We propose two different methods for generating random orthogonal polygons with a given number of vertices. One is a polynomial time algorithm and it is supported by a technique we developed to obtain polygons with an increasing number of vertices starting from a unit square. The other follows a constraint programming approach and gives great control on the generated polygons. In particular, it may be used to find all n-vertex orthogonal polygons with no collinear edges that can be drawn in an (Formula presented) grid, for small n, with symmetries broken.
