Drawing Free Tress Inside Convex Regions Using Polygon Skeleton

Drawing Free Trees Inside Simple Polygons Using Polygon Skeleton

Most of graph drawing algorithms draw graphs on unbounded planes. In this paper we introduce a new polyline grid drawing algorithm for drawing free trees on plane regions which are bounded by simple polygons. Our algorithm uses the simulated annealing (SA) method, and by means of the straight skeletons of the bounding polygons guides the SA method to uniformly distribute the vertices of the giv...

Largest Placement of One Convex Polygon Inside Another

We show that the largest similar copy of a convex polygon P with m edges inside a convex polygon Q with n edges can be computed in O mn logn time We also show that the combinatorial complexity of the space of all similar copies of P inside Q is O mn and that it can also be computed in O mn logn time Let P be a convex polygon with m edges and Q a convex polygon with n edges Our goal is to nd the...

Convex Polygon Intersection Graphs

Geometric intersection graphs are graphs determined by the intersections of certain geometric objects. We study the complexity of visualizing an arrangement of objects that induces a given intersection graph. We give a general framework for describing classes of geometric intersection graphs, using arbitrary finite base sets of rationally given convex polygons and rationally-constrained affine ...

Finding the Maximum Area Centrosymmetric Polygon in a Convex Polygon

Inaccessibility-Inside Theorem for Point in Polygon

The manuscript presents a theoretical proof in conglomeration with new definitions on Inaccessibility and Inside for a point S related to a simple or self intersecting polygon P. The proposed analytical solution depicts a novel way of solving the point in polygon problem by employing the properties of epigraphs and hypographs, explicitly. Contrary to the ambiguous solutions given by the cross o...