Straight Skeletons by Means of Voronoi Diagrams Under Polyhedral Distance Functions
نویسندگان
چکیده
We consider the question under which circumstances the straight skeleton and the Voronoi diagram of a given input shape coincide. More precisely, we investigate convex distance functions that stem from centrally symmetric convex polyhedra as unit balls and derive sufficient and necessary conditions for input shapes in order to obtain identical straight skeletons and Voronoi diagrams with respect to this distance function. This allows us to present a new approach for generalizing straight skeletons by means of Voronoi diagrams, so that the straight skeleton changes continuously when vertices of the input shape are dislocated, that is, no discontinuous changes as in the Euclidean straight skeleton occur.
منابع مشابه
Generalized Offsetting Using a Variable-Radius Voronoi Diagram
We investigate ways to extend offsetting based on skeletal structures beyond the well-known constant-radius and mitered offsets supported by Voronoi diagrams and straight skeletons for which the orthogonal distance of offset elements to their input elements is uniform. We introduce a new geometric structure called the variableradius Voronoi diagram, which supports the computation of variable-ra...
متن کاملApproximations of 3D generalized Voronoi diagrams
We introduce a new approach to approximate generalized 3D Voronoi diagrams for different site shapes (points, spheres, segments, lines, polyhedra, etc) and different distance functions (Euclidean metrics, convex distance functions, etc). The approach is based on an octree data structure denoted Voronoi-Octree (VO) that encodes the information required to generate a polyhedral approximation of t...
متن کاملGeneralized Voronoi Diagrams on Polyhedral Terrains
We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a polyhedral terrain in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) ...
متن کاملComputing generalized higher-order Voronoi diagrams on triangulated surfaces
We present an algorithm for computing exact shortest paths, and consequently distance functions, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex triangulated polyhedral surface. The algorithm is generalized to the case when a set of generalized sites is considered, providing their distance field that implicitly represents the Voronoi diag...
متن کاملEfficient Computation of Discrete Voronoi Diagram and Homotopy-Preserving Simplified Medial Axis of a 3D Polyhedron
AVNEESH SUD: Efficient Computation of Discrete Voronoi Diagram and Homotopy-Preserving Simplified Medial Axis of a 3D Polyhedron. (Under the direction of Dinesh Manocha.) The Voronoi diagram is a fundamental geometric data structure and has been well studied in computational geometry and related areas. A Voronoi diagram defined using the Euclidean distance metric is also closely related to the ...
متن کامل