The Translation-Scale-Rotation Diagram for Point-Containing Placements of a Convex Polygon.
Gill Barequet, Matthew T. Dickerson · Canadian Conference on Computational Geometry · 2000
We present a diagram that captures containment information for scalable rotated and translated versions of a convex polygon. For a given polygon P and a contact point q in a point set S, the diagram parameterizes possible translations, rotations, and scales of the polygon in order to represent containment regions for each additional point v in S. We present geometric and combinatorial properties for this diagram, and describe how it can be computed and used in the solution of several geometric problems.