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Topic: De Boor algorithm

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	De Boor algorithm - Wikipedia, the free encyclopedia
		In the mathematical subfield of numerical analysis the De Boor algorithm is a fast and numerically stable algorithm for evaluating spline curves in B-spline form.
		It is a generalization of De Casteljau's algorithm for Bézier curves.
		De Boor's algorithm, described in the next section, is a procedure which efficiently evaluates the expression for
	en.wikipedia.org /wiki/De_Boor_algorithm (239 words)

	List of algorithms - Wikipedia, the free encyclopedia
		See also the list of data structures, list of algorithm general topics and list of terms relating to algorithms and data structures.
		Snapshot algorithm: a snapshot is the process of recording the global state of a system
		Rainflow-counting algorithm: Reduces a complex stress history to a count of elementary stress-reversals for use in fatigue analysis
	en.wikipedia.org /wiki/List_of_algorithms (1208 words)

	De Boor's Algorithm
		De Boor's algorithm is a generalization of de Casteljau's algorithm.
		First, under de Casteljau's algorithm, the dividing points are computed with a pair of numbers 1 - u and u that never change throughout the computation procedure, while under de Boor's algorithm these pairs of numbers are different and depend on the column number and control point number.
		Second, de Casteljau's algorithm can be used for curve subdivision, while the intermediate control points generated by de Boor's algorithm are not sufficient for this purpose.
	www.cs.mtu.edu /~shene/COURSES/cs3621/NOTES/spline/de-Boor.html (868 words)

	Sample Parameter Files for scurvy
		In this case, the spline's de Boor points are the Bézier points of the one and only spline segment.
		It has the same de Boor points as the previous example, but the shape is different because of the higher degree.
		Finally, animating the movement of a particle - with the interpolating lines made visible - produces a visualization of the de Boor algorithm for quartic curves, which is substantially more complex than in the cubic case.
	graphics.stanford.edu /courses/cs348c-95-fall/software/scurvy/samples.html (880 words)

	CHAPTER 4: B-SPLINE CURVES
		By introducing the de Boor algorithm for polynomial curves of just one piece, we have just changed the set of points which we calculated the blossom with.
		The de Boor algorithm can be easily used for curves consisting on N parabolic pieces of degree n.
		The de Boor algorithm expresses that piecewise polynomial parametrizations are barycentric combinations of B-spline polygon vertices, and therefore they have the same properties of Bézier curves.
	debin.etsin.upm.es /~leonardo/etema4.htm (3143 words)

	[No title]
		Reasoning about a distributed algorithm is simplified if we can ignore the time needed to send and deliver messages and can instead pretend that a process sends a collection of messages as a single atomic action, with the messages delivered instantaneously as part of the action.
		A distributed algorithm running on the switch processors computes the routes packets are to follow and fills in the packet forwarding table in each switch.
		The algorithm is a generalization of reference counting; it maintains a set of identifiers for processes with references to an object.
	ftp.digital.com /pub/DEC/SRC/research-reports/ABSTRACTS-SRC.REPORTS (16519 words)

	B-spline Surfaces: de Boor's Algorithm
		Once you know de Casteljau's algorithm for Bézier surfaces, de Boor's algorithm for B-spline surface and its modification for NURBS surfaces is only a small step away.
		In fact, with the local modification property in hand, de Boor's algorithm looks very similar to de Casteljau's algorithm.
		Hence, de Boor's algorithm can be used again for this purpose.
	www.cs.mtu.edu /~shene/COURSES/cs3621/NOTES/surface/bspline-de-boor.html (485 words)

	Angewandte Geometrie & Computergraphik - Prof. Boehm
		This further interpretation of this well-known algorithm proved to be a successfull tool in geometric modeling, in particular, subdividing techniques, interactive styling systems, intersections and boolean combinations, as well as the use of the Bernstein-Bézier technique.
		These algorithms and further developments made an important part of the multivariate spline package developed at the University of Braunschweig in 1984-1986.
		Topics were the representation and the use of cyclides, the representation of quadrics, and the use of osculants, the last giving the geometric foundation of the new so-called principle of blossoming.
	www.amueller.de /wb (975 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		pp 10-18 The algorithm represents polygons using a graph of the boundaries of the polygons.
		Algorithm is hierarchical, first finding potential collisions over large volumes, and then refining the solution to smaller volumes.
		Algorithms for performing coll- ision detection during simulation on bodies composed of both polyhedra and strictly convex curved surfaces are also presented.
	www.unh.edu /dml/publications/bibliography.txt (14954 words)

	Citations: Ray Tracing Trimmed Rational Surface Patches - Nishita, Sederberg, Kakimoto (ResearchIndex) (Site not responding. Last check: 2007-10-19)
		This algorithm uses the convex hull property in a more powerful manner, by determining parameter ranges which guarantee that they do not include points of intersection.
		Due to the simplicity of the Bezier representation, most of the algorithms are based on the utilization of Bezier representations.
		is an iterative geometric algorithm that finds all solutions of the ray patch intersection problem up to an user definable accuracy within the parameter domain of a B ezier patch of arbitrary degree, either integral or rational.
	citeseer.ist.psu.edu /context/75619/0 (3138 words)

	De Boor algorithm -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-19)
		De Boor algorithm -- Facts, Info, and Encyclopedia article
		It is a generalization of (Click link for more info and facts about De Casteljau's algorithm) De Casteljau's algorithm for (Click link for more info and facts about Bézier curve) Bézier curves.
		So the value is determined by the controlpoints ; the other control points have no influence.
	www.absoluteastronomy.com /encyclopedia/d/de/de_boor_algorithm.htm (289 words)

	Powell's Books - Pyramid Algorithms: A Dynamic Programming Approach to Curves and Surfaces for Geometric Modeling ... (Site not responding. Last check: 2007-10-19)
		Ideal as a comprehensive introduction to fundamental algorithms for basic curves and surfaces, or for a deeper understanding of entities they may be familiar with, this book presents a simple approach to the entire structure of algorithms.
		Pyramid Algorithms presents a clear and unified approach to understanding, analyzing, and computing the most common polynomial and spline curve and surface schemes, employing a dynamic programming method based on recursive pyramids.
		Pyramid Algorithms presents a simple, elegant approach that reveals entire structures of algorithms, as well as relationships between algorithms, at a glance.
	www.powells.com /biblio?isbn=1558603549 (758 words)

	CAGD-Applets: Curves
		Bézier representation of polynomial curves and evaluation with the de Casteljau algorithm.
		Evaluation of a polynomial spline curve by de Boor's algorithm.
		An uniform subdivision algorithm corresponding to uniform B-splines.
	i33www.ira.uka.de /applets/mocca/html/noplugin/curves.html (130 words)

	[No title]
		Authors' Abstract Sweeping a collection of figures in the Euclidean plane with a straight line is one of the novel algorithmic paradigms that have emerged in the field of computational geometry.
		Author's Abstract As an exercise in synchronization without mutual exclusion, algorithms are developed to implement both a monotonic and a cyclic multiple-word clock that is updated by one process and read by one or more other processes.
		Author's Abstract Reasoning about a distributed algorithm is simplified if we can ignore the time needed to send and deliver messages and can instead pretend that a process sends a collection of messages as a single atomic action, with the messages delivered instantaneously as part of the action.
	www.mit.edu:8001 /afs/net/user/tytso/papers/ABSTRACTS-SRC.REPORTS (11708 words)

	CS171 Homework 5: NURBS Editor
		To display the spline, you should break the continuous function (the one that only lives in the World of Mathematics) into many discrete segments via the Cox de Boor algorithm (in the handout) for blending functions, at an appropriately fine resolution (see the extra credit on adaptive parameterization).
		The shape of the curve is preserved and a new control point appears in the region of the curve where the user clicked.
		The purpose of doing this with NURBS instead of some other spline is that the curve stays the same when you use the knot insertion algorithm.
	www.cs.caltech.edu /courses/cs171/assignments/hw5.shtml (1211 words)

	CS 348A - Class Contributions
		However, the fundamental algorithm which forms the basis for the constructions and calculation for Bézier curves is now credited to de Casteljau.
		For the evaluation of a Bezier curve, use the de Casteljau algorithm to compute points on the curve.
		For the evaluation of a B-spline curve, use the de Boor algorithm to generate points on the curve.
	students.engr.scu.edu /~jliang/cs348a (458 words)

	B-spline (Site not responding. Last check: 2007-10-19)
		B-splines are a generalization of the Bézier curves and can be further generalized to NURBS, allowing the accurate modelling of more general classes of geometry.
		The De Boor algorithm is a numerically stable way to evaluate B-splines.
		A polygon can be constructed by connecting the de Boor points with lines, starting with P
	www.worldhistory.com /wiki/B/B-spline.htm (666 words)

	B-Spline curves of order m (Site not responding. Last check: 2007-10-19)
		Double buffering to avoid flicker, combination of the Add and Move modes into one mode.
		de Boor's algorithm for drawing the red circle is only implemented for B-Splines of order m=3 and Bezier curves of any order.
		B-Spline of order m=2 is equivalent to Chaikin's algorithm.
	www.ugcs.caltech.edu /~dmitri/cs284/h2 (162 words)

	boor - OneLook Dictionary Search
		Boor, boor(machine) (de) : AllWords.com Multi-Lingual Dictionary [home, info]
		Phrases that include boor: de boor algorithm, like a boor
		Words similar to boor: churl, barbarian, goth, lout, peasant, tike, tyke, yahoo, bumpkin, clod, clodhopper, clown, jerk, vulgarian, yokel, more...
	www.onelook.com /?w=boor (212 words)

	C++ Programming
		This is a wee simple sample of how to render a number of cubic b-spline segments to create a clamped curve.
		This example uses the Cox-De-Boor algorithm to calculate the points on a single Nurbs Curve.
		Moving on from the previous bezier patch example, we now need to start worrying about rendering the surface as triangle strips, handling the texture co-ords, and calculating the surface normals.
	www.robthebloke.org /opengl_programming.html (1473 words)

	Using Bitmaps for Automatic Generation of Large-Scale Terrain Models
		In addition to that (just to make your life more difficult), this terrain model must conform to a loose, preexisting map specification (in other words, the general map layout and major landmark locations are known relative to each other, but there is no concrete data set describing the terrain, such as satellite imagery).
		In smoothing the terrain bitmap, neither the straightforward smoothing algorithms described above nor any other image processing technique used for scaling or smoothing images can be applied.
		All of these methods have potential to introduce new color values into the final image, and only the terrain values contained in the original terrain bitmap can be present in the final bitmap.
	www.gamasutra.com /features/20000427/martin_pfv.htm (3589 words)

	W01 CS679 Project: Chris Ingram (Site not responding. Last check: 2007-10-19)
		Numerically stable, coefficient-based algorithms exist for the evaluation of both Bezier curves and B-Splines, namely the de Casteljau and de Boor algorithms.
		The de Casteljau algorithm is generalizable to the Bezier Patches, allowing for simple and stable evaluation.
		The first portion of my project was to devise a simple patch visualizer that would allow the user to manipulate the control points of two neighbouring patches in a surface.
	www.cs.uwaterloo.ca /~c2ingram/tbs.html (1425 words)

	World History :: Encyclopedia Index -- De (Site not responding. Last check: 2007-10-19)
		INDEX OF ARTICLES: De Articles are indexed by the first word of the title, including "A," "The," etc.
		De La Salle - College of Saint Benilde
		Decreto Número 99.226, de 27 de Abril de 1990
	www.worldhistory.com /wiki/De.htm (189 words)

	CGTalk - History of Nurbs?
		I.J. Shoenberg used B-splines for statistical data smoothing and it was his 1946 paper on data approximation that gave rise to modern spline theory.
		M.G. Cox (1971) and C. de Boor (1972) independently developed a recursive definition of B-splines: the so-called Cox-de Boor algorithm that became a very important tool in the development of B-splines.
		And NURMS is just max's gimmick name for their subdivision algorithm (same as everyone else uses, catmull-clark I think).
	forums.cgsociety.org /printthread.php?t=66347&pp=50 (2560 words)

	DigiPen - Programs & Academics - Course Catalog - Math
		Topics include: Bezier curves, control points, de Casteljau algorithm, splines, de Boor algorithm for polynomial curves, bipolynomial and total degree surfaces.
		Topics include: mathematical foundations for non-uniform rational B-spline (NURBS) curves and surfaces, de Casteljau and de Boor algorithms, knot insertion, and subdivision.
		Topics from number theory include: divisibility, Euclidean Algorithm, congruences, and quadratic reciprocity, factoring algorithms, finite fields, number fields, arithmetic of elliptic curves.
	www.digipen.edu /programs/catalog/mat.html (1214 words)

	Programas (Site not responding. Last check: 2007-10-19)
		Teaching and research activities take place in the following areas: algorithms and combinatorics; artificial intelligence; computer architecture and operating systems; computer graphics; computer networks; data bases; optimization; social aspects of computing; and software engineering.
		COS878 Advanced Topics in Distributed Algorithms — This course aims at the study of the most recent developments in the field of distributed algorithms.
		Topics of interest include new approaches to the modeling of distributed systems, to the design and analysis of algorithms, and applications.
	www.coppe.ufrj.br /english/programas/info_programa.php?programa=21 (1915 words)

	Digital Systems Research Center: Report 19 (Site not responding. Last check: 2007-10-19)
		Blossoming a Bezier curve or surface provides lucid labels both for its Bezier points and for all of the intermediate points that arise in the de Casteljau Algorithm.
		Blossoming a spline curve with parametric continuity provides lucid labels for its de Boor points and for the points that arise in the de Boor Algorithm.
		Spline curves with geometric continuity and spline surfaces with triangular patches present unsolved labeling challenges, however.
	gatekeeper.dec.com /pub/DEC/SRC/research-reports/abstracts/src-rr-019.html (193 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		Employing a dynamic programming method based on recursive pyramids, this text presents an approach to understanding, analysing, and computing the most common polynomial and spline curve and surface schemes used in computer-aided geometric design.
		It includes chapters on Bezier curves and surfaces, B-splines, blossoming and multi-sided Bezier patches, and concludes each section with both practical and theoretical exercises that enhance and elaborate upon the discussion in the text.
		Contents: Foundations; Lagrange interpolation and Neville's algorithm; Hermite interpolation and the extended Neville algorithm; Newton interpolation and difference triangles; Bezier approximation and Pascal's triangle; blossoming; B-spline approximation and the de Boor algorithm; pyramid algorithms for multi-sided Bezier patches.
	www.holbornbooks.co.uk /details.aspx?sn=1242615 (253 words)

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