Spelling suggestions: "subject:"curves anda surfaces"" "subject:"curves ando surfaces""
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On interactive design using the PDE method.Ugail, Hassan, Bloor, M.I.G., Wilson, M.J. January 1998 (has links)
No
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Data reduction and knot removal for non-uniform B-spline surfacesMarcaly, Fred W. 17 January 2009 (has links)
B-Spline curves and surfaces are being used throughout the aircraft industry for geometric modeling. Geometric models having accurate surface representations in the non-uniform B-Spline surface format can contain very large quantities of data. The computing power required by a CAD system for visualization and analysis is directly influenced by these large amounts of data. Accordingly, a method for reducing the amount of data in a geometric model while maintaining accuracy is needed to reduce the computing power necessary to visualize and analyze a design. This thesis describes the refinement and implementation of a data reduction algorithm for non-uniform cubic B-Spline curves and non-uniform bi-cubic B-Spline surfaces. The topic of determining the significance of knots in non-uniform cubic B-Spline curves and non-uniform bi-cubic B-Spline surfaces is addressed. Also, a method for determining the order in which knots should be removed from non-uniform cubic B-Spline curves or non-uniform bi-cubic B-Spline surfaces during data reduction is presented. Finally, an algorithm for performing data reduction by removing knots from non-uniform cubic B-Spline curves and non-uniform bi-cubic B-Spline surfaces is presented. / Master of Science
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Geodesics of surface of revolutionChang, Wenli 01 January 2011 (has links)
The purpose of this project was to study the differential geometry of curves and surfaces in three-dimensional Euclidean space. Some important concepts such as, Curvature, Fundamental Form, Christoffel symbols, and Geodesic Curvature and equations are explored.
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Geodesic on surfaces of constant Gaussian curvatureChiek, Veasna 01 January 2006 (has links)
The goal of the thesis is to study geodesics on surfaces of constant Gaussian curvature. The first three sections of the thesis is dedicated to the definitions and theorems necessary to study surfaces of constant Gaussian curvature. The fourth section contains examples of geodesics on these types of surfaces and discusses their properties. The thesis incorporates the use of Maple, a mathematics software package, in some of its calculations and graphs. The thesis' conclusion is that the Gaussian curvature is a surface invariant and the geodesics of these surfaces will be the so-called best paths.
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Ternary interpolatory subdivisionVan der Walt, Maria Dorothea 12 1900 (has links)
Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Subdivision is an important and e cient tool for rendering smooth curves and
surfaces in computer graphics, by repeatedly applying a subdivision (re ning)
scheme to a given set of points. In the literature, attention has been mostly
restricted to developing binary subdivision schemes. The primary emphasis of
this thesis is on ternary subdivision, and in particular on the interpolatory case.
We will derive a symmetric ternary interpolatory subdivision scheme for the
rendering of curves, satisfying analogous properties to the Dubuc-Deslauriers
binary scheme. Explicit construction methods, as well as a corresponding
convergence analysis, will be presented. Graphical illustrations of the results
will also be provided. / AFRIKAANSE OPSOMMING: Subdivisie bied 'n belangrike en doeltre ende metode om gladde krommes
en oppervlakke in rekenaargra ka te genereer. Hierdie metode behels dat 'n
subdivisieskema (of verfyningskema) herhaaldelik toegepas word op 'n gegewe
versameling punte. In die literatuur word daar hoofsaaklik gefokus op die ont-
wikkeling van bin^ere subdivisieskemas. In hierdie tesis word die klem gel^e op
tern^ere subdivisieskemas, en in die besonder op interpolerende skemas. Ons sal
'n simmetriese tern^ere interpolerende subdivisieskema, wat analo e eienskappe
as di e van die Dubuc-Deslauriers bin^ere skema bevredig, ontwikkel, om krom-
mes te lewer. Eksplisiete konstruksiemetodes en ooreenkomstige konvergensie-
analise, asook gra ese illustrasies van die resultate, sal getoon word.
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Optimization and differential geometry for geometric modelingLiu, Yang, 劉洋 January 2008 (has links)
published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy
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A computation of the action of the mapping class group on isotopy classes of curves and arcs in surfacesPenner, Robert Clark January 1982 (has links)
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE / Bibliography: leaves 155-156. / by Robert Clack Penner. / Ph.D.
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A technique for interactive shape deformation on non-structured objects / Uma técnica para deformação interativa de objetos não estruturadosBlanco, Fausto Richetti January 2007 (has links)
Este trabalho apresenta uma técnica para deformação interativa de objetos 3D não estruturados que combina o uso de sketches em 2D e manipulação interativa de curvas. Através de sketches no plano de imagem, o usuário cria curvas paramétricas a serem usadas como manipulares para modificar a malha do objeto. Um conjunto de linhas desenhadas sobre a projeção do modelo pode ser combinado para criar um esqueleto composto de curvas paramétricas, as quais podem ser interativamente manipuladas, deformando assim a superfície associada a elas. Deformações livres são feitas movendo-se interativamente os pontos de controle das curvas. Alguns outros efeitos interessantes, como torção e escalamento, são obtidos operando-se diretamente sobre o campo de sistemas de coordenadas criado ao longo da curva. Um algoritmo para evitar inter-penetrações na malha durante uma sessão de modelagem com a técnica proposta também é apresentado. Esse algoritmo é executado a taxas interativas assim como toda a técnica apresentada neste trabalho. A técnica proposta lida naturalmente com translações e grandes rotações, assim como superfícies não orientáveis, não variedades e malhas compostas de múltiplos componentes. Em todos os casos, a deformação preserva os detalhes locais consistentemente. O uso de curvas esqueleto permite implementar a técnica utilizando uma interface bem intuitiva, e provê ao usuário um controle preciso sobre a deformação. Restrições sobre o esqueleto e deformações sem inter-penetrações são facilmente conseguidos. É demonstrada grande qualidade em torções e dobras nas malhas e os resultados mostram que a técnica apresentada é consideravelmente mais rápida que as abordagens anteriores, obtendo resultados similares. Dado seu relativo baixo custo computacional, esta abordagem pode lidar com malhas compostas por centenas de milhares de vértices a taxas interativas. / This work presents a technique for interactive shape deformation of unstructured 3D models, based on 2D sketches and interactive curve manipulation in 3D. A set of lines sketched on the image plane over the projection of the model can be combined to create a skeleton composed by parametric curves, which can be interactively manipulated, thus deforming the associated surfaces. Free-form deformations are performed by interactively moving around the curves’ control points. Some other interesting effects, such as twisting and scaling, are obtained by operating directly over a frame field defined on the curve. An algorithm for mesh local self-intersection avoidance during model deformation is also presented. This algorithm is executed at interactive rates as is the whole technique presented in this work. The presented technique naturally handles both translations and large rotations, as well as non-orientable and non-manifold surfaces, and meshes comprised of multiple components. In all cases, the deformation preserves local features. The use of skeleton curves allows the technique to be implemented using a very intuitive interface, and giving the user fine control over the deformation. Skeleton constraints and local self-intersection avoidance are easily achieved. High-quality results on twisting and bending meshes are also demonstrated, and the results show that the presented technique is considerably faster than previous approaches for achieving similar results. Given its relatively low computational cost, this approach can handle meshes composed by hundreds of thousand vertices at interactive rates.
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Degree 2 curves in the Dwork pencilXu, Songyun, January 2008 (has links)
Thesis (Ph. D.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 44).
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A technique for interactive shape deformation on non-structured objects / Uma técnica para deformação interativa de objetos não estruturadosBlanco, Fausto Richetti January 2007 (has links)
Este trabalho apresenta uma técnica para deformação interativa de objetos 3D não estruturados que combina o uso de sketches em 2D e manipulação interativa de curvas. Através de sketches no plano de imagem, o usuário cria curvas paramétricas a serem usadas como manipulares para modificar a malha do objeto. Um conjunto de linhas desenhadas sobre a projeção do modelo pode ser combinado para criar um esqueleto composto de curvas paramétricas, as quais podem ser interativamente manipuladas, deformando assim a superfície associada a elas. Deformações livres são feitas movendo-se interativamente os pontos de controle das curvas. Alguns outros efeitos interessantes, como torção e escalamento, são obtidos operando-se diretamente sobre o campo de sistemas de coordenadas criado ao longo da curva. Um algoritmo para evitar inter-penetrações na malha durante uma sessão de modelagem com a técnica proposta também é apresentado. Esse algoritmo é executado a taxas interativas assim como toda a técnica apresentada neste trabalho. A técnica proposta lida naturalmente com translações e grandes rotações, assim como superfícies não orientáveis, não variedades e malhas compostas de múltiplos componentes. Em todos os casos, a deformação preserva os detalhes locais consistentemente. O uso de curvas esqueleto permite implementar a técnica utilizando uma interface bem intuitiva, e provê ao usuário um controle preciso sobre a deformação. Restrições sobre o esqueleto e deformações sem inter-penetrações são facilmente conseguidos. É demonstrada grande qualidade em torções e dobras nas malhas e os resultados mostram que a técnica apresentada é consideravelmente mais rápida que as abordagens anteriores, obtendo resultados similares. Dado seu relativo baixo custo computacional, esta abordagem pode lidar com malhas compostas por centenas de milhares de vértices a taxas interativas. / This work presents a technique for interactive shape deformation of unstructured 3D models, based on 2D sketches and interactive curve manipulation in 3D. A set of lines sketched on the image plane over the projection of the model can be combined to create a skeleton composed by parametric curves, which can be interactively manipulated, thus deforming the associated surfaces. Free-form deformations are performed by interactively moving around the curves’ control points. Some other interesting effects, such as twisting and scaling, are obtained by operating directly over a frame field defined on the curve. An algorithm for mesh local self-intersection avoidance during model deformation is also presented. This algorithm is executed at interactive rates as is the whole technique presented in this work. The presented technique naturally handles both translations and large rotations, as well as non-orientable and non-manifold surfaces, and meshes comprised of multiple components. In all cases, the deformation preserves local features. The use of skeleton curves allows the technique to be implemented using a very intuitive interface, and giving the user fine control over the deformation. Skeleton constraints and local self-intersection avoidance are easily achieved. High-quality results on twisting and bending meshes are also demonstrated, and the results show that the presented technique is considerably faster than previous approaches for achieving similar results. Given its relatively low computational cost, this approach can handle meshes composed by hundreds of thousand vertices at interactive rates.
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