Not an answer; just a tangential remark.
In general it is not an easy problem to reconstruct a
polygon from various sets of data. If the data does not
uniquely determine the polygon, it would not be easy
to "generate a credible figure," to quote the OP, compatible
with the partial reconstruction.
For example, the paper below reconstructs a polygon from its "visibility angles," which do uniquely determine the polygon.
Chen, Danny Z., and Haitao Wang. "An improved algorithm for reconstructing a simple polygon from the visibility angles." In International Symposium on Algorithms and Computation, pp. 604-613. Springer, Berlin, Heidelberg, 2011.
Fig. 1: Visibility angles at a vertex $v$. & Fig. 3.
Polygon reconstruction problems arise from the need for
a mobile robot to navigate an environment using sensor/scanner measurements to avoid wall collisions. The
Chen-Wang paper above cites 10 papers exploring
a variety of reconstruction problems.