Some techniques of drawing random polygons.
See our recent paper and presentation on this topic at SVG Open, Paris, 2010.
A friend and former colleague of mine, Leonard Zusne, wrote a book: Visual Perception of Form Academic Press - 1970. The book was a collection of studies on the psychophysics surrounding the perception of shapes. I recall one study which generated random polygons for use as stimuli in perceptual research: Given a positive integer, n, a collection of n pairs of the form P_{i}=(alpha_{i}, d_{i}) is generated in which 0≤ alpha_{i }< 2π represents an angle, and d represents a distance from the origin.
P2
Borrowing from the terminology of the later-posed art gallery lighting problem, the polygons thus constructed are those lightable by a single lamp.
P3
P4
P5
P6