Searching edges in the overlap of two plane graphs

Consider a pair of plane straight-line graphs, whose edges are colored red and blue, respectively, and let n be the total complexity of both graphs. We present a O(n log n)-time O(n)-space technique to preprocess such pair of graphs, that enables efficient searches among the red-blue intersections along edges of one of the graphs. Our technique has a number of applications to geometric problems. This includes: (1) a solution to the batched red-blue search problem [Dehne et al. 2006] in O(n log n) queries to the oracle; (2) an algorithm to compute the maximum vertical distance between a pair of 3D polyhedral terrains one of which is convex in O(n log n) time, where n is the total complexity of both terrains; (3) an algorithm to construct the Hausdorff Voronoi diagram of a family of point clusters in the plane in O((n+m) log^3 n) time and O(n+m) space, where n is the total number of points in all clusters and m is the number of crossings between all clusters; (4) an algorithm to construct the farthest-color Voronoi diagram of the corners of n axis-aligned rectangles in O(n log^2 n) time; (5) an algorithm to solve the stabbing circle problem for n parallel line segments in the plane in optimal O(n log n) time. All these results are new or improve on the best known algorithms.Comment: 22 pages, 6 figure

Computational geometry in two and a half dimensions

In this thesis, we study computational geometry in two and a half dimensions. These so-called polyhedral terrains have many applications in practice: computer graphics, navigation and motion planning, CAD/CAM, military surveillance, forest fire monitoring, etc.We investigate a series of fundamental problems regarding polyhedral terrains and present efficient algorithms to solve them. We propose an O(n) time algorithm to decide whether or not a geometric object is a terrain and an O(n log n) time algorithm to compute the shortest watchtower of a polyhedral terrain. We study the terrain guarding problem, obtain tight bounds for vertex and edge guards and O(n) algorithms to place these guards. We study the tetrahedralization of certain simple and non-simple polyhedra (which include some special classes of solid terrains) and present efficient algorithms to tetrahedralize them. We also investigate the problem of computing the $alpha$-hull of a terrain. Finally, we present efficient algorithms for the intersection detection and computation of Manhattan terrains

8th. International congress on archaeology computer graphica. Cultural heritage and innovation

El lema del Congreso es: 'Documentación 3D avanzada, modelado y reconstrucción de objetos patrimoniales, monumentos y sitios.Invitamos a investigadores, profesores, arqueólogos, arquitectos, ingenieros, historiadores de arte... que se ocupan del patrimonio cultural desde la arqueología, la informática gráfica y la geomática, a compartir conocimientos y experiencias en el campo de la Arqueología Virtual. La participación de investigadores y empresas de prestigio será muy apreciada. Se ha preparado un atractivo e interesante programa para participantes y visitantes.Lerma García, JL. (2016). 8th. International congress on archaeology computer graphica. Cultural heritage and innovation. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/73708EDITORIA