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Many problems in radar scattering, antenna and microwave fields can be solved by applying the method of moments (MoM) to the surface integral equations (SIEs). The geometry of the analyzed structure is usually modeled by triangular or quadrilateral patches of finite size. Such modeling can be very tedious, when the original structure is of a complicated shape. Very often this complicated shape can be easily represented as a combination of polygonal surfaces. Hence, there is continuous interest for algorithms that subdivide polygons into triangles or quadrilaterals. The main goal of this paper is to present a method for automated meshing of a structure made of polygonal surfaces into convex quadrilateral patches (in such a manner that two neighboring patches have a common edge between two common nodes).