Extractions: From Wikipedia, the free encyclopedia Jump to: navigation search Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry . Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing ( CAD CAM ), but many problems in computational geometry are classical in nature, and may come from mathematical visualization Other important applications of computational geometry include robotics (motion planning and visibility problems), geographic information systems (GIS) (geometrical location and search, route planning), integrated circuit design (IC geometry design and verification), computer-aided engineering (CAE) (programming of numerically controlled (NC) machines). The main branches of computational geometry are: Combinatorial computational geometry , also called algorithmic geometry , which deals with geometric objects as discrete entities. A groundlaying book in the subject by Preparata and Shamos dates the first use of the term "computational geometry" in this sense by 1975.
Computational Geometry Pages Jeff Erickson s directory of computational geometry resources, including bibliographies, journals, software, and related hubs. http://compgeom.cs.uiuc.edu/~jeffe/compgeom/
Extractions: Computational Geometry Pages Welcome to the Computational Geometry Pages, a (hopefully) comprehensive directory of computational geometry resources both on and off the Internet. If there is something you'd like to see here, please send me email. Contributions and suggestions from the community are always welcome! Other essential computational geometry sites include Nina Amenta 's Directory of Computational Geometry Software 's CG Tribune (a newsletter with events and announcements), David Eppstein 's Geometry in Action (describing applications of computational geometry in the Real World), and the 's collection of computational geometry papers new recent current search ] moderated by Joe O'Rourke There are also several excellent Web pages devoted to theoretical computer science in general. See especially Suresh Venkatasubramanian 's Theoretical Computer Science on the Web and the ACM SIGACT home page Web Directories ... Computer science in general For conference proceedings, see
Extractions: Online proceedings from the ACM Digital Library (provided you or your institution has a subscription) Conference web sites: Business meetings: old minutes: (Please send the webmaster other old minutes you may have) minutes blog minutes report of the PC ... About the logo CCCG web site EuroCG web site Announcements subscription and recent archive archive (1998-2006) Discussions ... Webmaster
Extractions: Sample Issue Online About this Journal Submit your Article Shortcut link to this Title ... New Article Feed Signed up for new Volumes / Issues [ remove Alert me about new Volumes / Issues Your selection(s) could not be saved due to an internal error. Please try again. Added to Favorites [ remove Add to Favorites No next vol/iss Font Size: Add to my Quick Links Volume 44, Issue 1, Pages 1-68 (January 2011) = Full-text available = Abstract only Volume 44 (2011) Volume 44, Issue 1 - selected
Extractions: "Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!" "The first test of potential in mathematics is whether you can get anything out of geometry." Quoted in D MacHale, Comic Sections(Dublin 1993) The significant problems we face cannot be solved at the same level of thinking we were at when we created them Einstein Algorithms Computer Architecture Compilers ... Parallel Computing Computational Geometry Lecture Notes Introduction Polygon Partitioning ... Quick Hull Voronoi Diagram Delaunay Triangulation Proximity Problem Appendix Algorithms Illustration (Applet) from "Computational Geometry in C" by J. O'Rourke
Extractions: Home Intranet Overview Online Manual Installation Guide Tutorials ... All Manuals Download License The CGAL Philosophy Acknowledging CGAL ... Release History FAQ Supported Platforms Reporting Bugs Mailing Lists Project Members Getting Involved Project Rules Partners and Funding Videos Events Classes Projects Using CGAL 3rd Party Software Related Links manual cgal.org cgal-discuss Computational Geometry Algorithms Library The goal of the CGAL Open Source Project is to provide easy access to efficient and reliable geometric algorithms in the form of a C++ library. CGAL is used in various areas needing geometric computation, such as: computer graphics, scientific visualization, computer aided design and modeling, geographic information systems, molecular biology, medical imaging, robotics and motion planning, mesh generation, numerical methods... More on the projects using CGAL web page. The Computational Geometry Algorithms Library ( CGAL ), offers data structures and algorithms like triangulations (2D constrained triangulations and Delaunay triangulations in 2D and 3D, periodic triangulations in 3D)
Extractions: ISBN: 978-3-540-77973-5 You can order the book here Introduction (Chapter 1, pdf) Delaunay Triangulations (Chapter 9, pdf) All figures (a pdf for each chapter, zip) All pseudocode (on separate pages, pdf) This third edition contains two major additions: In Chapter 7, on Voronoi diagrams, we now also discuss Voronoi diagrams of line segments and farthest-point Voronoi diagrams. In Chapter 13, we have included an extra section on binary space partition trees for low-density scenes, as an introduction to realistic input models. In addition, a large number of small and some larger errors have been corrected (see the list of errata for the second edition on the Web site). We have also updated the notes and comments of every chapter to include references to recent results and recent literature. We have tried not to change the numbering of sections and exercises, so that it should be possible for students in a course to still use the second edition.
Computational Geometry - Definition In computer science, computational geometry is the study of algorithms to solve problems stated in terms of geometry. Some purely geometrical problems arise out of the study of http://www.wordiq.com/definition/Computational_geometry
Extractions: In computer science computational geometry is the study of algorithms to solve problems stated in terms of geometry . Some purely geometrical problems arise out of the study of computational geometric algorithms, and the study of such problems is also considered to be part of computational geometry. The main driving force for the development of computational geometry as a discipline was progress in computer graphics , computer-aided design and manufacturing ( CAD CAM ), but many problems in computational geometry are classical in nature. Other important "customers" of computational geometry inlude Robotics (motion planning and visibility problems), Geographic Information Systems GIS ) (geometrical location and search, route planning), Integrated circuit design (IC geometry design and verification), computer-aided engineering (CAE) (programming of numerically controlled (NC) machines). There are two main flavors of computational geometry: Combinatorial Computational Geometry , also called Algorithmic Geometry , which deals with geometric objects as discrete entities.
Extractions: Journals This page lists journals that publish research and expository papers in computational geometry and closely related fields. Journals marked either explicitly solicit computational geometry papers or are cited frequently in the Geometry Literature Database . Items marked have recently appeared or changed. If articles are available electronically, a list of available formats is given in parentheses. Unless indicated otherwise, electronic contents are available only to current subscribers or at subscribing institutions. Rob Kirby , a mathematics professor at Berkeley, recently published an open letter discussing the rising subscription prices of mathematics journals . Although he doesn't include them in his discussion, exactly the same issues apply to discrete mathematics and computer science journals. The annotations MathSciNet HBP Search ACM , and CSBib indicate bibliographies or search pages for the journal that are part of a larger bibliography collection. These annotations are explained on a separate web page . Most of these journals are also (at least partially) indexed in the Geometry Literature Database Upcoming special issues are listed on a separate web page DCG: Germany or New York (PDF, LaTeX)
Extractions: 320 Soda Hall Combinatorial geometry: Polygons, polytopes, triangulations, planar and spatial subdivisions. Constructions: triangulations of polygons, convex hulls, intersections of halfspaces, Voronoi diagrams, Delaunay triangulations, arrangements of lines and hyperplanes, Minkowski sums; relationships among them. Geometric duality and polarity. Numerical predicates and constructors. Upper Bound Theorem, Zone Theorem. Algorithms and analyses: Sweep algorithms, incremental construction, divide-and-conquer algorithms, randomized algorithms, backward analysis, geometric robustness. Construction of triangulations, convex hulls, halfspace intersections, Voronoi diagrams, Delaunay triangulations, arrangements, and Minkowski sums. Geometric data structures: Doubly-connected edge lists, quad-edges, face lattices, trapezoidal maps, conflict graphs, history DAGs, spatial search trees (a.k.a. range search), binary space partitions, quadtrees and octrees, visibility graphs. Applications: Line segment intersection and overlay of subdivisions for cartography and solid modeling. Triangulation for graphics, interpolation, and terrain modeling. Nearest neighbor search, small-dimensional linear programming, database queries, point location queries, windowing queries, discrepancy and sampling in ray tracing, robot motion planning.
Computational Geometry - Elsevier Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in http://www.elsevier.com/locate/comgeo
Computational Geometry On The Web Go to Specific Links Related to COMP507 (Computational Geometry course). Geometryalgorithms.com ( Fantastic Resource Page for Computational Geometry! http://cgm.cs.mcgill.ca/~godfried/teaching/cg-web.html
Extractions: RPI The aim of this workshop is to bring together, in an informal setting conducive to stimulate collaboration, researchers from academia and industry, as well as students working in Computational Geometry and Geometric Applications. The goal is to learn from each other of recent progress on problems of common interest, leaving sufficient time for discussions and posing of new problems emerging from on-going research. Topics of interest span all algorithmic aspects of geometrical problems, either classical or emerging from applied computational areas, including but not limited to: Algorithmic methods in geometry Animation of geometric algorithms Applications of geometric algorithms Bio-geometry Combinatorial geometry Computer-aided design Computer graphics Computational metrology Computational statistics Computational topology Computer vision Experimental studies of geometric algorithms Geometric approximation algorithms Geometric computation in Computational biology Geometric data structures Geometry of geographic information systems Graph drawing Implementation issues for geometric algorithms I/O-scalable geometric algorithms Kinetic data structures Manufacturing applications of geometry Mesh generation Modeling new problems with geometry Motion generation, folding and unfolding
Computational Geometry -- From Wolfram MathWorld The study of efficient algorithms for solving geometric problems. Examples of problems treated by computational geometry include determination of the convex hull and Voronoi http://mathworld.wolfram.com/ComputationalGeometry.html
Extractions: Computational Geometry The study of efficient algorithms for solving geometric problems. Examples of problems treated by computational geometry include determination of the convex hull and Voronoi diagram for a set of points, triangulation of points in a plane or in space, and other related problems. SEE ALSO: Convex Hull Delaunay Triangulation Discrete Geometry Geometric Probability ... Voronoi Diagram REFERENCES: Amenta, N. "Directory of Computational Geometry Software." http://www.geom.umn.edu/software/cglist/ de Berg, M.; van Kreveld, M.; Overmans, M.; and Schwarzkopf, O. Computational Geometry: Algorithms and Applications, 2nd rev. ed. Berlin: Springer-Verlag, 2000. Erickson, J. "Computational Geometry Pages." http://compgeom.cs.uiuc.edu/~jeffe/compgeom/ Erickson, J. "Computational Geometry Code." http://compgeom.cs.uiuc.edu/~jeffe/compgeom/code.html Goodman, J. E. and O'Rourke, J. Handbook of Discrete and Computational Geometry.
Computational Geometry Code Jeff Erickson's links to freely available implementations of geometric algorithms and software. http://compgeom.cs.uiuc.edu/~jeffe/compgeom/code.html
Extractions: Code This page lists "small" pieces of geometric software available on the Internet. Most of the software is available free of charge. Unless otherwise specified, C or C source code is available for all programs. Software libraries and collections and programs that can be run interactively over the web are listed on separate web pages. Caveat Surfor I can't make any claims about the usefulness or quality of the programs listed here. I don't have the time or equipment to try them all. If you have experience with any of these programs, either positive or negative, please tell me about it The programs on this page are divided into several categories, some of which are divided into further sub-categories. (Eventually, each category will get its own separate web page.) Each program is listed only once, but I've provided cross-links between overlapping categories, and I've tried to arrange similar categories near each other. Each category also includes links to relevant pages in Nina Amenta 's comprehensive Directory of Computational Geometry Software , which I strongly encourage you to visit!