Area-Proportional Drawings of Intersecting Families of Simple Closed Curves.

摘要: A FISC, or family of intersecting simple closed curves, is a collection curves in the plane with properties that there some open region common to interiors all and every two intersect finitely many points arcs. Let F be FISC set regions R. said area-proportional respect weight function ω : R → if positive constant α such for any finite regions, r1 r2, area(r1)/area(r2) = αω(r1)/ω(r2). We consider as directed graph, ~ G(F), where curve intersections are vertices arcs between edges. Edges so each ’s traversed clockwise fashion. The dual denoted D(F), has edges oriented indicate inclusion fewer curves. graph G(F) an drawing C can transformed into by continuous transformation plane. describe O(n|V |) algorithm creating (V,E) n D(F) only one source sink. For case n-Venn diagrams, since |V | ≤ 2 − 2, this yields O(|V |lg|V algorithm.