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Topic: Boundary representation

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General Giap

Jutta Kulmsee

	Shape Boundary Representation
		A common technique in shape representation for robots is therefore to describe this boundary explicitly, rather than as an implicit line between occupied and unoccupied regions.
		Explicit boundary representation provides important benefits both in pure vision systems, and in systems where a robot arm is controlled using a visually acquired shape representation.
		The boundaries of a workpiece are very important in controlling a robot arm, since it interacts with the workpiece only along those boundaries.
	www.cl.cam.ac.uk /~afb21/publications/masters/node15.html (309 words)

	Boundary representation - Wikipedia, the free encyclopedia
		In facetted and advanced surface BREP STEP format (part 42), the Euler topological representation is vertex, edge, half-edge, face loop, face, shell, and body and refer to the underlying geometric representations.
		Due to the work of Braid, Euler boolean operations have gained favor because the operations generate an Euler consistent (satisfies the Euler characteristic) BREP at every stage of the constructions process.
		Often, this is implanted by capturing the representation in a change state, so that if a problem is encountered (e.g.
	en.wikipedia.org /wiki/Boundary_representation (282 words)

	Feature extraction (Site not responding. Last check: 2007-10-10)
		Meaningful representation: The representation should retain properties of the shape that are meaningful to the application.
		Boundary Representation: In biomedical images, minor differences in outlines of the anatomy could be significant.
		With a proper representation of the contour points of a polygon, Fourier descriptors have been used to measure shape similarity that is insensitive to translation, rotation, and scaling [64].
	archive.nlm.nih.gov /pubs/reports/bosc02/node23.html (1702 words)

	The Basic Idea
		Thereby, a small-scale boundary representation of volumetric objects is generated (figure 5.1, Sect.
		The first step to obtain an efficient representation of bounded objects within a volumetric data set is the identification and extraction of voxels which contribute to the object's visual representation, i.e., the boundary of the object.
		Compared with a polygonal representation of the boundary surfaces, this approach preserves the full accuracy of the data set at much lower memory cost, allows interactive rendering on low-end hardware and provides more flexibility with respect to rendering parameters.
	www.cg.tuwien.ac.at /~mroz/diss/html/node47.html (530 words)

	Boundary Representation Bibliography
		A boundary representation of a solid, three-dimensional object represents the object by its surface boundary.
		Boundary representations incorporate a variety of data structures, including the much-discussed winged-edge data structure.
		Unfortunately, a comprehensive discussion of boundary representation methods is not to be found in the literature, particularly if you are interesting in actually implementing them for solid modeling applications.
	www.csse.monash.edu.au /mirrors/bibliography/Graphics/b-rep.html (304 words)

	Combinatorial Solid Geometry, Boundary Representations, and Non-Manifold Geometry
		One would expect that a representation that depicted the boundaries of an object from several views would provide sufficient information for computing a whole variety of useful facts about the model, such as center of mass, volume, cross-sectional area, etc. Two-dimensional drafting systems were not designed for this sort of interrogation.
		In an explicit boundary representation, each solid is described by an explicit specification of all the points on the surface of the solid, typically by exhaustively listing the vertices of many planar facets.
		Boundary representations offer the advantage of being able to naturally model solid objects with arbitrarily shaped surfaces, but can require a large amount of information to achieve acceptable results.
	ftp.arl.mil /~mike/papers/90nmg/joined.html (20066 words)

	Thesis (Site not responding. Last check: 2007-10-10)
		Indeed, it is the existence of the operation of boundary completion which obviates the need for an explicit representation of those boundaries by providing a mechanism capable of reconstructing the boundaries on demand, given the stimulus of the inducers at the vertices.
		Effect of contrast, as represented by the input magniutde, on the salience of the illusory boundary, showing that the salience of the illusory boundary, as indicated by the height of the plot between the inducers, is increased as the input magnitude varies through one (A), two (B), and three (C).
		Long range boundary completion can still occur beyond the last dot despite the action of the first harmonic at the illusory "line ending" due to the subliminal activation due to the second harmonic, which is responsible (in part) for the extended trail of activation beyond the line endings.
	cns-alumni.bu.edu /~slehar/webstuff/thesis/thesis.html (19165 words)

	55:148,55:247 Chapter 6, Part 2
		A polygonal representation approximates a region by a polygon, the region being represented using its vertices.
		Boundary segmentation into segments of constant curvature or curve segmentation into circular arcs and straight lines is used.
		Representation of curves using piecewise polynomial interpolation to obtain smooth curves is widely used in computer graphics.
	www.icaen.uiowa.edu /~dip/LECTURE/Shape2.html (1981 words)

	A Two Dimensional Derivative of Boundary Representation
		Solid modelling using boundary representation requires a larger amount of information to describe basic three dimensional shape than the combination of constructive solid geometry and generalised cones does, but it can also describe a wider range of objects.
		This is because objects only contact other objects on their boundaries, so a description of the boundary must be available to the reasoning system, whether it is given explicitly, or determined by computation from a constructed solid description.
		The generalised cones method requires that a method of representing two dimensional shape be used to describe the cross section for ``sweeping'' operations, but a boundary representation must describe the two dimensional shape of every face in the three dimensional object.
	www.cl.cam.ac.uk /~afb21/publications/masters/node45.html (371 words)

	Anatomical Shape Representation in Spine X-ray Images
		An outstanding problem in the extraction of feature vectors from the raw boundary data is development of an effective shape representation and similarity method that simultaneously provides for data reduction while preserving the shape characteristics that are essential for the end use of the database.
		It was realized that the shape representation method would need to serve the dual purpose of providing a rich description of the vertebra shape while being acceptable to the end user community consisting of medical professionals, educators, researchers, and epidemiologists who typically employ coarser models.
		In case of the shape representation methods, the Polygon Approximation method with modifications suggested in [30], is very useful in reducing the granularity of the boundary data while keeping the visual aspect of the shape data intact.
	archive.nlm.nih.gov /pubs/antani/396-131/396-131.php (3845 words)

	UAX #29: Text Boundaries
		Boundaries used in line breaking (also called word wrapping) are to be found in [LineBreak].
		Boundary determination is specified in terms of an ordered list of rules, indicating the status of a boundary position.
		Boundaries may be further tailored for requirements of different languages, such as the addition of Indic, Thai, or Tibetan character clusters.
	www.unicode.org /reports/tr29 (6079 words)

	[No title]
		Multiple boundaries force a distinction that is not a cleaving of the space; instead, it is a differentiation of the boundaries.
		Boundary mathematics is a representational and computational paradigm for mathematics, based on the concept of distinction.
		In the boundary calculus, the paradoxes must be considered at the level of boundaries, with as little dependence on number type as possible.
	www.rgshoup.com /lof/doc/jjames-thesis.txt (15548 words)

	Knowledge-at-work
		Representations are physical, tangible and material, they allow ideas and experience to have an independent existence in an externalized form, they help to capture emergent thought.
		Boundary objects (concept maps, ontologies, source documents) serve as a vehicle, container and carrier, for ideas and meaning (reification).
		When a representation crosses (community) boundaries, there is often a loss of meaning and context, which is counter-balanced by an opportunity for new negotiations, different views and altered meaning.
	denham.typepad.com /km (1905 words)

	QMG project: Geometric objects and datatypes
		The second representation is called the chunk representation, because in this representation the brep occupies a contiguous chunk of memory.
		Internal boundaries usually serve one of two purposes in a scientific computation: they act as demarcations between separate regions of the domain (for instance, the domain may represent an object that is a composite of several materials) or they act as ``singular'' boundaries, for example, in modeling a region with a slit or crack.
		An SL internal boundary corresponds to a ``slit.'' An SL internal boundary behaves in most contexts like a child in the childlist of a face that is repeated twice (and hence acts like a slit).
	www.cs.cornell.edu /home/vavasis/qmg1.0/geom.html (3363 words)

	Boundary Representation
		Once we have identified the boundary pixels of a region, we can encode them by only storing the relative difference as we go from pixel to pixel clockwise around the contour.
		Another method for compacting the boundary information is to fit line segments or other primitives to the boundary.
		Another useful method for breaking a boundary into segments is to identify the points of maximum positive or minimum negative curvature.
	rivit.cs.byu.edu /morse/550-F95/node27.html (1285 words)

	Boundary representation: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-10)
		Computer-aided design (cad) is the use of a wide range of computer-based tools that assist engineers and architects in their design activities....
		The geometric representation is the point, EHandler: no quick summary.
		In cad or csg, the change state or delta state (as defined by spatial technologies acis) refers to the intermediate modifications made to a document before it...
	www.absoluteastronomy.com /encyclopedia/b/bo/boundary_representation.htm (377 words)

	Publikationen (Site not responding. Last check: 2007-10-10)
		Implicit representations are equations or relations such as the set of zeros of a functional with three unknowns.
		For objects with piecewise C² boundaries, relationships between the curvature of the boundary and the position of the medial axis are developed.
		If the boundary of M is not empty then we assume that M is a topological manifold whose boundary is an (n-1)-dimensional topological manifold.
	www.gdv.uni-hannover.de /research/publications.php (5623 words)

	Document Object Model Range
		This chapter refers to two different representations of a document: the text or source form that includes the document markup and the tree representation similar to the one described in the introduction section of the DOM Level 2 Core [
		The relationship between locations in a text representation of the document and in the Node tree interface of the DOM is illustrated in the following diagram:
		Note that because the same location in a text representation of the document can correspond to two different positions in the DOM tree, it is possible for two boundary-points to not compare equal even though they would be equal in the text representation.
	www.w3.org /TR/DOM-Level-2-Traversal-Range/ranges.html (3981 words)

	Research at Applied Numerical Algorithms Group at LBNL
		The representation of complex geometries is based on an embedded boundary model, in which the boundary of a complex domain cuts away at a regular Cartesian grid.
		This allows the use of highly efficient and well understood methods in the regions of the grid away from the boundary, and confines the use of irregular grid methods to the small region of the domain near the boundary.
		The compressible gas dynamics project is developing 2D and 3D adaptive methods to simulate time-dependent compressible flows in complex geometries using an embedded boundary representation.
	seesar.lbl.gov /ANAG/research.html (393 words)

	Sci.Op-Research USENET Group: Re: Computing a boundary representation from lin. inequalities (Site not responding. Last check: 2007-10-10)
		Sci.Op-Research USENET Group: Re: Computing a boundary representation from lin.
		Maybe in reply to: Ulrich Frenkel: "Computing a boundary representation from lin.
		> inequalities to a boundary represenation of the corresponding
	mat.gsia.cmu.edu /OP-RESEARCH/0003.html (150 words)

	The McMillan Law Firm, APC - We Are A Results Oriented Law Firm
		The cases that we have undertaken have ranged in complexity from basic employment law disputes involving the failure to pay minimum wage and overtime, business litigation cases involving convoluted issues of fraud and contract breach, and highly technical litigation involving antitrust claims.
		After we have agreed to undertake representation, we initiate our unique litigation strategy, which is applied at the outset of a case.
		”...Your representation of me and my Nevada Corporation against this exasperating, frivolous law suit has finally concluded in an irrevocable motion for summary judgment in which you prevailed and we were awarded total dismissal of the case despite the plaintiff’s treacherous changing of accusations, facts and representation over the course of the events...”
	www.mcmillanlaw.us (688 words)

	Internal representation of boundary models
		The internal representation of boundary models can be based on faces, on vertices, or on edges.
		In this representation, a solid consists of a list of faces, a list of edges and a list of vertices.
		Each face consists of a list of loops, one of which being marked as outer loop of the face.
	www.ipf.tuwien.ac.at /fr/buildings/diss/node33.html (404 words)

	Space-Efficient Boundary Representation of Volumetric Objects - Mroz, Hauser, Grller (ResearchIndex) (Site not responding. Last check: 2007-10-10)
		Space-Efficient Boundary Representation of Volumetric Objects - Mroz, Hauser, Grller (ResearchIndex)
		Abstract: In this paper we present a compression technique for efficiently representing boundary objects from volumetric data-sets.
		Exploiting spatial coherency within object contours, we are able to reduce the size of the volumetric boundary down to the size of just a few images.
	citeseer.ist.psu.edu /mroz00spaceefficient.html (409 words)

	Boundary Representation
		If you don't know what boundary representation means, here's a quick, probably insufficient, summary.
		It's also fun, because it can easily represent shapes that extend into infinity (just leave off the boundary part in "boundary representation").
		My current goal is just to be able to find the intersection, union, and difference of arbitrary solids.
	www.kimbly.com /code/brep/index.html (969 words)

	Jarek Rossignac's publications (Site not responding. Last check: 2007-10-10)
		Indeed, the characteristic curve of the moving object, i.e.: the edges subset that generates the envelope containing the sweep boundary, remains constant throughout the entire screw motion and is simple to compute.
		The drawback of these techniques is their need for storing an explicit representation of the disjunctive form, which may grow exponentially with the number of leaves in the original graph.
		Surfels are generated on the boundary of each primitive P in a CSG model and tested against the I-zone of P. Surfels in the I-zone are guaranteed to lie on or in the CSG solid and are rendered into a z-buffer.
	www.gvu.gatech.edu /~jarek/papers10.html (6775 words)

	Sci.Op-Research USENET Group: Re: Computing a boundary representation from lin. inequalities (Site not responding. Last check: 2007-10-10)
		Next in thread: Tuomo Takkula: "Re: Computing a boundary representation from lin.
		>inequalities to a boundary represenation of the corresponding
		pick a representation for your points that allows them to be
	mat.gsia.cmu.edu /OP-RESEARCH/0011.html (342 words)

	Continental Properties Tenant Representation
		During this time, CRS has been a procuring cause for over 1 million square feet of commercial sales and leasing in the Hampton Roads Region.
		In addition, the CRS corporate representation effort has produced results for numerous local, regional, and national companies doing business in the Commonwealth of Virginia.
		Transactions have been completed for corporate interests from Virginia Beach to Roanoke and for office, flex, distribution, and industrial clients with commercial facilities needs ranging in transaction size from 2,000 to over 200,000 square feet.
	www.cpcrealty.com /tenant.html (205 words)

	Boundary Representation
		Models are a more explicit representation than CSG.
		The object is represented by a complicated data structure giving information about each of the object's faces, edges and vertices and how they are joined together.
		Appears to be a more natural representation for Vision since surface information is readily available.
	www.cs.cf.ac.uk /Dave/Vision_lecture/node57.html (145 words)

	[No title]
		Implementation of a topological data structure similar to the WINGED EDGE data structure, representing the boundary of a polyhedral solid.
		The boundary (surface) of a solid is represented by means of a set of topological entities.
		Tony C. Woo, "A Combinatorial Analysis of Boundary Data Structure Schemata", IEEE Computer Graphics and Applications, March 1985.
	breplibrary.sourceforge.net (1034 words)

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