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Thesis (doctoral)--Wilhelm-Universität zu Münster.

Thesis (doctoral)--Universität Bern.

The City of South Lake Tahoe currently does not have an adopted subdivision ordinance. This has caused confusion about the approval process and regulatory requirements as well as delays in application processing. This Professional Project will explore the opportunity for the City to adopt a subdivision ordinance that would provide direction for subdivision design and approval and further the City’s smart growth and sustainability policies. However, there would need to be careful consideration for the potential increase in costs that are associated with additional fees or off-site improvement requirements. The Subdivision Ordinance would be written with the goals of achieving a streamlined process and incorporating design standards consistent with smart growth principles and sustainability consistent with the City’s Sustainability Plan. In addition, the Subdivision Ordinance must be consistent with the goals, policies, and programs of the City of South Lake Tahoe General Plan. The project would begin with a literature review on subdivision regulation and the regulatory environment in South Lake Tahoe. Several subdivision ordinances would be reviewed for their ability to meet the goals of the South Lake Tahoe Ordinance. Throughout the process there will be consultation with other professionals. The final product will be a draft subdivision ordinance and an analysis of how well the draft achieves the goals.

Les schémas de subdivision et les schémas de subdivision inverse sont largement utilisés en informatiquegraphique; les uns pour lisser des objets 3D, et les autres pour minimiser le coût d’encodagede l’information. Ce sont les deux aspects abordés dans cette thèse.Les travaux présentés dans le cadre de la subdivision décrivent l’études et la construction d’un nouveautype de schémas de subdivision. Celui-ci unifie deux schémas de subdivision de type géométriquesdifférents. Cela permet de modéliser des objets 3D composés de zones issues de l’applicationd’un schéma approximant et de zones issues de l’application d’un schéma interpolant. Dans le cadrede la subdivision inverse, Nous présentons une méthode de construction des schémas de subdivisionbi-réguliers inverses (quadrilatères et triangles) / Subdivision schemes are commonly used to generate a smooth shape from a much more coarseone. The reverse subdivision is designed to describe a high resolution mesh from a coarse one. Bothof these tools are used in numerous graphical modelisation domains. In this thesis, we focused ontwo distinct aspects: on one hand the construction of quasi-linear subdivision schemes and on theother hand the construction of reverse quad/triangle subdivision schemes. The work, presented inthe context of the subdivision, describes the construction of a new type of subdivision schemes, andtheirs applications to solve some problems coming from the application of linear subdivision schemes.The work presented in the context of the reverse subdivision describes a new method to reverse thequad/triangle subdivision schemes

Thesis (MSc)--Stellenbosch University, 2013. / Please refer to full text to view abstract.

La Conception Assistée par Ordinateur (C.A.O) qui permet de concevoir des objets physiques à partir de modèles mathématiques est utilisée dans de nombreux secteurs de l’industrie.On constate actuellement une volonté généralisée de tirer parti de deux approches jusqu’à présent plutôt antagonistes : la modélisation géométrique continue qui crée des objets continus représentant par la modélisation à partir de surfaces B-splines ou NURBS) et la modélisation géométrique discrète qui qu’il s’agisse de maillages ou de surfaces de subdivision.Cette dualité d’approche a de nombreuses applications industrielles potentielles et présente donc un intérêt scientifique important. Les surfaces polyédriques et en particulier les surfaces de subdivision offrent intrinsèquement la discrétisation, sont d’une manipulation très simple, mais elles ne remplacent pas les surfaces B-splines ou NURBS. Les travaux présentés dans la thèse et qui ont abouti au passage réciproque d’une surface paramétrique à une surface polyédrique. Nous nous intéressons plus particulière aux surfaces de subdivision considérant comme une liaison entre la surface polyédriquee et la surface paramétrique parce qu’après quelques étapes de subdivision, le polyèdre caractéristique converge à une surface paramétrique correspondant. Nous y proposons des schémas de la subdivision inverse permettent de récréer les surface polyédrique grossier de subdivision précédent. Nous avons donc développé deux méthodes pour la reconstruction d’une courbe/surface paramétrique en utilisant le schéma de subdivision inverse uniforme et le schéma de subdivision inverse non-uniforme. Pour améliorer les résultats de reconstruction par la subdivision inverse, nous associons à ces méthodes une possibilité d’ajustement d’approximation qui permet de diminuer grandement l’erreur de reconstruction. Les résultats obtenus ont été comparés à une méthode bien connu de reconstruction sens au sens des moindres carrés. Nos méthodes sont très prometteuses en termes d’approximation et de compression / Computer Aided Geometric Design (CAGD) which allows us to design the physical objects from mathematical models is used in many sectors of industry. It is currently a general wish to take advantage of the two these approaches rather than the antagonists : The goal that the continuous geometric model creates the continuous objects represented by the modelof the surfaces B-splines or NURBS) and the discreet geometric model made by eitherthe meshes or the subdivision surfaces. This duality of the approach has many potential industrial applications and therefore submits interesting significant science. The polyhedral surfaces and the subdivision surfaces in particular which offer the intrinsically discretization,are a very simple manipulation, but they do not replace the surfaces B-splines or NURBS.The works presented in this thesis aim to the reciprocal passage from a parametric surfaceto a polyhedral surface. We are more specialy interested to subdivisions surfaces considering as a liaison between the polyhedral surface and the parametric surface, because after a few steps of subdivision, the polyhedron characteristic converges to a parametric surface corresponding.We have proposed the schemas of the inverse subdivision allowing recreating the polyhedral surface coarse of subdivision precedent. We thus presented two methods for there construction of a parametric curve/surface : one for using the schema of uniform inverse subdivision and the other for non-uniform inverse subdivision. To improve the results of reconstruction by the inverse subdivision methods, we associate these methods with the process of adjustment the approximation which allows reducing the error of reconstruction.The results obtained have been compared with a well-known least squares method. Our methods are very promising in terms of approximation and compression.

Thesis (MSc)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: In this thesis we study the underlying mathematical principles of stationary subdivision, which can be regarded as an iterative recursion scheme for the generation of smooth curves and surfaces in computer graphics. An important tool for our work is Fourier analysis, from which we state some standard results, and give the proof of one non-standard result. Next, since cardinal spline functions have strong links with subdivision, we devote a chapter to this subject, proving also that the cardinal B-splines are refinable, and that the corresponding Euler-Frobenius polynomial has a certain zero structure which has important implications in our eventual applications. The concepts of a stationary subdivision scheme and its convergence are then introduced, with as motivating example the de Rahm-Chaikin algorithm. Standard results on convergence and regularity for the case of positive masks are quoted and graphically illustrated. Next, we introduce the concept of interpolatory stationary subdivision, in which case the limit curve contains all the original control points. We prove a certain set of sufficient conditions on the mask for convergence, at the same time also proving the existence and other salient properties of the associated refinable function. Next, we show how the analysis of a certain Bezout identity leads to the characterisation of a class of symmetric masks which satisfy the abovementioned sufficient conditions. Finally, we show that specific special cases of the Bezout identity yield convergent interpolatory symmetric subdivision schemes which are identical to choosing the corresponding mask coefficients equal to certain point evaluations of, respectively, a fundamental Lagrange interpolation polynomial and a fundamental cardinal spline interpolant. The latter procedure, which is known as the Deslauriers-Dubuc subdivision scheme in the case of a polynomial interpolant, has received attention in recent work, and our approach provides a convergence result for such schemes in a more general framework. Throughout the thesis, numerical illustrations of our results are provided by means of graphs. / AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ons die onderliggende wiskundige beginsels van stasionêre onderverdeling, wat beskou kan word as 'n iteratiewe rekursiewe skema vir die generering van gladde krommes en oppervlakke in rekenaargrafika. 'n Belangrike stuk gereedskap vir ons werk is Fourieranalise, waaruit ons sekere standaardresuJtate formuleer, en die bewys gee van een nie-standaard resultaat. Daarna, aangesien kardinale latfunksies sterk bande het met onderverdeling, wy ons 'n hoofstuk aan hierdie onderwerp, waarin ons ook bewys dat die kardinale B-Iatfunksies verfynbaar is, en dat die ooreenkomstige Euler-Frobenius polinoom 'n sekere nulpuntstruktuur het wat belangrike implikasies het in ons uiteindelike toepassings. Die konsepte van 'n stasionêre onderverdelingskema en die konvergensie daarvan word dan bekendgestel, met as motiverende voorbeeld die de Rahm-Chaikin algoritme. Standaardresultate oor konvergensie en regulariteit vir die geval van positiewe maskers word aangehaal en grafies geïllustreer. Vervolgens stelons die konsep van interpolerende stasionêre onderverdeling bekend, in welke geval die limietkromme al die oorspronklike kontrolepunte bevat. Ons bewys 'n sekere versameling van voldoende voorwaardes op die masker vir konvergensie, en bewys terselfdertyd die bestaan en ander toepaslike eienskappe van die ge-assosieerde verfynbare funksie. Daarna wys ons hoedat die analise van 'n sekere Bezout identiteit lei tot die karakterisering van 'n klas simmetriese maskers wat die bovermelde voldoende voorwaardes bevredig. Laastens wys ons dat spesifieke spesiale gevalle van die Bezout identiteit konvergente interpolerende simmetriese onderverdelingskemas lewer wat identies is daaraan om die ooreenkomstige maskerkoëffisientegelyk aan sekere puntevaluasies van, onderskeidelik, 'n fundamentele Lagrange interpolasiepolinoom en 'n kardinale latfunksie-interpolant te kies. Laasgenoemde prosedure, wat bekend staan as die Deslauriers-Dubuc onderverdelingskema in die geval van 'n polinoominterpolant, het aandag ontvang in onlangse werk, en ons benadering verskaf 'n konvergensieresultaat vir sulke skemas in 'n meer algemene raamwerk. Deurgaans in die tesis word numeriese illustrasies van ons resultate met behulp van grafieke verskaf.

Thesis (M.C.R.P.) -- University of Texas at Arlington, 2008.

This report is not intended to argue how sprawl is to be stopped. Infill development is too limited to support the growth cities are expecting, and with a market of buyers who desire to live outside of the city and own a little piece of the country, can there really be an end to sprawl? Rather, this report identifies a method of sprawling smartly: conservation development. As an alternative to conventional subdivision, conservation subdivision developments perpetually preserve a significant portion— usually half—of the development site as open space. This report examines the conservation subdivision ordinances that municipalities have adopted as an alternative or, in some cases, to replace conventional subdivision regulations, and the strategies they exercise that affect a change in the way we sprawl. / text