61. 52: Convex And Discrete Geometry 52 convex and discrete geometry. Introduction. convex and discrete geometry includes the study of convex subsets of http://www.math.niu.edu/~rusin/known-math/index/52-XX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 52: Convex and discrete geometry Introduction Convex and discrete geometry includes the study of convex subsets of Euclidean space. A wealth of famous results distinguishes this family of sets (e.g. Brouwer's fixed-point theorem, the isoperimetric problems). This classification also includes the study of polygons and polyhedra, and frequently overlaps discrete mathematics and group theory; through piece-wise linear manifolds, it intersects topology. This area also includes tilings and packings in Euclidean space. History Applications and related fields Subfields General convexity, especially 52A55: Spherical geometry 52B: Polytopes and polyhedra Discrete geometry Browse all (old) classifications for this area at the AMS. Textbooks, reference works, and tutorials Klee, Victor: "What is a convex set?", Amer. Math. Monthly 78 1971 616631. MR44#3202 Software and tables LEDA can perform calculations with geometric and combinatorial objects.

62. Geometry In Action: Convex Hulls Castalia and Deimos. Philip Stook at U. Western Ontario mentions an application of 3d convex hulls in mapping the surfaces of these two asteroids. convex hulls and interpolation. a copying machine, using the convex hulls of images of the pages. Part of geometry in Action, a collection of http://www.ics.uci.edu/~eppstein/gina/hull.html

Convex Hulls Castalia and Deimos . Philip Stook at U. Western Ontario mentions an application of 3d convex hulls in mapping the surfaces of these two asteroids. Convex hull, Voronoi diagram, and Delaunay triangulation software from Nina Amenta's CG software directory Convex hulls and interpolation . Ken Clarkson describes some implementation details of algorithms for convex hulls, alpha shapes, Voronoi diagrams, and natural neighbor interpolation. Image Processing and Pattern Recognition in Soil Structure . D. Luo of Glasgow uses convex hulls and other geometric techniques to analyze images of soil particles. Pneumonea and tuberculosis diagnosis . Jason Everhart of Los Alamos uses convex hulls as part of a heuristic for estimating the percentage of lung volume occupied by a pneumonea infection. This initial guess of the lung contour is then iteratively refined to a more accurate representation. US Patent 4704694 uses convex hulls to recognize objects from video images. US Patent 5086482 seems to cover gift-wrapping methods of computing convex hulls in bitmap images. US Patent 5159645 performs character recognition by using convex hulls to find the counters in each character. A similar idea also occurs in

63. Computational Geometry, Algorithms And Applications Recent book with a focus on applications, by Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf. Includes chapters on linesegment intersection, polygon triangulation, linear programming, range searching, point location, Voronoi diagrams, arrangements and duality, Delaunay triangulations, geometric data structures, convex hulls, binary space partitions, robot motion planning, visibility graphs. http://www.cs.ruu.nl/geobook/

About the book Cover Table of contents Errata (1st edition) Errata (2nd edition) ... Order Implementation CGAL LEDA More software Further reading Books Bibliography Web sites Comments to geobook@cs.uu.nl Last modified Oct 9, 2000 Computational Geometry: Algorithms and Applications Second Edition Mark de Berg Marc van Kreveld Mark Overmars Utrecht (the Netherlands) Otfried Schwarzkopf Hong Kong (China) published by Springer-Verlag 2nd rev. ed. 2000. 367 pages, 370 fig. Hardcover DM 59 ISBN: 3-540-65620-0 You can order the book here This textbook on computational geometry has 367 pages. The pages are almost square with a large margin containing over 370 figures. To get an idea about the style and format, take a look at the Introduction or chapter 7 on Voronoi diagrams Computational geometry Computational geometry emerged from the field of algorithms design and analysis in the late 1970s. It has grown into a recognized discipline with its own journals, conferences, and a large community of active researchers. The success of the field as a research discipline can on the one hand be explained from the beauty of the problems studied and the solutions obtained, and, on the other hand, by the many application domains-computer graphics, geographic information systems (GIS), robotics, and others-in which geometric algorithms play a fundamental role. For many geometric problems the early algorithmic solutions were either slow or difficult to understand and implement. In recent years a number of new algorithmic techniques have been developed that improved and simplified many of the previous approaches. In this textbook we have tried to make these modern algorithmic solutions accessible to a large audience. The book has been written as a textbook for a course in computational geometry, but it can also be used for self study.

64. CC012 Supported by the European Research Training Network Classical Analysis, Operator Theory, geometry of Banach spaces, their interplay and their applications . Anogia, Crete; 1824 August 2001. http://www.math.uoc.gr/AXAK/CC/CC012.html

CONVEX GEOMETRIC ANALYSIS Anogia, Crete, August 18 - 24, 2001 This conference is coorganized by the University of the Aegean (Department of Mathematics). It is additionally supported by the European Research Training Network "Classical Analysis, Operator Theory, Geometry of Banach spaces, their interplay and their applications". Organizers : A. Giannopoulos (Crete, Greece), V. Milman (Tel Aviv, Israel), R. Schneider (Freiburg, Germany), S. Szarek (Case Western Reserve University, U.S.A. / Paris VI, France) Main speakers : K. Ball (University College London, United Kingdom), I. Barany (Hungarian Academy of Sciences), P. Gruber (Wien, Austria), A. Koldobsky (University of Missouri, Columbia, U.S.A.), G. Schechtman (Weizmann Institute, Israel), S. Szarek (Case Western Reserve University, U.S.A. / Paris VI, France) Workshop Topic and Purpose Keynote Speakers For questions regarding travel to Anogia and your stay there, please see the

65. Computational Geometry In C (Second Edition) A wellknown textbook by Joseph O'Rourke, including chapters on polygon triangulation, polygon partitioning, convex hulls in 2D and 3D, Voronoi diagrams, arrangements, search and intersection, and motion planning. Sample code in C and Java. http://turing.csc.smith.edu/~orourke/books/compgeom.html

Computational Geometry in C (Second Edition) by Joseph O'Rourke Second Edition: printed 28 September 1998. Purchasing information: Hardback: ISBN 0521640105, $69.95 (55.00 PST) Paperback: ISBN 0521649765, $29.95 (19.95 PST) Cambridge University Press servers: in Cambridge in New York ; Cambridge (NY) catalog entry (includes jacket text and chapter titles). Also amazon.com Contents: Chapter Titles Table of Contents Fully Detailed Table of Contents Some highlights: 376+xiii pages, 270 exercises, 210 figures, 259 references. Although I've retained the title ...in C , all code has been translated to Java, and both C and Java code is available free. Java Applet to permit interactive use of the code: CompGeom Java Applet First Edition code improved: Postscript output, more efficient, more robust. New code (see below). Expanded coverage of randomized algorithms, ray-triangle intersection, and other topics (see below). Basic statistics (in comparison to First Edition): approx. 50 pages longer 31 new figures. 49 new exercises.

66. Arbitrary Dimensional Convex Hull, Voronoi Diagram, Delaunay Triangulation Up Directory of Computational geometry Software. Arbitrary dimensional convex hull, Voronoi diagram, Delaunay http://www.geom.umn.edu/software/cglist/ch.html

Up: Directory of Computational Geometry Software Arbitrary dimensional convex hull, Voronoi diagram, Delaunay triangulation qhull Arbitrary-dimensional convex hull. Computes approximate hulls. Floating-point arithmetic with many parameters for tolerancing. Very fast. Deterministic incremental algorithm with heuristics. Does Voronoi diagrams and Delaunay triangulations and, in low dimensions, Geomview output. Check out the qhull home page for more information. By Brad Barber, David Dobkin and Hannu Huhdanpaa, The Geometry Center. To get the code, go to our qhull download page chD Arbitrary-dimensional convex hull. Computes exact hull of infinitesimally perturbed input. The symbolic perturbations handle all degenerate cases and break output faces up into simplices. Deterministic incremental algorithm. Does Voronoi diagrams and Delaunay triangulations and, in low dimensions, Geomview output. The options are described in the README file for chD. By Ioannis Emiris, U.C. Berkeley. The code, and the relevant papers, are available by ftp from Berkeley Hull Arbitrary dimensional convex hulls, Delaunay triangulations, alpha shapes, volumes of Voronoi cells; no non-degeneracy assumptions. ANSI C, about 3K lines. Exact arithmetic, with moderate speed penalty over floating point. Incremental algorithm, with performance guarantees if sites are added in random order. Output formats include postscript in 2D, geomview in 3D.

67. The Volume Of Convex Bodies And Banach Space Geometry - Cambridge A selfcontained presentation of results relating the volume of convex bodies andBanach space geometry. The Volume of convex Bodies and Banach Space geometry. http://books.cambridge.org/052166635X.htm

68. Algorithms In Combinatorial Geometry One of the wellknown early textbooks, by Herbert Edelsbrunner. Includes chapters on arrangements, convex hulls, linear programming, planar point location, Voronoi diagrams, and separation and intersection. http://www.springer.de/cgi-bin/search_book.pl?isbn=3-540-13722-X

69. Computational Geometry An Introduction One of the wellknown early textbooks, by Franco P. Preparata and Michael Ian Shamos. Includes chapters on geometric searching, convex hulls, proximity, intersections, and rectangles. http://www.springer.de/cgi-bin/search_book.pl?isbn=3-540-96131-3

70. Askold Khovansky - Algebraic Geometry And Geometry Of Convex Polyhedra polyhedra provide a connection between Algebraic geometry and geometry of convex Polyhedra. This connection is useful http://www.cms.math.ca/CMS/Events/winter98/w98-abs/node16.html

home about the CMS media releases search ... other societies Next: Don O'Shea - Limits Up: Previous: Lisa Jeffrey - The Askold Khovansky - Algebraic geometry and geometry of convex polyhedra ASKOLD KHOVANSKY, Department of Mathematics, University of Toronto, Toronto, Ontario M5S 3G3, Canada Algebraic geometry and geometry of convex polyhedra Newton polyhedra provide a connection between Algebraic Geometry and Geometry of Convex Polyhedra. This connection is useful in both directions. On the one hand it gives visible and understandable answers on the numerous questions which came from Algebraic Geometry. On the other hand it suggests algebraic intuition in the Geometry of Convex polyhedra. The talk will contain a review of the subject including some new results. comments? search for?

71. 3D Convex Hull Algorithm In Java 3D convex Hull algorithm in Java Joseph O'Rourke is Olin Professor of Computer Science at Smith College in Northampton, Massachusetts. His text Computational geometry in C has become one of the definitive computational geometry resources. http://www.cs.sunysb.edu/~algorith/implement/orourke/implement.shtml

3D Convex Hull algorithm in Java Joseph O'Rourke is Olin Professor of Computer Science at Smith College in Northampton, Massachusetts. His text Computational Geometry in C has become one of the definitive computational geometry resources. The programs coded in the text have been made freely available by anonymous ftp from Smith College and have been included at this site as well. In this distribution are standard C and Java language routines for simple computational geometric methods (determining whether a point lies inside a polygon, for instance) as well as robust implementations of complex computational geometry algorithms. Addressed are problems in motion planning, nearest neighbor determination (through the use of Delaunay triangulations and Voronoi diagrams), polygon intersection, convex hull computation, and polygon triangulation. Download Files (Smith College) Download Files (local site) Go to Joseph O'Rourke 's Home Page Problem Links Robust Geometric Primitives (6) Convex Hull (6) Nearest Neighbor Search (5) Intersection Detection (5) ... The Stony Brook Algorithm Repository go to front page This page last modified on Sep 1, 1999.

72. Home Page For Qhull Software(With C code) from the geometry Center for Fast Delaunay Triangulation in any Dimension.Category Science Math geometry Software...... programming; Lambert's Java visualization of convex hull algorithms;Stony Brook Algorithm Repository, computational geometry. BGL http://www.geom.umn.edu/software/qhull/

Up: Past Software Projects of the Geometry Center URL: http://www.geom.umn.edu/software/qhull Home page for Qhull Qhull computes convex hulls, Delaunay triangulations, halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay triangulations, and furthest-site Voronoi diagrams. It runs in 2-d, 3-d, 4-d, and higher dimensions. It implements the Quickhull algorithm for computing the convex hull. Qhull handles roundoff errors from floating point arithmetic. It computes volumes, surface areas, and approximations to the convex hull. Qhull does not support constrained Delaunay triangulations, triangulation of non-convex surfaces, mesh generation of non-convex objects, or medium-sized inputs in 9-D and higher. News about Qhull How is Qhull used? Download Qhull Examples of Qhull output Qhull development at Savannah Manual for Qhull and rbox qconvex convex hull qdelaunay Delaunay triangulation qvoronoi Voronoi diagram qhalf halfspace intersection about a point rbox generate point distributions Qhull functions , macros, and data structures with source Frequently asked questions about Qhull Geomview 3-D and 4-D visualization of Qhull output MATLAB's qhull functions: convhulln delaunayn griddatan tsearch ... voronoin . MATLAB has not upgraded to version 3.1 and triangulated output ('Qt'). GNU Octave uses Qhull for their computational geometry functions . Octave has not upgraded to version 3.1 and triangulated output ('Qt'). Mathematica's Delaunay interface: qh-math Send e-mail to

73. Convex And Computational Geometry Research Division Contact us. Links. convex and Computational geometry research division. Researchstaff Gábor Fejes Tóth, head of research division; Imre Bárány; András Bezdek; http://www.renyi.hu/staff/geometry.html

* Text version * A R I NSTITUTE OF M ATHEMATICS Home People The Institute - General ... Links Convex and Computational Geometry research division Research staff , head of research division Endre Makai Associated members Contact the webmaster

74. Convex And Computational Geometry Research Division convex and Computational geometry research division. Research staff GáborFejes Tóth, head of research division; Imre Bárány; András Bezdek; http://www.renyi.hu/staff/geometry-text.html

Home People The Institute Periodicals ... Links Convex and Computational Geometry research division Research staff , head of research division Endre Makai Associated members Contact the webmaster

75. Computational Geometry On The Web Course notes and resource links.Category Science Math geometry Computational geometry...... 9. Complexity, convexity and Unimodality convex Set, convex function;Unimodal distance functions in geometry; Binary Search. 10. convex http://cgm.cs.mcgill.ca/~godfried/teaching/cg-web.html

"The book of nature is written in the characters of geometry." - Galileo Go to Specific Links Related to 308-507 (Computational Geometry course). General Links - Computational Geometry: Geometryalgorithms.com ( Fantastic Resource Page for Computational Geometry!) Jeff Erickson's Computational Geometry Pages Geometry in Action Geometry Publications by Author ... A Gallery of JAVA Sketchpad Examples in Constructive Geometry Software: JeoEdit - A Java tool for editing polygons and points on the web Directory of Computational Geometry Software CGAL Computational Geometry Library Algorithmic Solutions.Com ... Basic Introduction to Computational Geometry (PostScript file) Godfried's Favourite Computational Geometry Links Computational Geometry on the Web Computational Geometry in Barcelona Computational Geometry Links ... Technology in the Geometry Classroom General Links - More Geometry: Experiencing Geometry (A really nice basic geometry course by David Henderson) Geometry and the Imagination Geometry from Euclid to Today General Geometric References ... Geometric Probability Specific Links Related to the Course Material: Chapter Links: Classical Geometry, Basic Concepts, Theorems and Proofs

76. WileyEurope :: Affine Geometry Of Convex Bodies WileyEurope Mathematics Statistics General Mathematics Mathematics Affine geometry of convex Bodies. Related Subjects, http://www.wileyeurope.com/cda/product/0,,3527402616|desc|2711,00.html

Shopping Cart My Account Help Contact Us By Keyword By Title By Author By ISBN By ISSN WileyEurope General Mathematics Mathematics Affine Geometry of Convex Bodies Related Subjects Historical Mathematics Popular Interest Mathematics Related Titles Mathematics Math Matters (Paperback) James V. Rauff Mathematics Beyond the Numbers (Hardcover) George T. Gilbert, Rhonda L. Hatcher Statistics: A Self-Teaching Guide, 4th Edition (Paperback) Donald J. Koosis Mathematics Beyond the Numbers, Student Solutions Manual (Paperback) George T. Gilbert, Rhonda L. Hatcher Briefwechsel Zwischen Karl Weierstrass und Sofja Kowalewskaja (Hardcover) Mathematics Affine Geometry of Convex Bodies ISBN: 3-527-40261-6 Hardcover 320 Pages May 1998 Add to Cart Description Table of Contents The theory of convex bodies is nowadays an important independent topic of geometry. The author discusses the equiaffine geometry and differential geometry of convex bodies and convex surfaces and especially stresses analogies to classical Euclidean differential geometry. These theories are illustrated by practical applications in areas such as shipbuilding. He offers an accessible introduction to the latest developments in the subject. Printer-ready version of this page E-mail a friend about this product by

77. JosseyBass :: Affine Geometry Of Convex Bodies Mathematics, Affine geometry of convex Bodies Kurt Leichtweiß ISBN 3527-40261-6Hardcover 320 Pages December 1998 US $100.00 Add to Cart. http://www.josseybass.com/cda/product/0,,3527402616,00.html

By Keyword By Title By Author By ISBN By ISSN Shopping Cart My Account Help Contact Us ... Mathematics Affine Geometry of Convex Bodies Related Subjects Historical Mathematics Popular Interest Mathematics Related Titles Mathematics Math Matters (Paperback) James V. Rauff Mathematics Beyond the Numbers (Hardcover) George T. Gilbert, Rhonda L. Hatcher Statistics: A Self-Teaching Guide, 4th Edition (Paperback) Donald J. Koosis The A to Z of Mathematics: A Basic Guide (Paperback) Thomas H. Sidebotham Differential Equations, Asymptotic Analysis, and Mathematical Physics (Hardcover) Michael Demuth (Editor), Bert-Wolfgang Schulze (Editor) Mathematics Affine Geometry of Convex Bodies ISBN: 3-527-40261-6 Hardcover 320 Pages December 1998 US $100.00 Add to Cart Description Table of Contents The theory of convex bodies is nowadays an important independent topic of geometry. The author discusses the equiaffine geometry and differential geometry of convex bodies and convex surfaces and especially stresses analogies to classical Euclidean differential geometry. These theories are illustrated by practical applications in areas such as shipbuilding. He offers an accessible introduction to the latest developments in the subject. Printer-ready version of this page E-mail a friend about this product by

78. Convex Hull -- From MathWorld sets containing S. For N points , , the convex hull C is then given by the expressionComputing the convex hull is a problem in computational geometry. http://mathworld.wolfram.com/ConvexHull.html

Geometry Computational Geometry Convex Hulls Recreational Mathematics ... LiveGraphics3D Applets Convex Hull The convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S . For N points , the convex hull C is then given by the expression Computing the convex hull is a problem in computational geometry . The indices of the points specifying the convex hull of a set of points in two dimensions is given by the command ConvexHull pts ] in the Mathematica add-on package DiscreteMath`ComputationalGeometry` (which can be loaded with the command ). Future versions of Mathematica will support n -dimensional convex hulls. In d dimensions, the "gift wrapping" algorithm, which has complexity , where is the floor function , can be used (Skiena 1997, p. 352). In two and three dimensions, however, specialized algorithms exist with complexity (Skiena 1997, pp. 351-352). Yao (1981) has proved that any decision-tree algorithm for the two-dimensional case requires quadratic or higher-order tests, and that any algorithm using quadratic tests (which includes all currently known algorithms) cannot be done with lower complexity than . However, it remains an open problem whether better complexity can be obtained using higher-order polynomial tests (Yao 1981). O'Rourke (1997) gives a robust two-dimensional implementation as well as an

79. Papers By AMS Subject Classification No papers on this subject. 52XX convex and discrete geometry / Classificationroot. 52-00 General reference works (handbooks, dictionaries http://im.bas-net.by/mathlib/en/ams.phtml?parent=52-XX

80. Wiley Canada :: Affine Geometry Of Convex Bodies Wiley Canada Mathematics Statistics General Mathematics Mathematics Affine geometry of convex Bodies. Related Subjects, http://www.wileycanada.com/cda/product/0,,3527402616|desc|2711,00.html

Shopping Cart My Account Help Contact Us By Keyword By Title By Author By ISBN By ISSN Wiley Canada General Mathematics Mathematics Affine Geometry of Convex Bodies Related Subjects Historical Mathematics Popular Interest Mathematics Related Titles Mathematics Math Matters (Paperback) James V. Rauff Mathematics Beyond the Numbers (Hardcover) George T. Gilbert, Rhonda L. Hatcher Statistics: A Self-Teaching Guide, 4th Edition (Paperback) Donald J. Koosis The A to Z of Mathematics: A Basic Guide (Paperback) Thomas H. Sidebotham Differential Equations, Asymptotic Analysis, and Mathematical Physics (Hardcover) Michael Demuth (Editor), Bert-Wolfgang Schulze (Editor) Mathematics Affine Geometry of Convex Bodies ISBN: 3-527-40261-6 Hardcover 320 Pages December 1998 US $100.00 Add to Cart Description Table of Contents The theory of convex bodies is nowadays an important independent topic of geometry. The author discusses the equiaffine geometry and differential geometry of convex bodies and convex surfaces and especially stresses analogies to classical Euclidean differential geometry. These theories are illustrated by practical applications in areas such as shipbuilding. He offers an accessible introduction to the latest developments in the subject. Printer-ready version of this page E-mail a friend about this product by

Page 4     61-80 of 88    Back | 1  | 2  | 3  | 4  | 5  | Next 20