PPT-Farthest-Point Voronoi Diagrams

I Farthest site II Voronoi cell Outline III Structure of FPVD IV Construction V SmallestWidth Annulus I Farthest Point                   Sites   Given a point . In this paper we consider farthest points and the farthest distance map of a closed bounded set in a Banach space We show inter alia that a strictly convex Banach space has the Mazurlike intersection property for weakly compact sets if and only if Inkulu httpwwwiitgacinrinkulu FarthestPoint Voronoi diagrams 1 6 brPage 2br Problem Given a set of sites preprocess them to output the farthest site among to any query point FarthestPoint Voronoi diagrams 2 6 brPage 3 Phase diagram: plot of pressure vs. Temperature summarizing all equilibria between phases.. Given a temperature and pressure, phase diagrams tell us which phase will exist.. Features of a phase diagram:. By Yoni Dabush. Topics:. Distance Problems:. Post Office Problem. Nearest Neighbors and Closest Pair. Largest Empty and Smallest Enclosing Circle. Sub graphs of Delaunay Triangulations:. MST and TSP problems. Prof. Andy Mirzaian. Voronoi Diagrams. &. Delaunay Triangulations. Voronoi Diagram & Delaunay Triangualtion. . Algorithms . Divide-&-Conquer. Plane Sweep. Lifting into d+1 dimensions. Alex Beutel. Duke University. Joint work with . Pankaj. K. . Agarwal. and Thomas . Mølhave. Light Detection and Ranging. (. LiDAR. ). Planes collect data with lasers. Each point recorded (. x,y,z. 13 – . Computational . Geometry. JJCAO. Computational Geometry. primitive . operations. convex . hull. closest . pair. voronoi. . diagram. 2. Geometric algorithms. Applications.. Data . mining.. VLSI . The Post Office Problem. POORiA Haddad. Haddad.pooria@yahoo.com. Computer Science Autumn 2014. Yazd University. Outline. Definition and Basic Properties. Computing the Voronoi Diagram. Voronoi Diagrams of Line Segments. . Advanced Algorithms. Computational Geometry. . Prof. Karen Daniels. . Spring, . 2010. Voronoi. Diagrams & Delaunay Triangulations. O’Rourke: Chapter 5. de Berg et al.: Chapters 7, 9 (and a touch of Ch. 8). Computational Geometry (EECS 396/496) – October 18th, 2017. Last time: . Voronoi. Diagrams (VDs). Input:. A collection . of input points (called . sites. ) in the plane. . Output:. A subdivision of the plane into . Given a temperature and pressure, phase diagrams tell us which phase will exist.. Features of a phase diagram:. Triple point: temperature and pressure at which all three phases are in equilibrium. . Vapor-pressure curve: generally as pressure increases, temperature increases.. Let S be a set of sites in the plane.. Each point in the plane is influenced by each point of S.. We would like to decompose the plane into regions.. Each region is the set of all points for which the influence of some point of S is the strongest.. Voronoi Diagrams and Problem Transformations Steven Love, supervised by: Jack Snoeyink and Dave Millman What is a Voronoi Diagram? A spatial decomposition A set of polygons A set of polyhedra Vanhoutte  .  .  .  .  . Sites.  . Given a point . , . is its . farthest point . if for all. .  .  . The farthest point of . is .  .  . Not Every Site Can be the Farthest.  .  .  .  .  .  .  .