3B.3 Mesh Sizing with Additively Weighted Voronoi Diagrams
نویسندگان
چکیده
We address the problem of generating mesh sizing functions from a set of points with specified sizing values. The sizing functions are shown to be maximal and K-Lipschitz, with arbitrary parameter K provided by the user. These properties allow generating low complexity meshes with adjustable gradation. After constructing an additively weighted Voronoi diagram, our algorithm provides fast and accurate answers to arbitrary point queries. We have implemented our mesh sizing technique as a sizing criterion for the 2D triangle meshing component from the CGAL library. We demonstrate the performance advantages of our technique through experimental results on various inputs.
منابع مشابه
Polyline-sourced Geodesic Voronoi Diagrams on Triangle Meshes
This paper studies the Voronoi diagrams on 2-manifold meshes based on geodesic metric (a.k.a. geodesic Voronoi diagrams or GVDs), which have polyline generators. We show that our general setting leads to situations more complicated than conventional 2D Euclidean Voronoi diagrams as well as point-source based GVDs, since a typical bisector contains line segments, hyperbolic segments and paraboli...
متن کاملAdditively Weighted Voronoi Diagram on the Oriented Projective Plane Additively Weighted Voronoi Diagram on the Oriented Projective Plane
We consider Voronoi diagrams deened on the oriented projective plane T 2. In this geometry, the closest and furthest site diagrams are antipodal. We give a simple on-line incremental algorithm for constructing the additively weighted diagram. This diagram, which may be disconnected in Euclidean plane, is always connected in T 2 and has exactly 3n ? 6 edges and 2n ? 4 vertices, where n is the nu...
متن کاملAdditively Weighted Voronoi Diagrams for Optimal Sequenced Route Queries
The Optimal Sequenced Route (OSR) query strives to find a route of minimum length starting from a given source location and passing through a number of typed locations in a specific sequence imposed on the types of the locations. In this paper, we propose a precomputation approach to OSR query in vector spaces. We exploit the geometric properties of the solution space and theoretically prove it...
متن کاملVoronoi Diagrams on Planar Graphs, and Computing the Diameter in Deterministic Õ(n5/3) Time
We present an explicit and efficient construction of additively weighted Voronoi diagrams on planar graphs. Let G be a planar graph with n vertices and b sites that lie on a constant number of faces. We show how to preprocess G in Õ(nb) time so that one can compute any additively weighted Voronoi diagram for these sites in Õ(b) time. We use this construction to compute the diameter of a directe...
متن کاملConvex Hull and Voronoi Diagram of Additively Weighted Points
We provide a complete description of dynamic algorithms for constructing convex hulls and Voronoi diagrams of additively weighted points of R. We present simple algorithms and provide a complete description of all the predicates. The algorithms have been implemented in R and experimental results are reported. Our implementation follows the CGAL design and, in particular, is made both robust and...
متن کامل