patches. Also, several figures illustrate quite nicely the author’s results.