81. CGAL - Computational Geometry Algorithms Library A collaborative effort to develop a robust, easy to use, and efficient C++ software library of geometric data structures and algorithms. http://www.cgal.org/

Home Intranet Documentation Overview Online Manual Installation Guide Tutorials ... All Manuals Software Download License The CGAL Philosophy Acknowledging CGAL ... Release History Support FAQ Supported Platforms Reporting Bugs Mailing Lists Project Project Members Getting Involved Project Rules Partners and Funding More information Videos Events Classes Other Resources Projects Using CGAL 3rd Party Software Related Links Search 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)

82. JeoEdit Two Java applets for editing polygons and point sets for input to computational geometry software. http://cgm.cs.mcgill.ca/~godfried/jeoedit/

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83. Directory Of Computational Geometry Software Lot of categories and links. http://www.geom.uiuc.edu/software/cglist/

Up: Geometry Center Downloadable Software Directory of Computational Geometry Software This page contains a list of computational geometry programs and packages. If you have, or know of, any others, please send me mail . I'm also interested in tools, like arithmetic or linear algebra packages. I have made no attempt to determine the quality of any of these programs, and their inclusion here should not be seen as any kind of recommendation or endorsement. But I am interested in hearing about your experiences with them. Nina Amenta , Collector Contents What's new? Collections Arbitrary dimensional convex hull, Voronoi diagram, Delaunay triangulation Low dimensional convex hull, Voronoi diagram, Delaunay triangulation ... Wish list! Other related algorithmic Web sites: comp.graphics.algorithms FAQ BSP tree FAQ Linear programming FAQ Robert Schneiders' Mesh generation page The computer vision source code page, off the CMU computer vision home page . The home page has lots of pointers to related areas like pattern recognition and robotics, which also have interesting software. Georg Sander's list of graph drawing software Eric Haines' and Nick Fotis' list of computer graphics ftp sites More sites of computational geometric interest: Jeff Erickson's computational geometry page The Carleton computational geometry resource guide David Eppstein's Geometry in Action page, listing applications of computational geometry, and his fascinating

84. Tips & Tricks To Gothic Geometry Full explanatory diagrams for constructing your own rose window, ogee arch, and trifoil tracery. http://www.newyorkcarver.com/geometry/geometry.htm

Search Stone carving , architecture, art...and the Middle Ages HOME Feature Articles Stone Carver's Tour Virtual Cathedral ... FAQ Front cover Introduction Sample Pages Introduction Ideal geometric shapes in architecture have imparted a feeling of order and harmony since the Greeks. The Romans, using only geometry and the repeated use of the semicircular arch, later built an empire. New innovations followed in the Middle Ages. The medieval flying buttress was born from the desire for building higher; and the pointed arch arose from the necessity of efficiently transferring the extra weight from above. Surprisingly, "Gothic" was first used as a term of derision by Renaissance critics who scorned the architectural style's lack of conformity to the standards of classic Greece and Rome. A closer look, however, reveals that the underpinnings of medieval architecture were firmly rooted in the ancient use of geometry and proportion. It's seen in the overall cruciform shape of a cathedral; in the rhythmic, intricate patterns found in stained glass windows; and in the rib vaulting that criss-crosses the ceiling.

85. Differential Geometry Page Contains several figures which are the result of easy codes using Mathematica, including Enneper s surface. http://math.bu.edu/people/carlosm/Diffeo.html

Differential Geometry Page This page contains a few figures which are the result of easy codes using Mathematica. Enneper's Surface Torus

86. Differential Geometry And Physics Lecture notes by Gabriel Lugo. http://people.uncw.edu/lugo/COURSES/DiffGeom/dg1.htm

Lectures Notes by Gabriel Lugo University of North Carolina at Wilmington Differential Geometry and Physics I. Vectors and Curves 1.1 Tangent Vectors 1.2 Curves 1.3 Fundamental Theorem of Curves II. Differential forms 2.1 1-Forms 2.2 Tensors and Forms of Higher Rank 2.3 Exterior Derivatives 2.4 The Hodge-* Operator III. Connections 3.1 Frames 3.2 Curvilinear Coordinates 3.3 Covariant Derivative 3.4 Cartan Equations IV Surfaces in R 4.1 Manifolds 4.2 First Fundamental form 4.3 Second Fundamental Form 4.4 Curvature Full set (DVI 228K) Full set (PDF 340Kb) Return to Courses home page Gabriel G. Lugo, lugo@uncw.edu Last updated April 10, 2004

87. Differential Geometry Lecture notes for an honors course at the University of Adelaide by Michael Murray in HTML with GIFs. http://www.maths.adelaide.edu.au/michael.murray/dg_exercises.pdf

88. Differential Geometry A textbook by Ruslan Sharipov (English and Russian versions). http://arxiv.org/PS_cache/math/pdf/0412/0412421v1.pdf

89. Riemannian Geometry Online textbook. http://www.math.ku.dk/~moller/f05/genotes.pdf

90. EDGE Bulgarian node of the European Differential Geometry Endeavour. http://www.fmi.uni-sofia.bg/ivanovsp/edge.html

THE EDGE MEMBERS Bogdan Alexandrov mail: alexandrovbt@fmi.uni-sofia.bg Vestislav Apostolov mail: ... Florin.Belgun@math.uni-leipzig.de Vasile Brinzanescu mail: brinzane@imar.ro Johan Davidov mail: jtd@math.bas.bg Catalin Gherghe mail: gherghe@adonix.cs.unibuc.ro Gueo Grantcharov mail: ... geogran@math.uconn.edu Stere Ianus mail: Stere.Ianus@imar.ro Stefan Ivanov mail: ... ivanovsp@fmi.uni-sofia.bg Oleg Muskarov mail: muskarov@math.bas.bg Liviu Ornea mail: ... Back

91. The Geometry Page Discussion of deltahedra, infinite and flexible polyhedra, with images, a java applet, and links. http://www.superliminal.com/geometry/geometry.htm

Geometry Page New: Tyler is a simple applet that lets you explore planar tilings using regular polygons. Please visit the Tyler Art Gallery to see the incredible variety of beautiful forms that can be easily created. With the Tyler applet you can create polygons of various sizes and attach them to edges of other polygons. Click the image above or the following link to try the Tyler applet yourself. The image is from is from Kepler's Harmonice Mundi volume 2 and is easily reconstructed using Tyler. For a mathematical description of planar tilings see Jim McNeill's excellent description Symmetry has always been attractive to mathematicians, and the most symmetric of all figures are the regular polyhedra, or Platonic solids . A regular polyhedron is defined as a finite polyhedron composed of a single type of regular polygon such that each element (vertex, edge and face) is surrounded identically. In three dimensions there are exactly five such polyhedra which don't intersect themselves, and four more that do. There are many other interesting such figures, many of which are defined by relaxing one or more of the conditions defining regular polyhedra. For instance, the figure above is composed of only regular triangular faces, but it has three types of edges and three types of vertices. (The three types of vertices are surrounded by 4, 6 and 10 triangles.) Click on the following link for more information on deltahedra I have done substantial work exploring an interesting and often overlooked class of polyhedra which satisfy most or all the criteria defining regular polyhedra except that they are not finite. In other words, it would take an infinite number of polygons to complete such a figure which would then fill all of space with a latticework. Of course an infinite model cannot be completely constructed, but large enough sections can be built to show their geometry and prove their existence. The image above (courtesy of Steve Dutch) shows a portion of one of the simplest such models. Many more elaborate and beautiful figures exist. Click the following link for a fuller description of

92. Projet Cabri The home site for Cabri Geometry, a dynamic geometry package . http://www-cabri.imag.fr/index-e.html

New Neu Nieuw Nouveau Novo Nuevo Nuovo ! Cabri 3D Le site universitaire de Cabri Cabri academic site ... English Les logiciels Cabri sont chez Cabrilog Cabri software home site

93. Seattle'05 Three one-week sessions Interactions with physics; Classical geometry; Arithmetic geometry. University of Washington, Seattle, WA, USA; 25 July 12 August 2005. http://www.math.princeton.edu/~rahulp/seattle05.html

Summer Institute in Algebraic Geometry July 25 - August 12, 2005 Program: Plenary / Full AMS information brochure Participant list Graduate student workshop The American Mathematical Society, the Clay Mathematics Institute, and the National Science Foundation will sponsor a three week Summer Institute in Algebraic Geometry at the University of Washington, Seattle from July 25 to August 12, 2005. The goals of the Institute are to review the major achievements of the past decade and to look forward to future developments. The focus will be structured by week: Interactions with physics Classical geometry Arithmetic geometry Plenary lecture series aimed at broad audiences will be scheduled in the morning. More specialized seminar sessions will take place in the afternoon. Financial support, as always, will be limited. Participants are encouraged to seek travel funds from their home institutions or funding agencies. The organizing committee

94. CASA Computer Algebra Software for constructive Algebraic geometry. Designed for performing computations and reasoning about geometric objects in classical algebraic geometry, in particular affine and projective algebraic geometry over an algebraically closed field of characteristic 0. http://www.risc.uni-linz.ac.at/software/casa/

CASA Computer Algebra System for Algebraic Geometry CASA is a special-purpose system for computational algebra and constructive algebraic geometry. The system has been developed since 1990. CASA is the ongoing product of the Computer Algebra Group at the Research Institute for Symbolic Computation (RISC-Linz), the University of Linz, Austria, under the direction of Prof. Winkler. The system is built on the kernel of the widely used computer algebra system Maple. Introduction Requirements, Distribution And Contact CASA: A Quick Tour What Is New ... Bibliography

95. Computational Geometry Impact Task Force Report Computational Geometry Impact Task Force Report, chaired by Bernard Chazelle, about the relation between computational geometry and various application fields. This page also archives the discussion that it caused (which was intended) and related links. http://compgeom.cs.uiuc.edu/~jeffe/compgeom/taskforce.html

The Computational Geometry Impact Task Force Report In April 1996, Bernard Chazelle 's Computational Geometry Impact Task Force published a report entitled "Application Challenges to Computational Geometry" . Anyone interested in computational geometry or geometric computing is strongly encouraged to read it! Hypertext from Seth Teller at MIT DVI (256 Kb), PostScript (467 Kb), and compressed PostScript (187 Kb) from MIT gzipped PostScript (156 Kb) from Duke Princeton technical report , also available from Bernard Chazelle's homepage . (For some reason, this version is much larger than the one from MIT.) Discussion Soon after the report's publication, comments by David Avis and Komei Fukuda sparked a lively discussion on the compgeom-discuss mailing list of some of the issues raised in the impact report. The same issues are still being discussed at computational geometry meetings - at SoCG 1998 , for example, there was a panel discussion on "The Theory/Applications Interface" - but activity on the mailing lists has died off. Archives of the discussion at Bell Labs Archives of the discussion [Many of the hypertext links in the following messages no longer work. -Jeff]

96. The Math Forum - Math Library - Projective Geom. Part of the Math Forum. http://mathforum.org/library/topics/projective_g/

Browse and Search the Library Home Math Topics Geometry Non-Euclidean Geom. : Projective Geom. Library Home Search Full Table of Contents Suggest a Link ... Library Help Selected Sites (see also All Sites in this category An Introduction to Projective Geometry (for computer vision) - Stan Birchfield The contents of this paper include: The Projective Plane; Projective Space; Projective Geometry Applied to Computer Vision; Demonstration of Cross Ratio in P^1; and a bibliography. (Euclidean geometry is a subset of projective geometry, and there are two geometries between them: similarity and affine.) Also at http://vision.stanford.edu/~birch/projective/. more>> Projective Geometry - Nick Thomas Basics, path curves, counter space, pivot transforms, and some people involved in the development of projective geometry, which is concerned with incidences: where elements such as lines planes and points either coincide or not. For example, Desargues Theorem says that if corresponding sides of two triangles meet in three points lying on a straight line, then corresponding vertices lie on three concurrent lines. The converse is also true: if corresponding vertices lie on concurrent lines, then corresponding sides meet in collinear points. This illustrates a fact about incidences and has nothing to say about measurements, which is characteristic of pure projective geometry. Projective geometry regards parallel lines as meeting in an ideal point at infinity. more>> PyGeo - Arthur Siegel A dynamic geometry toolset written in Python, with dependencies on Python's Numeric and VPython extensions. It defines a set of geometric primitives in 3d space and allows for the construction of geometric models that can be manipulated interactively, while defined geometric relationships remain invariant. It is particularly suitable for the visualization of concepts of Projective Geometry. PyGeo comes with complete source code.

97. PROJECTIVE GEOMETRY Rudolf Steiner s approach. http://www.nct.anth.org.uk/

Projective geometry is a beautiful subject which has some remarkable applications beyond those in standard textbooks. These were pointed to by Rudolf Steiner who sought an exact way of working scientifically with aspects of reality which cannot be described in terms of ordinary physical measurements. His colleague George Adams worked out much of this and pointed the way to some remarkable research done by Lawrence Edwards in recent years. Steiner's spiritual research showed that there is another kind of space in which more subtle aspects of reality such as life processes take place. Adams took his descriptions of how this space is experienced and found a way of specifying it geometrically, which is dealt with in the Counter Space Page A brief introduction to the basics of the subject is given in the Basics Page See also Britannica: projective geometry The work of Lawrence Edwards is introduced in the Path Curves Page , and some explorations of his work on further aspects is described in the Pivot Transforms Page . This is mostly pictorial, with reference to documentation.

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