"The whole is more than the sum of its parts." - Aristotle

However, in the mean time you can look at the Polygonization Tutorial by Tony Ruso and Valeriu Sitaru on three methods for constructing simple polygons through sets of points. You can also play with their interactive Java applet. Concerning the problem of constructing simple polygons through line segments, you can read about the topic in the following PostScript file.

• Godfried T. Toussaint, "Computing simple circuits from a set of line segments," Discrete and Computational Geometry, vol. 5, 1990, pp. 289-304. (with D. Rappaport and H. Imai)
  
• compressed PostScript file circuits.ps.gz

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