A technique for decomposition of polygons into simpler components is described and illustrated with applications in the analysis of handwritten Chinese characters and chromosomes. Polygonal approximations of such objects are obtained by methods described in the literature and then parts of their concave angles are examined recursively for separating convex or other simple shape components. Further decomposition of the latter is possible. The final result can be expressed as a labeled graph and processed further through the introduction of either fuzzy predicates or syntactic pattern recognition techniques.