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Topic: Computational geometry

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List of computer graphics and descriptive geometry topics

Combinatorial geometry

List of geometry topics

List of geometers

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Discrete mathematics

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	Computational geometry - Wikipedia, the free encyclopedia
		In computer science, computational geometry is the study of algorithms to solve problems stated in terms of geometry.
		Often, the latter kind of computational geometry is considered to be branch of computer graphics and/or CAD, and the former one is called simply computational geometry.
		The primary goal of research in combinatorial computational geometry is to develop efficient algorithms and data structures for solving problems stated in terms of basic geometrical objects: points, line segments, polygons, polyhedra, etc.
	en.wikipedia.org /wiki/Computational_geometry (655 words)

	Strategic Directions in Computational Geometry Working Group Report (Site not responding. Last check: 2007-10-07)
		As a consequence, the excitement of the computational geometry community at its theoretical accomplishments was mitigated by a sense of discomfort at the perceived loosening of ties with the very same applications that motivated the establishment of the discipline.
		Computational geometry is typically taught in specialized courses, or as a single short section in algorithms classes.
		Computational geometry is a lively discipline that is undergoing a crucial phase of its evolution.
	cs.brown.edu /people/rt/sdcr/report/report.html (7069 words)

	Computational Geometry (Site not responding. Last check: 2007-10-07)
		Computational geometry is the study of algorithms for solving geometric problems on a computer.
		The field of computational geometry is less than 20 years old and a thriving community of researchers has emerged working on fundamental problems relevant to several application domains including computer graphics, solid modeling, computer generated forces,virtual reality, simulated training, computer-aided ma nufacturing, robotics, computer vision, VLSI design, CAD/CAM, geographic information systems, and statistics.
		This all-new introduction to computational geometry is a textbook for high-level undergraduate and low-level graduate courses.
	longwood.cs.ucf.edu /courses/cot5520 (525 words)

	Computational Geometry, Algorithms and Applications
		Computational geometry emerged from the field of algorithms design and analysis in the late 1970s.
		The choice of the applications was guided by the topics in computational geometry we wanted to cover; they are not meant to provide a good coverage of the application domains.
		Having said this, we believe that knowledge of computational geometry is important to solve geometric problems in application areas efficiently.
	www.cs.uu.nl /geobook (750 words)

	Strategic Directions in Computational Geometry Working Group Report (Site not responding. Last check: 2007-10-07)
		As a testimony to the original success of this mission, the initial body of computational geometry literature had a prominent presence both in the field of theory of computing and in applied areas, such as graphics, robotics, mechanical engineering, and pattern matching (see, e.g., the 1984 survey of the area [LP84]).
		Researchers should be able to build and maintain a reputation within the computational geometry community, while at the same time making their applied results known to the community of the application area.
		The vision for many in the computational geometry community is that computational geometry emerge as the discipline where for geometry, theory meets practice, where problems of an applied nature inspire and inform research problems in computational geometry and mathematics, where theoretical results are implemented, made usable, and disseminated to application domains.
	www.cs.brown.edu /people/rt/sdcr/report/report.html (7069 words)

	analysis (Site not responding. Last check: 2007-10-07)
		Compute the N dimensional FFT of A using subroutines from FFTW.
		Compute the inverse FFT of A using subroutines from FFTW.
		Compute the invesre N dimensional FFT of A using subroutines from FFTW.
	octave.sourceforge.net /index/analysis.html (663 words)

	Computational Geometry (Site not responding. Last check: 2007-10-07)
		Computational geometry is the algorithmic study of geometric problems and objects.
		The emphasis is on careful and correct implementation (in C language) of the fundamental algorithms of computational geometry.
		The leading conference in computational geometry is the ACM Symposium on Computational Geometry, held annually in late May or early June.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE183.HTM (527 words)

	Computational Geometry at Stony Brook
		Computational geometry is the study of efficient algorithms to solve geometric problems.
		The methodologies of computational geometry allow one to design and analyze algorithms for the efficient solution of numerous geometric problems that arise in application areas such as manufacturing, computer-aided design, robotics, computer vision, graphics, and cartography.
		The series of fall workshops in computational geometry were started at Stony Brook in 1991 and have become an established venue for the field of computational geometry.
	www.ams.sunysb.edu /~jsbm/comp_geom/comp_geom.html (1018 words)

	Open Directory - Science: Math: Geometry (Site not responding. Last check: 2007-10-07)
		Geometry and the Imagination in Minneapolis - Geometry exercises for a two-week summer workshop led by John Conway, Peter Doyle, Jane Gilman and Bill Thurston at the Geometry Center in Minneapolis, June 1991.
		Geometry Formulas and Facts - Excerpts from the 30th Edition of the CRC Standard Mathematical Tables and Formulas (1995), namely, the geometry section minus differential geometry.
		Geometry from the Land of the Incas - Presents problems involving circles and triangles, with proofs, SAT practice quizzes and famous quotes.
	dmoz.org /Science/Math/Geometry (929 words)

	The Math Forum - Math Library - Computatnl Geom. (Site not responding. Last check: 2007-10-07)
		A short article designed to provide an introduction to computational geometry, intended for topics whose geometric aspects are fairly straightforward, but for which the main questions involve efficient, accurate computation.
		A collection of applications of computational geometry: areas in which ideas from discrete and computational geometry (meaning mainly low-dimensional Euclidean geometry) meet some real world applications, with brief descriptions of those applications and the geometric questions arising from them, including pointers to web pages and other sources of further information.
		Computational Geometry is concerned with designing algorithms and computer programs to perform geometric computations.
	mathforum.org /library/topics/comp_geom (2137 words)

	CS 235: Computational Geometry
		Despite their apparent simplicity, they raise challenging combinatorial and algorithmic problems that are fundamental to many applied fields, such as computer graphics, robotics, visualization, molecular biology, and databases.
		This course introduces the fundamental concepts and algorithmic techniques of computational geometry for dealing with these problems.
		The textbook for the course is Computational Geometry, by de Berg, van Kreveld, Overmars, and Schwarzkopf.
	www.cs.ucsb.edu /~suri/cs235/235.html (423 words)

	.:: FastGEO - By Arash Partow ::.
		FastGEO is a library that contains a wide range of highly optimized computational geometry algorithms and routines for many different types of geometrical operations such as geometrical primitives and predicates, hull construction, triangulation, clipping, rotations and projections.
		In the past it has been widely acknowledged by many computational geometers that vectorized primitives are in general the most efficient and highly optimized path for computational geometry solutions.
		Free use of the FastGEO computational geometry library is permitted under the guidelines and in accordance with the most current version of the "Common Public License."
	www.partow.net /projects/fastgeo (853 words)

	68U: Computer graphics and computational geometry
		At present there is really nothing here regarding computer graphics per se; this is primarily focused on computational geometry.
		In keeping with the general pattern of use of the Mathematics Subject Classifications, computational topics primarily focused on geometry are classified in sections 51: Geometry and 52: Convex Geometry and their subareas such as 52B: Polygons and polyhedra.
		Computing the envelope of a planar polygon (all points a given distance away).
	www.math.niu.edu /~rusin/known-math/index/68U05.html (564 words)

	14th Annual Fall Workshop on Computational Geometry
		We hope that the interaction with the computational geometry community will be stimulating both to computational geometers and to those involved in applying techniques of computational geometry to other disciplines.
		The twelfth workshop (2002) was part of the Special Focus on Computational Geometry and Applications at DIMACS, while the thirteenth (2003) was part of the Special Semester on Computational Geometry at the Mathematical Sciences Research Institute, Berkeley.
		In 2004, we are proud to host the Fall Workshop on Computational Geometry at MIT, bringing the workshop to the Boston area for the first time and returning to the original format.
	cgw2004.csail.mit.edu (638 words)

	The Geomblog
		But it is telling that some of the most bedrock developments in algorithms came way before computers were fashionable; the whole of the 70s was a golden era for the study of basic algorithms.
		We study the computational complexity of the physical problem of finding vacua of string theory which agree with data, such as the cosmological constant, and show that such problems are typically NP hard.
		Grad school in computer science is so hot right now that most computer science majors get rejected, they expect you to not only have computer science, but probably math as a major.
	geomblog.blogspot.com (5603 words)

	UPC Computational Geometry Research Group (Site not responding. Last check: 2007-10-07)
		Computational Geometry studies geometric problems from the viewpoint of computation, and is strongly connected to the field of Discrete and Combinatorial Geometry.
		To extract "the shape" of a geometric object or arrangement using algorithms and operators from Computational Geometry is the main concern of Computational Morphology.
		Computer Algebra is the study of polynomial systems of equations in several variables.
	www-ma2.upc.es /~geomc/gcwww.html (1599 words)

	The Math Forum - Math Library - Geometry (Site not responding. Last check: 2007-10-07)
		A collection of handouts for a two-week summer workshop entitled 'Geometry and the Imagination', led by John Conway, Peter Doyle, Jane Gilman and Bill Thurston at the Geometry Center in Minneapolis, June 17-28, 1991.
		Some notes on a most general definition of "geometry," first elucidated by Felix Klein, which is based on a set of geometric invariants under a group of transformations.
		The FoCM's primary aim is to further the understanding of the deep relationships between mathematical analysis, topology, geometry and algebra and the computational process as they are evolving together with the modern computer.
	mathforum.org /library/topics/geometry (2298 words)

	ACM Symposium on Computational Geometry (Site not responding. Last check: 2007-10-07)
		The Program Co-Chairs have assembled a committee spanning both theoretical and applied interests in computational geometry to continue the tradition of encouraging submissions of theoretical, applied, or experimental nature to the conference.
		This review showcases the use of visualization in computational geometry for exposition and education, for the visual exploration of geometry in research, and as an interface and a debugging tool in software development.
		Algorithm animations, visual explanations of structural theorems, descriptions of applications of computational geometry, and demonstrations of software systems are all appropriate.
	socg.poly.edu /CFP.htm (786 words)

	Elsevier.com - Computational Geometry
		Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry.
		All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects.
		Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems.
	www.elsevier.com /inca/publications/store/5/0/5/6/2/9 (259 words)

	Amazon.com: Handbook of Discrete and Computational Geometry: Books: Jacob E. Goodman,Joseph O'Rourke (Site not responding. Last check: 2007-10-07)
		Computational Geometry in C (Cambridge Tracts in Theoretical Computer Science) by Joseph O'Rourke
		Computational topology is a relatively young field, having been in existence only since the early 1990's.
		The interplay between topology and finding better algorithms in computational geometry is one that will flourish no doubt in years to come.
	www.amazon.com /exec/obidos/tg/detail/-/0849385245?v=glance (1174 words)

	Computational Geometry
		robot motion, the computer must generate a model of the obstacles surrounding the robot, find a position for the robot that is suitable for whatever action the robot is asked to perform, construct a plan for moving the robot to that position, and translate that plan into controls of the robot's actuators.
		scientific computation such as the simulation of the airflow around a wing, one typically partitions the space around the wing into simple regions such as triangles (as shown below), and uses some simple approximation (such as a linear function) for the flow in each region.
		The computation of this approximation involves the numerical solution of differential equations and is outside the scope of this class.
	www.ics.uci.edu /~eppstein/161/960307.html (2502 words)

	Computational Geometry Course Materials
		Many K-12 and college geometry courses use computers as teaching tools, but that's not what I mean by "computational geometry courses".
		For more general geometry teaching materials, see the Swarthmore College Math Forum, or David Eppstein's page of lesson plans and teaching materials (from his Geometry Junkyard).
		Universität Trier: Computational Convexity I and Computational Convexity II (auf deutsch)
	granmapa.cs.uiuc.edu /~jeffe/compgeom/courses.html (317 words)

	Computational Geometry Code
		Computational geometry software by Ioannis Emiris: perturbed convex hulls in arbitrary dimensions, exact convex hulls in two and three dimensions, mixed volume in arbitrary dimensions, and mixed subdivisions in the plane.
		Vinci (also here): a program for computing volumes of convex polytopes, presented as either the convex hull of a set of points, the intersection of a set of halfspaces, or both (with the vertex-facet incidence graph).
		Robust computation of Voronoi diagrams and offset curves for planar shapes bounded by straight line segments and circular arcs.
	compgeom.cs.uiuc.edu /~jeffe/compgeom/code.html (2441 words)

	Algorithmic Geometry
		There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry.
		-- is a set of C++ class libraries which supports the precision-driven approach to implementation of exact algorithms in computational geometry.
		His main interests and fields of research are computational geometry, digital geometry processing, data compression, data structures and optimization techniques.
	www.personal.kent.edu /~rmuhamma/Compgeometry/compgeom.html (819 words)

	Course Page -- Computational Geometry (CMSC 754) (Site not responding. Last check: 2007-10-07)
		Course Overview: Introduction to algorithms and data structures for computational problems in discrete geometry (for points, lines, and polygons) primarily in 2 and 3 dimensions.
		Computational Geometry in C, Joseph O'Rourke, Cambridge University Press, 1994.
		Computational Geometry: An Introduction, F. Preparata and M. Shamos, Springer-Verlag, 1985.
	www.cs.umd.edu /~samir/754/754.html (443 words)

	Fall Workshop on Computational Geometry, 2000
		We are pleased to announce the eleventh in a series of annual fall workshops on Computational Geometry.
		Following the tradition of the previous fall workshops on Computational Geometry, the format of the workshop will be informal, extending over 2 days, with several breaks scheduled for discussions.
		Invited speakers are eminent leaders in their respective fields and have witnessed first-hand the need for geometric computing and its applications.
	www.ams.sunysb.edu /~jsbm/cgworkshop.html (553 words)

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