Proceedings of the Annual Symposium on Computational Geometry
We solve two open problems posed by Goodman and Pollack[GP84] about sets of signed circular permutations (clusters of stars) arising from generalized configurations of points: recognition and efficient reconstruction (drawing). As a biproduct we get an O(n2) space data structure constructible in O(n2) time, representing the order type of a (generalized) configuration of points and from which the orientation of each triple can be found in constant time, a problem posed in [EHN].
Streinu, Ileana, "Clusters of Stars" (1997). Computer Science: Faculty Publications, Smith College, Northampton, MA.