Charshape
The characteristic shape reduction method provided by PolyShell is a novel polygon reduction built upon the characteristic shape algorithm of Duckham et al.1
Characteristic Shape Algorithm
The algorithm presented by Duckham et al. proposes an efficient method for generating simple polygons which "characterize" a set of points in the plane. The method works by computing the triangulation of a point cloud, iteratively removing outward-facing edges until a shape is found which conforms to the point cloud without over-fitting.
Characteristic shape of a point cloud. Adapted from Duckham et al.1
Adaptation to a Polygon Reduction Algorithm
The problem of polygon reduction can be viewed in a very similar way to that considered by Duckham et al. In this instance, we still have a cloud of points in the plane, albeit with additional topological information. To satisfy PolyShell's axioms, it is necessary that the front never recedes into the initial shape. A minor modification is to compute a constrained triangulation, removing only edges which do not lie on the original polygon.