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A method for meshing an irregular polygon with an arbitrary number of sides into quadrilaterals is described. The polygon is defined with reference to the coordinates of a set of primary nodes. The polygon sides are the lines joining these nodes and can be straight lines or arcs of circles. Each side may be further subdivided into an arbitrary number of equal length segments. The interior of the polygon is automatically subdivided into quadrilaterals with specification of the primary nodes, side subdivision and side curvature being the only requirements.