1. An Introduction To Projective Geometry (for Computer Vision) An Introduction to Projective geometry ( for computer vision) Intersections and unions of points, lines, and planes. Projective geometry Applied to computer Vision. Image formation http://robotics.stanford.edu/~birch/projective

Next: Introduction An Introduction to Projective Geometry (for computer vision) Stan Birchfield Printable version: [PDF 247KB] [ps.gz 71 KB] ** Erratum ** In Section 2.1.3, "The unit sphere," it is stated that the projective plane is topologically equivalent to a sphere. In fact, it is only locally topologically equivalent to a sphere, as pointed out by John D. McCarthy Introduction The Projective Plane Four models ... Stan Birchfield April 23, A.D. 1998

2. Page Personnelle Pmaillot Site contains a set of 2D and 3D mathematical studies and algorithms for use in computer graphics, for geometry pipelines and rendering. http://www.chez.com/pmaillot/

Page Personnelle pmaillot Bienvenue! Welcome! Page maintenue par / Page maintained by Patrick-Gilles Maillot. Mars 2004

3. Computer Graphics computer Graphics. MiraLab computer Graphics Animation Group. EPFL AHPCRC Graphics Software. computer Graphics at the University of Utah. The geometry Center, University of http://mambo.ucsc.edu/psl/cg.html

Computer Graphics EPFL Laboratoire d'Infographie Computer Graphics International 2000 Conference International Conference in Central Europe on Computer Graphics and Visualization Electronic Visualization Laboratory Army Research Labs - Scientific Visualization AHPCRC Graphics Software Computer Graphics at the University of Utah The Geometry Center, University of Minnesota Manchester Visualisation Centre Graphics, Visualization, and Usability Center UNIVERSITY of PENNSYLVANIA - Center for Human Modeling and Simulation UCSC - Perceptual Science Laboratory UCSC - Santa_Cruz Laboratory for Visualization and Graphics Thant's Animations Index 3D WEB CRS4 Sci Viz Group UBC IMAGER Computer Graphics Lab NASA Scientific Applications and Visualization Branch ICASE Visualization and Graphics The Princeton University Graphics Group Center for Complex Systems and Visualization (CeVis) at Bremen Geometric Modeling at Aizu University Computer Graphics Research Group at Zurich Cornell Program of Computer Graphics Visualization at the Cornell Theory Center SHASTRA Collaborative Visualization Laboratory Visualization Research at Leeds CICA Graphics (Indiana) Brown Computer Graphics Group Laboratory of Eidomatics, Milan

4. Personal Page Of Martin Held University of Salzburg Computational geometry, computer graphics, program design, algorithms and data structures, computer-aided design and manufacturing. http://www.cosy.sbg.ac.at/~held/held.html

me address how to reach my office research interests ... Internet campaigns Martin Held AMS Dept. of the State University of New York at Stony Brook, Stony Brook, USA; see the homepage of the Computational Geometry Lab at SUNYSB. Address snail mail FB Scientific Computing Jakob-Haringer Str. 2 A-5020 Salzburg ... Austria e-mail held@cosy.sbg.ac.at phone fax How to Reach My Office Please see my WWW page on driving directions and maps Research Interests Computational Geometry and Computer Graphics Program Design, Algorithms and Data Structures Computer-Aided Design and Manufacturing Research Projects I have recently started to assemble a few pages with short descriptions of (or color images related to) some of the application-oriented research projects which I have (or had been) working on. This WWW presentation of current and previous research projects is work in progress; please bear with me (and check back to see whether I've already gotten around to adding new stuff). Courses and Office Hours Local students are invited to browse through a few announcements related to my teaching . (Folks, be warned that some of these pages are in German!).

5. The Geometer's Sketchpad® - Geometry Of Computer Graphics The geometry of computer Graphics1. Proceedings of the 1997 St. Olaf geometry Conference The recent field of computer graphics nicely merges many elegant and simple geometric ideas http://www.keypress.com/sketchpad/talks/comp_graphics

Home Resources Technical Support JavaSketchpad ... Site Map Resources Bibliography 101 Project Ideas Sketchpad Links Sketchpad for Cassiopeia ... TI Graphing Calculators JavaSketchpad About JSP JSP Gallery JSP Download Center JSP Developer's Grammar ... JSP Links Instructor Resources Download Instructor's Evaluation Edition Workshop Guide Professional Development Recent Talks Technical Support FAQ Product Updates Tech Support Request Form General Information Product Info How to Order Curriculum Modules Other Key Sites Key Curriculum Press Key College Publishing KCP Technologies Keymath.com The Geometry of Computer Graphics Proceedings of the 1997 St. Olaf Geometry Conference Nicholas Jackiw Key Curriculum Press njackiw@keypress.com August 1997 Abstract The recent field of computer graphics nicely merges many elegant and simple geometric ideas with concerns about function, realism, and aesthetics. In so doing, it provides a stimulating context for exploring many traditional topics of an introductory geometry course. In this paper, which is based on my after-dinner presentation at the St. Olaf conference, I develop a number of problems and activities drawn from the field of computer graphics, and illustrate them with dynamic sketches from The Geometer's Sketchpad. Table of Contents Why Computer Graphics?

6. Macaulay Macaulay is a computer algebra system for mathematical computations in algebraic geometry and commutative algebra. At its core is a carefully tuned implementation of Grobner basis methods for manipulating systems of polynomial equations. http://www.math.columbia.edu/~bayer/Macaulay.html

7. Mathematical Structures In Computer Science Focuses on the application of areas such as logic, algebra, geometry and category theory to theoretical computer science. http://uk.cambridge.org/journals/msc/

Home Journals Features Related Journals Journals By Title By Subject Highlights New Journals 2004 ... Advanced Search Cambridge Alerts Free journal TOC alerts New title information alerts Mathematical Structures in Computer Science Edited by G. Longo CNRS and Ecole Normale Supérieure, Paris, France Editorial Board Instructions for Contributors Advertising Rates Links Aims and Scope Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. Print ISSN: 0960-1295 Online ISSN: 1469-8072 Full pricing details Current volume: 14:1 - 14:6, 2004 All issues View a free sample of this journal Cambridge University Press 2004.

8. Developing Geometry Concepts Using Computer Programming Environments The Gateway to StandardsBased Mathematics Education. Internet resources to improve teaching learning of school mathematics based on the NCTM Priniples and Standards for School Mathematics. own http://illuminations.nctm.org/imath/prek2/GeometryConcepts

Pre-K - 2 Across Lessons SWRs Tools i-Maths Inquiry Search Standards Contact Us Home i-Math Investigation / Pre-K - 2 PC Mac Help Developing Geometry Concepts Using Computer Programming Environments This activity provides opportunities for creative problem solving while encouraging young students to estimate length and angle measure. Students are asked to enter a sequence of LOGO commands to help the turtle get to the pond. Children can write their own solutions using LOGO commands and input them into the computer. The turtle will then move and leave a trail or path according to the instructions given. Two possible solutions or paths that students might have produced can be seen. You can 'clear' any path and then create a new path that will get the turtle to the pond. Can You Get the Turtle to the Pond? Directions: You can try out "path 1" or "path 2" by checking the box and pressing "draw". To erase a path, press "clear". To create a new path, adjust the length by using the blue sliders and then press the "forward", "back", or "turn" buttons. In an activity like the one described above, once children have found paths to the pond, they can share their programs with other students. Discussing their programs and the turtle paths with other students helps children reflect on their own method of solving the problem and on the relationships between distance and turtle movement and angle and turtle movement. Teachers can prompt further discussion and investigation with the following questions:

9. Institute For Theoretical Computer Science ETH, Zurich. The members are active in teaching and research in topics including design and analysis of algorithms, in particular in graph theory and computational geometry; data structures, in particular for spatial data; computability and complexity; information security and cryptography; and parallel computation. http://www.inf.ethz.ch/department/TI/

10. An Introduction To Projective Geometry (for Computer Vision) An Introduction to Projective geometry ( for computer vision) Intersections and unions of points, lines, and planes. Projective geometry Applied to computer Vision. Image formation http://vision.stanford.edu/~birch/projective/projective.html

Next: Introduction An Introduction to Projective Geometry (for computer vision) Stan Birchfield Printable version: [pdf.gz 153KB] [pdf 247KB] [ps.gz 71 KB] Introduction ... Stan Birchfield April 23, A.D. 1998

11. Computer Graphics à La Ken Turkowski Antialiasing, color spaces, testure mapping, shading, geometry, image registration, numerical computation, open source articles. http://www.worldserver.com/turk/computergraphics/

Computer Graphics from the viewpoint of Ken Turkowski Papers Other Computer Graphics Pages Gamma Correction Resampling Kernels Open Source Links to Other Computer Graphics Pages ... Apple Home Page last revised:

12. Computational Geometry Bibliographies Bibliographies of computational geometry papers Computational geometry. Bibliographies. Items marked should be of Price's Annotated computer Vision Bibliography includes several 2d and a few http://compgeom.cs.uiuc.edu/~jeffe/compgeom/biblios.html

Computational Geometry Bibliographies Items marked should be of particular interest to computational geometers. Items marked have recently appeared or changed. I guess this is the best place to mention Janice Walker's MLA-Style Citation Format for Electronic Resources , which describes citation formats for PostScript preprints, mailing list messages, Web pages, and so forth, in a style consistent with the MLA Handbook for Writers of Research Papers The Geometry Literature Database The Geometry Literature Database is a BibT E X database of papers in computational geometry, maintained as a collective effort by members of the computational geometry community, under the gentle supervision of Bill Jones at the University of Saskatchewan. Bill releases revisions of the database three times a year. The most recent revision was released on December 8, 1998 . It contains entries and requires just under 4 Mb of disk space. Bill's announcement of the latest release has more details. Detailed information about the database WWW search pages: 's search page at Universiteit Utrecht (usually current) [New URL] Search page at McGill University (usually current) Eric Grosse's search page at netlib (1996 version) To get your own copy (as a 1.2Mb gzipped tar file)...

13. Geometry Around Black Holes A WWW Exhibition in Relativistic computer Dynamics and Visualization http://www.astro.ku.dk/~cramer/RelViz/

Award June 10th 1997 Award July 7th 2000 'Highly Rated by Schoolzone' Cramer's Homepage Geometry Around Black Holes A WWW Exhibition in Relativistic Computer Dynamics and Visualization By Michael Cramer Andersen, June 1996. Contents of this WWW Visualization Exhibition: General Relativity and Black Holes. Curvature and lightcones. Kerr's rotating Black Holes. Gravitational redshift. ... Other sites with black holes... You are guest no. Updated June 18th 1997 by cramer@astro.ku.dk . Links to this site: http://www.astro.ku.dk/~cramer/RelViz/

14. Geometry In Action: Graphics quite closely connected with computational geometry; for instance ACM TOG often publishes geometry for computer graphics. Teaching materials from the ITTI Gravigs Project http://www.ics.uci.edu/~eppstein/gina/graphics.html

Graphics This area is quite closely connected with computational geometry; for instance ACM TOG often publishes computational geometry papers. Geometric research topics in graphics include data structures for ray tracing, clipping, and radiosity; hidden surface elimination algorithms; automatic simplification for distant objects; morphing; clustering for color quantization; converting triangulated surfaces to strips of triangles (some graphics engines take inputs in this form to save bandwidth); and construction of low-discrepancy point sets (for oversampling to eliminate Moire effects in ray tracing). Specialized applications of graphics in which other geometric ideas are needed include architecture virtual reality , and video game programming . This area is also related to mesh generation in several ways: both fields use triangulation algorithms to partition complex surfaces into simpler pieces, and radiosity calculations in graphics are essentially a special case of the finite element method. ACM Special Interest Group on Graphics (SIGGRAPH) ACM Transactions on Graphics Annotated bibliography on object representation schemes for 3d graphics , H.-G. Park, Air Force Inst. Tech.

15. Index Of /~cramer/RelViz/text/exhib1 An exhibition on relativistic computer dynamics used to present the theory of black holes. http://www.astro.ku.dk/~cramer/RelViz/text/exhib1

Index of /~cramer/RelViz/text/exhib1 Name Last modified Size Description ... Parent Directory 22-Sep-1999 08:23 - contents.pl 14-Jun-1996 23:34 1k exhib1.css 14-Jun-1996 23:34 1k exhib1.html 15-Jun-1996 01:41 4k images.aux 14-Jun-1996 23:34 1k images.log 14-Jun-1996 23:34 3k images.pl 14-Jun-1996 23:34 1k images.tex 14-Jun-1996 23:34 1k img1.gif 14-Jun-1996 23:34 1k img2.gif 14-Jun-1996 22:15 1k img3.gif 14-Jun-1996 22:15 1k img4.gif 14-Jun-1996 22:15 1k img5.gif 14-Jun-1996 23:07 1k img6.gif 14-Jun-1996 23:07 1k img7.gif 14-Jun-1996 23:07 1k img8.gif 14-Jun-1996 22:16 1k img9.old 14-Jun-1996 22:15 1k node1.html 14-Jun-1996 23:34 2k sections.pl 14-Jun-1996 23:34 1k test.gif 14-Jun-1996 23:23 1k Apache/1.3.9 Server at www.astro.ku.dk Port 80

16. Geometry In Action: CAD Related areas computer graphics, computer aided manufacturing, solid modeling, constraing solving, architecture, VLSI design. Academic CAD sites on the web ( primarily VLSI rather than other kinds http://www.ics.uci.edu/~eppstein/gina/cad.html

Computer Aided Design Related areas: computer graphics computer aided manufacturing solid modeling constraing solving ... Academic CAD sites on the web (primarily VLSI rather than other kinds of CAD). Computational Topology . Survey paper by Dey, Edelsbrunner, and Guha, presented at the conference "Computational Geometry Ten Years After". Includes descriptions of applications in image processing, cartography, graphics, solid modeling, mesh generation, and molecular modeling. Computer Aided Geometric Design Computer aided geometric design at Leeds U. , including work on ship and aircraft shapes. Curves and surfaces for geometric modeling , and Geometric Methods and Applications for Computer Science and Engineering , reviews and supplementary material for two books by Jean Gallier . See also his courses CIS 610 and CIS 700 based on the second book. Digital Design Media online textbook. Geometric approaches to mesh generation ", by Christoph Hoffman of Purdue, argues for a tighter coupling between mesh generation and computer aided design. GIS and CAD . John Thomas describes Rochester's experience with the interface between GIS (for large-scale geographic data) and CAD (for smaller scale architectural information such as street layout). Kinematics-driven Geometric Modeling: A Framework for Simultaneous Sculptured Surface Design and CNC Tool Path Generation , Q. Jeffrey Ge, 5th MSI Worksh. Comp. Geom., makes a case for tighter coupling between CAD and CAM.

17. SpringerLink - Publication Discrete Computational geometry is an international journal of mathematics and computer science, covering a broad range of topics in which geometry plays a fundamental role. http://link.springer.de/link/service/journals/00454/

Articles Publications Publishers Home Publication Discrete and Computational Geometry Publisher: Springer-Verlag New York, LLC ISSN: 0179-5376 (Paper) 1432-0444 (Online) Subject: Computer Science Mathematics Issues in bold contain article full text that you are entitled to view. Online First Volume 32 Number 1 Volume 31 Number 4 Number 3 Number 2 Number 1 ... Request a sample Volume 30 Number 4 Number 3 Number 2 Number 1 Volume 29 Number 4 Number 3 Number 2 Number 1 Volume 28 Number 4 Number 3 Number 2 Number 1 Volume 27 Number 4 Number 3 Number 2 Number 1 Volume 26 Number 4 Number 3 Number 2 Number 1 Volume 25 Number 4 Number 3 Number 2 Number 1 Volume 24 Number 4 Numbers 2-3 Number 1 Volume 23 Number 4 Number 3 Number 2 Number 1 Volume 22 Number 4 Number 3 Number 2 Number 1 Volume 21 Number 4 Number 3 Number 2 Number 1 Volume 20 Number 4 Number 3 Number 2 Number 1 Volume 19 Number 4 Number 3 Number 2 Number 1 Volume 18 Number 4 Number 3 Number 2 Number 1 Volume 17 Number 4 Number 3 Number 2 Number 1 Volume 16 Number 4 Number 3 Number 2 Number 1 Volume 15 Number 4 Number 3 Number 2 Number 1 Publication 1 of 1 Previous Publication Next Publication Linking Options About This Journal Editorial Board Manuscript Submission ... Vol. 1 (1986) - 14 (1995)

18. Computer Software For Tiling computer Software for Tiling. Compiled by Doris Schattschneider, Moravian College, schattdo@moravian.edu. Tiling Software for LowEnd Platforms. PlaneTiling Mathematica Package, by Xah Lee. is also available from the geometry Center. This program will run on any computer with a Java capable web browser http://www.geom.umn.edu/software/tilings/TilingSoftware.html

Up: Tessellation Resources Computer Software for Tiling Compiled by Doris Schattschneider, Moravian College, schattdo@moravian.edu Tiling Software for Low-End Platforms PlaneTiling Mathematica Package , by Xah Lee. PlaneTiling is a graphics package for generating wallpaper designs, tilings, plane group symmetry illustrations, and contains general two dimensional graphics tools. Requires Mathematica version 3.x or 2.x. The Geometer's Sketchpad , by Nicholas Jackiw, Key Curriculum Press, 1995. Cabri Geometry II , by Jean-Marie Laborde and Frank Bellemain, IMAG-CNRS-UJF, 1994 (available from Texas Instruments). Two interactive dynamic programs for Macintosh or PC with Windows that can be used to investigate symmetry of two-dimensional figures, construct polygons and tilings, and verify theorems about the properties of isometries. Symmetry Studio , by Timothy Binkley, Van Nostrand Reinhold, 1992. An interactive program for Macintosh that automatically generates symmetric rosette, border, or wallpaper designs from motifs freely drawn with the mouse. User specifies symmetry type and the program uses the chosen symmetry group to generate simultaneous copies of the motif as it is created freehand with the mouse. RepTiles huson (or delgado)@mathematik.uni-bielefeld.de

19. Art, Geometry, Astract Sculpture computer Graphics, Art, Math, geometry, and Abstract Sculpture are closely related. These activities are trying to transcend the boundaries between the fields. With images of models and sculptures. http://www.cs.berkeley.edu/~sequin/ART/

Art, Geometry, and Abstract Sculpture Computer Graphics, Art, Math, Geometry, and Abstract Sculpture are closely related. In the activities below we are trying to transcend the boundaries between these fields. ART-MATH Conferences Art Exhibits Abstract Sculptures A small sampling of great contemporary sculptures. "Rainbow Bit" Sculpture The story of the CD-ROM sculpture in Soda Hall Scherk-Collins Sculpture Generator My original parameterized program to generate Scherk-Collins towers and toroids. A pictorial gallery of my own efforts with physical structures. FermiLab Art Exhibit Sculpture Models exhibited at the FermiLab Art Gallery from May 13 till July 7, 1998. Science - Art Exhibit Sculpture Models exhibited at "Science in the Arts Art in the Sciences", June, 1999. 2nd Generation Sculpture Generator An emerging library of modules providing more generality, built by Jordan Smith. Minimum-Variation Surfaces Work with Henry Moreton to find a functional that encodes the fairness of surfaces. Geometry and Topology Klein Bottles, Boy's Surface, and Zonohedra also have an aesthetic appeal.

20. Computer Science Department of computer Science. Research areas include Parallel and distributed computing, evolutionary and neural computing, heuristics for combinatorial optimization, computational spectral theory, vision, computational geometry, and federated information systems, objectoriented systems, contraints, data warehousing and data mining. http://www.cs.cf.ac.uk/

RESEARCH Areas of research Seminars TEACHING About Admissions For current students I T society SCHOOL Contact addresses Administration Jobs Staff FOR USERS Systems information Web based applications Search Cardiff School of Computer Science Information about... Undergraduate schemes BSc Computer Science BSc Joint Honours Computing BSc/BEng/MEng Computer Systems Engineering BSc Information Systems is a new degree scheme starting in Sept. 2004 Postgraduate studies MSc in Computing MSc Information Systems Engineering Studying for a PhD Information for students studying... BSc Computer Science BSc Joint Honours Computing BSc/BEng/MEng Computer Systems Engineering MSc in Computing ... for a PhD About our research Overview Distributed Collaborative Computing Evolutionary Computing Geometric Computing and Computer Vision ... Seminars For your Diary About the School Spring Semester ends : Final year project vivas end : MSc visit : Graduation : MSc (full time) dissertations due : Members of staff Jobs For users: Web mail Users' personal home pages Searching this site...

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