Shortcut hulls: Vertex-restricted outer simplifications of polygons

Let P be a polygon and C set of shortcuts, where each shortcut is directed straight-line segment connecting two vertices P. A hull another that encloses whose oriented boundary composed elements from C. We require the output to weakly simple polygons, which we define as generalization polygons. Shortcut hulls find their application in cartography, common task compute simplified representations area features. aim at has small perimeter. Our optimization objective minimize convex combination these criteria. If no holes are allowed, problem admits straight-forward solution via computation shortest paths. For more challenging case may contain holes, present polynomial-time algorithm based on computing constrained, weighted triangulation input polygon's exterior. use this starting point for investigating further variants, e.g., restricting number edges or bends. demonstrate can used schematization