Subdivision Surfaces
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Introduction To The Mathematics Of Subdivision Surfaces
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Author : Lars-Erik Andersson
language : en
Publisher: SIAM
Release Date : 2010-01-01
Introduction To The Mathematics Of Subdivision Surfaces written by Lars-Erik Andersson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.
This is an introduction to the mathematical theory which underlies subdivision surfaces, as it is used in computer graphics and animation. Subdivision surfaces enable a designer to specify the approximate form of a surface that defines an object and then to refine it to get a more useful or attractive version. A considerable amount of mathematical theory is needed to understand the characteristics of the resulting surfaces, and this book explains the material carefully and rigorously. The text is highly accessible, organising subdivision methods in a unique and unambiguous hierarchy which builds insight and understanding. The material is not restricted to questions related to regularity of subdivision surfaces at so-called extraordinary points, but gives a broad discussion of the various methods. It is therefore an excellent preparation for more advanced texts that delve more deeply into special questions of regularity.
Subdivision Surface Modeling Technology
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Author : Wenhe Liao
language : en
Publisher: Springer
Release Date : 2017-10-11
Subdivision Surface Modeling Technology written by Wenhe Liao and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-11 with Computers categories.
This book offers a comprehensive introduction to Subdivision Surface Modeling Technology focusing not only on fundamental theories but also on practical applications. It furthers readers’ understanding of the contacts between spline surfaces and subdivision surfaces, enabling them to master the Subdivision Surface Modeling Technology for analyzing subdivision surfaces. Subdivision surface modeling is a popular technology in the field of computer aided design (CAD) and computer graphics (CG) thanks to its ability to model meshes of any topology. The book also discusses some typical Subdivision Surface Modeling Technologies, such as interpolation, fitting, fairing, intersection, as well as trimming and interactive editing. It is a valuable tool, enabling readers to grasp the main technologies of subdivision surface modeling and use them in software development, which in turn leads to a better understanding of CAD/CG software operations.
Subdivision Surfaces
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Author : Jörg Peters
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-24
Subdivision Surfaces written by Jörg Peters and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-24 with Mathematics categories.
Since their first appearance in 1974, subdivision algorithms for generating surfaces of arbitrary topology have gained widespread popularity in computer graphics and are being evaluated in engineering applications. This development was complemented by ongoing efforts to develop appropriate mathematical tools for a thorough analysis, and today, many of the fascinating properties of subdivision are well understood. This book summarizes the current knowledge on the subject. It contains both meanwhile classical results as well as brand-new, unpublished material, such as a new framework for constructing C^2-algorithms. The focus of the book is on the development of a comprehensive mathematical theory, and less on algorithmic aspects. It is intended to serve researchers and engineers - both new to the beauty of the subject - as well as experts, academic teachers and graduate students or, in short, anybody who is interested in the foundations of this flourishing branch of applied geometry.
Subdivision Surfaces
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Author : Jörg Peters
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-07
Subdivision Surfaces written by Jörg Peters and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-07 with Computers categories.
Since their first appearance in 1974, subdivision algorithms for generating surfaces of arbitrary topology have gained widespread popularity in computer graphics and are being evaluated in engineering applications. This development was complemented by ongoing efforts to develop appropriate mathematical tools for a thorough analysis, and today, many of the fascinating properties of subdivision are well understood. This book summarizes the current knowledge on the subject. The focus of the book is on the development of a comprehensive mathematical theory, and less on algorithmic aspects. It is intended to serve researchers and engineers - both new to the beauty of the subject - as well as experts, academic teachers and graduate students or, in short, anybody who is interested in the foundations of this flourishing branch of applied geometry.
Nurbs Compatible Subdivision Surfaces
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Author : Thomas Joseph Cashman
language : en
Publisher:
Release Date : 2010
Nurbs Compatible Subdivision Surfaces written by Thomas Joseph Cashman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
Analysis And Design Of Univariate Subdivision Schemes
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Author : Malcolm Sabin
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-16
Analysis And Design Of Univariate Subdivision Schemes written by Malcolm Sabin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-16 with Mathematics categories.
‘Subdivision’ is a way of representing smooth shapes in a computer. A curve or surface (both of which contain an in?nite number of points) is described in terms of two objects. One object is a sequence of vertices, which we visualise as a polygon, for curves, or a network of vertices, which we visualise by drawing the edges or faces of the network, for surfaces. The other object is a set of rules for making denser sequences or networks. When applied repeatedly, the denser and denser sequences are claimed to converge to a limit, which is the curve or surface that we want to represent. This book focusses on curves, because the theory for that is complete enough that a book claiming that our understanding is complete is exactly what is needed to stimulate research proving that claim wrong. Also because there are already a number of good books on subdivision surfaces. The way in which the limit curve relates to the polygon, and a lot of interesting properties of the limit curve, depend on the set of rules, and this book is about how one can deduce those properties from the set of rules, and how one can then use that understanding to construct rules which give the properties that one wants.
Interactive Shape Design
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Author : Marie-Paule Cani
language : en
Publisher: Springer Nature
Release Date : 2022-05-31
Interactive Shape Design written by Marie-Paule Cani and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.
Providing an intuitive modeling system, which would enable us to communicate about any free-form shape we have in mind at least as quickly as with real-world tools, is one of the main challenges of digital shape design. The user should ideally be able to create, deform, and progressively add details to a shape, without being aware of the underlying mathematical representation nor being tied by any constraint on the geometrical or topological nature of the model. This book presents the field of interactive shape design from this perspective. Since interactively creating a shape builds on the humans ability of modeling by gesture, we note that the recent advances in interactive shape design can be classified as those that rely on sculpting as opposed to sketching metaphors. Our synthetic presentation of these strategies enables us to compare the different families of solutions, discuss open issues, and identify directions for future research. Table of Contents: Introduction / Sculpting Metaphors / Sketching Systems / Future Directions: Modeling by Gesture
A Dynamic Framework For Subdivision Surfaces
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Author : Chhandomay Mandal
language : en
Publisher:
Release Date : 2019-05-31
A Dynamic Framework For Subdivision Surfaces written by Chhandomay Mandal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-31 with Computers categories.
Abstract: Subdivision surfaces are extensively used to model smooth shapes of arbitrary topology. Recursive subdivision on a user-defined initial control mesh generates a visually pleasing smooth surface in the limit. However, users have to carefully select the intiail mesh and.or manipulate the control vertex positions at different levels of subdivision hierarchy to satisfy the functional and aesthetic requirements in the smooth limit surface. This modeling drawback results fromt eh lack of direct manipulation tools for the limit surface. In this dissertation, techniques from physics-based modeling are integrated with geometric subdivision methodology, and a dynamic framework is presented for direct manipulation of the smooth limit surface generated by the subdivision schemes using physics based "force" tools. In a typical subdivision scheme, the user starts with an initial control mesh which is refined recursively using a fixed set of subdivision rules, and a smooth surface is produced in the limit. Most often this limit surface does not have an analytic expression, and hence poses challenging problems in incorporating mass and damping distribution functions, internal deformation energy, forces, and other physical quantities required to develop a physics-based subdivision surface model. In this dissertation, local parameterization techniques suitable for embedding the geometric subdivision surface model in a physics-based modeling framework have been developed. Specific local parameterization techniques have been fully developed for the Catmull-Clark, modified butterfly and the Loop subdivision schemes. Techniques for assigning material properties to geometric subdivision surfaces are derived, and a motion equation for the dynamic model has been formulated using Lagrangian dynamics. Furthermore, advantages of the physics-based deformable models are incorporated into the conventional subdivision schemes, and a dynamic hierarchical control of this model is introduced. Finally, a multiresolution representation of the control mesh is developed and a unified approach for deriving subdivision surface-based finite elements is presented. The proposed dynamic framework enhances the applicability of the subdivision surfaces in modeling applications. It is also useful for hierarchical shape recovery from large range and volume data sets, as well as for non-rigid motion tracking from a temporal sequence of data sets. Multiresolution representation of the initial mesh controlling the smooth limit surface enables global and local editing of the shape as desired by the modeler. This dynamic framework has also been used for synthesizing natural terrain models from sparse elevation data. Dissertation Discovery Company and University of Florida are dedicated to making scholarly works more discoverable and accessible throughout the world. This dissertation, "A Dynamic Framework for Subdivision Surfaces" by Chhandomay Mandal, was obtained from University of Florida and is being sold with permission from the author. A digital copy of this work may also be found in the university's institutional repository, IR@UF. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation.
Mathematical Tools In Computer Graphics With C Implementations
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Author : Alexandre Hardy
language : en
Publisher: World Scientific
Release Date : 2008
Mathematical Tools In Computer Graphics With C Implementations written by Alexandre Hardy and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Computers categories.
Presents introductory and advanced topics in the field of computer graphics with mathematical descriptions and derivations. This book offers a balance of theory, applications, and code, and derives the underlying numerical methods and algorithms. It contains the classes in C# necessary for computer graphics, and offers an explanation of the code.
Shape Analysis And Structuring
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Author : Leila de Floriani
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-24
Shape Analysis And Structuring written by Leila de Floriani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-24 with Mathematics categories.
With a lot of recent developments in the field, this much-needed book has come at just the right time. It covers a variety of topics related to preserving and enhancing shape information at a geometric level. The contributors also cover subjects that are relevant to effectively capturing the structure of a shape by identifying relevant shape components and their mutual relationships.