Puzzhull: Cavity and protrusion hierarchy to fit conformal polygons

In this paper, we present a simple definition for, and a method to find, cavities and protrusions of a 2D polygon. Using these, we fit conformal polygonswith each other, which is similar to a jigsaw puzzle and in a general case is NP-hard to solve. We first build a hierarchy of cavities and protrusions for each polygon and use this hierarchy to check for matches between these geometric features of two polygons. This data structure allows for early rejection of mismatches and thus speeds up the fitting process. We show using many examples, that most of the common configurations in exact polygon fitting can be handled by this algorithm in polynomial time. In case of exact, yet non-unique matches, this algorithm will solve the problem in exponential time. © 2013 Elsevier Ltd. All rights reserved.