This paper defines a polygonal decomposition into regular and singular regions, a concept that is useful for skeleton extraction and part analysis of shapes, specially, elongated figures. We define a closeness criterion among segments using the Voronoi diagram of a polygon that together with a parallelism criterion gives support to a new definition of regular regions. Regular regions correspond to the ones surrounded by smooth quasi-parallel contour lines, while singular regions are the polygonal regions that are not regular. We present an efficient algorithm to calculate the decomposition, and some experiments.