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Topic: 2D geometric model

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	2D geometric model - Wikipedia, the free encyclopedia
		A 2D geometric model is a geometric model of an object as two-dimensional figure, usually on the Euclidean or Cartesian plane.
		Even though all material objects are three-dimensional, a 2D geometric model is often adequate for certain flat objects, such as paper cut-outs and machine parts made of sheet metal.
		2D geometric models are also convenient for describing certain types of artificial images, such as technical diagrams, logos, the glyphs of a font, etc. They are an essential tool of 2D computer graphics and often used as components of 3D geometric models, e.g.
	en.wikipedia.org /wiki/2D_geometric_model (138 words)

	Molecule - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		In the 3D model on the left, carbon atoms are represented by gray spheres, white spheres represent the hydrogen atoms and the cylinders represent the bonds.
		The model is enveloped in a "mesh" representation of the molecular surface, colored by areas of positive (red) and negative (blue) electric charge.
		In the 3D model (center), the light-blue spheres represent carbon atoms, the white spheres are hydrogen atoms, and the cylinders in between the atoms correspond to single-bonds.
	www.americancanyon.us /project/wikipedia/index.php/Molecule (494 words)

	Geometric model - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-11-06)
		A geometric model describes the shape of a physical or mathematical object by means of geometric concepts.
		Geometric models are used in computer graphics, computer-aided design and manufacturing, and many applied fields such as medical image processing.
		Geometric models are usually distinguished from procedural and object-oriented models, which define the shape implicitly by an algorithm.
	www.arikah.com /encyclopedia/Geometric_model (246 words)

	Search Encyclopedia.com (Site not responding. Last check: 2007-11-06)
		model and modeling model and modeling, in painting, the use of light and shade to simulate volume in the representation of solids.
		Murray, John, 2d marquess and 1st duke of Atholl Murray, John, 2d marquess and 1st duke of Athollmûr´ē, ăth´el, 1660-1724, Scottish nobleman; son of the 2d earl and 1st marquess.
		geometric problems of antiquity geometric problems of antiquity, three famous problems involving elementary geometric constructions with straight edge and compass, conjectured by the ancient Greeks to be impossible but not proved to be so until modern times.
	www.encyclopedia.com /searchpool.asp?target=2D+geometric+model (597 words)

	Geometric model -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		Geometric models can be built for objects of any (The magnitude of something in a particular direction (especially length or width or height)) dimension in any geometric space.
		Geometric models are usually distinguished from procedural and object-oriented models, which define the shape implicitly by an (A precise rule (or set of rules) specifying how to solve some problem) algorithm.
		Also, the modeling of ((mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry) fractal objects often requires a combination of geometric and procedural techniques.
	www.absoluteastronomy.com /encyclopedia/g/ge/geometric_model.htm (212 words)

	2D computer graphics -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		2D computer graphics is the (A machine for performing calculations automatically) computer-based generation of (Click link for more info and facts about digital image) digital images—mostly from two-dimensional models (such as (Click link for more info and facts about 2D geometric model) 2D geometric models, text, and digital images) and by techniques specific to them.
		These components can be modified and manipulated by two-dimensional geometric transformations such as (A written communication in a second language having the same meaning as the written communication in a first language) translation, (The act of rotating as if on an axis) rotation, (Ascent by or as if by a ladder) scaling.
		Layers that consist of complex geometric objects (such as (The words of something written) text or polylines) may be broken down into simpler elements ((A written symbol that is used to represent speech) characters or line segments, respectively), which are then painted as separate layers, in some order.
	www.absoluteastronomy.com /encyclopedia/2/2D/2D_computer_graphics1.htm (1808 words)

	Geometric model (Site not responding. Last check: 2007-11-06)
		Geometric model(l)ing is the construction or use ofgeometric models.
		They are also contrasted with digitalimages and volumetricmodels ; and with implicit mathematical models such as the zero set of an arbitrary polynomial.
		However, the distinction is often blurred: for instance, geometric shapes can be representedby objects ; a digital image can beinterpreted as a collection of colored squares ;and geometric shapes such as circles are defined by implicit mathematical equations.Also, the modeling of fractal objects often requires a combination of geomtric andprocedural techniques.
	www.therfcc.org /geometric-model-210374.html (209 words)

	Dimensional Reduction (Site not responding. Last check: 2007-11-06)
		This was achieved using the medial axis transform, an alternative skeleton-like representation of the geometric model having properties relevant to model simplification.
		The first stage is to subdivide the 2D model into subregions which are suitable for representation by 1D beam elements, and those which are not to either by 2D elements, or by an equivalent 0D point mass.
		In both cases the mode shapes obtained are representative of the 2D model, and the analysis results are good given the small number of degrees of freedom in the reduced models.
	sog1.me.qub.ac.uk /research/dimred/dimred.php (751 words)

	Search Encyclopedia.com (Site not responding. Last check: 2007-11-06)
		Worcester, Edward Somerset, 6th earl and 2d marquess of Worcester, Edward Somerset, 6th earl and 2d marquess ofwoos´ter, 1601?-1667, English soldier and inventor.
		Tweeddale, John Hay, 2d earl and 1st marquess of Tweeddale, John Hay, 2d earl and 1st marquess of, 1626-97, Scottish statesman.
		Townshend, Charles Townshend, 2d Viscount Townshend, Charles Townshend, 2d Viscounttoun´zĕnd, 1674-1738, English statesman.
	www.encyclopedia.com /search.asp?target=2D+geometric+model&rc=10&fh=19&fr=11 (363 words)

	A RELATIONAL GEOMETRIC MODEL FOR VARIATIONAL GEOMETRY
		A geometric object in a relational geometric model is represented based on its geometric relationship to other geometric objects and is unilaterally dependent on these objects.
		Geometric relationships are represented as equations or rules outside the geometric model which are then used to control the behaviour of the model.
		A geometric relationship among a group of geometric objects is represented as unilateral dependency of a certain object in the group on the other objects of the group.
	www.uni-koblenz.de /~ros/artic2.htm (3994 words)

	2D geometric model (Site not responding. Last check: 2007-11-06)
		A 2D geometric model is a geometric model of anobject as two-dimensional figure, usually on the Euclidean or Cartesian plane.
		Even though all material objects are three-dimensional, a 2D geometric model is often adequate for certain flat objects, suchas paper cut-outs and machine parts made of sheet metal.
		2D geometric models are also convenient for describing certain types of artificial images, such as technical diagrams, logos, the glyphs of a font, etc. Theyare an essential tool of 2D computer graphics and oftenused as components of 3D geometric models, e.g.
	www.therfcc.org /2d-geometric-model-77679.html (116 words)

	"A Geometric Model for Active Contours in Image Processing" Citations (Site not responding. Last check: 2007-11-06)
		The proposed modeling scheme consists of representing shapes by pedal curves and surfaces-pedal curves/surfaces are the loci of the foot of perpendiculars to the tangents of a fixed curve/surface from a fixed point called the pedal point.
		The resulting active contour model, in contrast to many other edge and region based models, is fully global in that the evolution of each curve depends at all times upon every pixel in the image and is directly coupled to the evolution of every other curve regardless of their mutual proximity.
		To constrain the movement of a geometric snake onto the surface of a mesh, we use the parameterization of the surrounding region of a geometric snake.
	iacl.ece.jhu.edu /projects/gvf/gvf_cite/caselles_cite_abstract.html (14635 words)

	OhioLINK ETD: Turer, Ahmet
		Geometric model generation and load definition for 2D-Grid and 3D finite element (FE) models are streamlined by developing computer programs, and generation/definition time is drastically reduced.
		The generated models are used to simulate x-brace and unintended composite action losses, which are believed to happen prior to reaching the rating load of a bridge.
		Grid models are easier to model and calibrate while 3D-FE models are more flexible in identifying most critical members as well as simulating loss of unintended composite action and similar phenomenon.
	www.ohiolink.edu /etd/view.cgi?ucin985895002 (373 words)

	Surface model
		The 3D surface is approximated by a triangular mesh to reduce geometric complexity and to tailor the model to the requirements of computer graphics visualization systems.
		Then a bounded thin plate model is employed with a second order spline to smooth the surface and to interpolate small surface gaps in regions that could not be measured.
		The obtained 3D surface model is shown in Figure 8.2 with shading and with texture.
	www.cs.unc.edu /~marc/tutorial/node123.html (388 words)

	Filter Effects (Site not responding. Last check: 2007-11-06)
		As a result, the expressiveness of the traditional 2D rendering model is greatly enhanced, while still preserving the device independence, scalability, and high level geometric description of the underlying graphics.
		According to the "painter's model", areas on the device which are outside of the vector graphic shapes remain unchanged from their previous contents (in this case the droplet pattern).
		The resulting imaging model remains as device-independent as the original one, except we are now using the 2D imaging model itself to generate images to render.
	www.w3.org /TR/1999/WD-SVG-19990211/filters.html (3257 words)

	Java 2D API: 1 -
		The Java 2D API automatically compensates for differences in rendering devices and provides a uniform rendering model across different types of devices.
		The Java 2D API defines three levels of configuration information that are maintained to support the conversion from user space to device space.
		For example, in an indexed color model, the result of a Boolean operation on two pixel values in an image is the composite of two indices, not two colors.
	java.sun.com /j2se/1.3/docs/guide/2d/spec/j2d-intro.fm2.html (1721 words)

	The Geometry Junkyard: Geometric Models
		See also the origami page, for models made of folded paper, and the toys page, for some commercially-available geometric model construction kits.
		Models of Mathematical Machines at the University Museum of Natural Science and Scientific Instruments of the University of Modena.
		Ram's Horn cardboard model of an interesting 3d spiral shape bounded by a helicoid and two nested cones.
	www.ics.uci.edu /~eppstein/junkyard/model.html (899 words)

	Map - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		Most usually a map is a two-dimensional, geometrically accurate representation of a three-dimensional space.
		Conventionally, on most geometrically accurate maps text is upright when the map is oriented with the north up, hence north is identified with the top of a sheet.
		The increase in detail is, of course, limited to the information contained in the file: enlargement of a curve may eventually result in a series of standard geometric figures such as straight lines or arcs of circles.
	www.sterlingheights.us /project/wikipedia/index.php/Map (2086 words)

	Geometric model - Definition up Erdmond.Com (Site not responding. Last check: 2007-11-06)
		Geometric models can be built for objects of any dimension in any geometric_space.
		Both 2D and 3D_geometric_models are extensively used in computer_graphics.
		Geometric models are usually distinguished from ; a digital_image can be interpreted as a collection of colored squares; and geometric shapes such as circles are defined by implicit mathematical equations.
	www.erdmond.com /Geometric_model.html (184 words)

	A history of CAD in Architecture at Michigan (Site not responding. Last check: 2007-11-06)
		The first, ARCH:MODEL, was a geometric modeling, computer graphics program written in Fortran running on the university's large mainframe computer and used locally via a cathode ray tube terminal such as a Comptek or Tektronix.
		Modeling tools such as found in today's commercial solid modelers were available (set operations, extrusions, interference detection,..).
		In the late 1980s, the ARL was asked to model a proposed outdoor, open air auditorium which was to be used for many types of performances.
	www-personal.umich.edu /~turner/history/history.html (359 words)

	Augmented Reality for Therapy (Site not responding. Last check: 2007-11-06)
		A series of transverse section ultrasound images are extracted from the scanned data using a slice-by-slice manner prior to image processing.
		The method proposed a new surface-based algorithm [2] that involves using a new 2D contour tessellation algorithm, propagating in a forward fashion to distribute points and maintaining an adequate topological scatter.
		Surface-based : A 3D modeling technique that begins with triangle primitives, and is used to defines the surfaces of the 3D object as a list of flat polygons that share common sides and vertices (commonly known as surface meshing).
	mrcas.mpe.ntu.edu.sg /groups/art/model_gen.html (373 words)

	Gallery 2 (Site not responding. Last check: 2007-11-06)
		Cardiac Activation A finite-element model was developed to explore the effects of the ventricular wall's geometric complexity, nonuniform muscle fiber orientation, and tissue heterogeneity on 2D and 3D cardiac impulse propagation.
		The model reproduced several physiologic phenomena thought to be important in arrhythmogenesis.
		Model and image by Jack Rogers for his Ph.D. dissertation research in bioengineering at UCSD, under guidance of Andrew McCulloch.
	www.sdsc.edu /Publications/SR93/gallery2.html (642 words)

	Molecule - Wikipedia, the free encyclopedia
		For a list of molecules see the List of compounds.
		3D (left and center) and 2D (right) representations of the terpenoid, atisane.
		In a molecule the atoms are joined by shared pairs of electrons in a chemical bond.
	www.wikipedia.org /wiki/Small_molecule (840 words)

	software (Site not responding. Last check: 2007-11-06)
		The simulator's sonar model is shown in Figure 3.4.
		The robot's world is modeled as a doubly linked list of line segments that represent the boundaries of the robot's world.
		Specular reflections are also not modeled, and only the range to the primary reflection from the closest virtual surface is returned.
	www.cs.nps.navy.mil /research/yamabico/manual/software.html (2082 words)

	Oct 13 - LEDAS Releases Geometric Solver LGS 2D v1.4 (Site not responding. Last check: 2007-11-06)
		The automated constraining functionality in LGS 2D is based on the use of a predefined set of the rules and priorities of the constraints.
		Independently of the type of used priorities, LGS 2D controls that the model is not over-defined for the set of the imposed constraints.
		LEDAS Geometric Solver LGS 2D is a family of software components including inexpensive and reliable products for small and medium sized software development companies with model needs, and exclusive solutions with extensive requirements of functionality, support, and consulting for companies with specific demands.
	www.tenlinks.com /NEWS/PR/ledas/101305_lgsv14.htm (629 words)

	Geometry Algorithm Overview
		Within the design models, engineering specifications need to be checked, and analysis (such as for stress or part failure) needs to be made using the geometry of the design.
		Even at the rudimentary level of cellular mechanisms, breakthroughs in geometric modeling and understanding may be the key to finding cures for genetic diseases (like cancer, Alzheimer's, etc).
		A specific promising problem is to model the spatial structure of proteins, and use this to design drugs that geometrically bind with their receptors.
	geometryalgorithms.com /overview.htm (2280 words)

	2D Geometric Model Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-11-06)
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	www.karr.net /search/encyclopedia/2D_geometric_model (336 words)

	Abstract of Simultaneous 2D images and 3D geometric model registration for texture mapping utilizing reflectance ... (Site not responding. Last check: 2007-11-06)
		Texture mapping on scanned objects, that is, the method to map current color images on a 3D geometric model measured by a range sensor, is a key technique of photometric modeling for virtual reality.
		Moreover, since a 2D texture image taken from one viewing point is a partial view of an object, several images must be mapped onto the object in order to cover the entire 3D geometric model.
		In this paper, we propose the new simultaneous registration technique of several images and geometric model based on 2D-3D edge correspondence and the epipolar constraint between images.
	www.cvl.iis.u-tokyo.ac.jp /papers/all/abst/0009.html (194 words)

	Model
		A first step in the finite element analysis is the construction of a geometric model of the object to be analyzed.
		Therefore often a simplified geometrical model of the object is used and many important details are lost.
		The objective of the research is to develop algorithms to generate 2D or 3D finite element meshes of agricultural products based on digital images, and to apply this to some real-life problems in agricultural engineering.
	www.agr.kuleuven.ac.be /aee/amc/staff/palj/Model.htm (260 words)

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