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Subdivision Surfaces

Subdivision Surfaces
Author: Jörg Peters
Publisher: Springer Science & Business Media
Total Pages: 212
Release: 2008-05-07
Genre: Computers
ISBN: 3540764054

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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.


Introduction to the Mathematics of Subdivision Surfaces

Introduction to the Mathematics of Subdivision Surfaces
Author: Lars-Erik Andersson
Publisher: SIAM
Total Pages: 373
Release: 2010-01-01
Genre: Mathematics
ISBN: 0898717612

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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 Surfaces

Subdivision Surfaces
Author: Jörg Peters
Publisher: Springer Science & Business Media
Total Pages: 212
Release: 2008-08-24
Genre: Mathematics
ISBN: 3540764062

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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 Surface Modeling Technology

Subdivision Surface Modeling Technology
Author: Wenhe Liao
Publisher: Springer
Total Pages: 307
Release: 2017-10-11
Genre: Computers
ISBN: 9811035156

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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.


Interactive Shape Design

Interactive Shape Design
Author: Marie-Paule Cani
Publisher: Springer Nature
Total Pages: 81
Release: 2022-05-31
Genre: Mathematics
ISBN: 3031795342

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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


Mathematical Tools in Computer Graphics with C# Implementations

Mathematical Tools in Computer Graphics with C# Implementations
Author: Alexandre Hardy
Publisher: World Scientific
Total Pages: 494
Release: 2008
Genre: Computers
ISBN: 9812791027

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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

Shape Analysis and Structuring
Author: Leila de Floriani
Publisher: Springer Science & Business Media
Total Pages: 305
Release: 2007-12-24
Genre: Mathematics
ISBN: 3540332650

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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.


Mathematical Methods for Curves and Surfaces

Mathematical Methods for Curves and Surfaces
Author: Morten Dæhlen
Publisher: Springer
Total Pages: 453
Release: 2010-02-12
Genre: Computers
ISBN: 3642116205

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This volume constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2008, held in Tønsberg, Norway, in June/July 2008. The 28 revised full papers presented were carefully reviewed and selected from 129 talks presented at the conference. The topics addressed by the papers range from mathematical analysis of various methods to practical implementation on modern graphics processing units.


Mathematics of Surfaces XI

Mathematics of Surfaces XI
Author: Ralph R. Martin
Publisher: Springer Science & Business Media
Total Pages: 481
Release: 2005-08-25
Genre: Computers
ISBN: 3540282254

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This book constitutes the refereed proceedings of the 11th IMA International Conference on the Mathematics of Surfaces, held in Loughborough, UK in September 2005. The 28 revised full papers presented were carefully reviewed and selected from numerous submissions. Among the topics addressed are Voronoi diagrams, linear systems, curvatures on meshes, approximate parameterization, condition numbers, pythagorean hodographs, artifacts in B-spline surfaces, Bézier surfaces of minimal energy, line subdivision, subdivision surfaces, level sets and symmetry, the topology of algebraic surfaces, embedding graphs in manifolds, recovery of 3D shape from shading, finding optimal feedrates for machining, and improving of range data.


The Mathematics of Surfaces IX

The Mathematics of Surfaces IX
Author: Roberto Cipolla
Publisher: Springer Science & Business Media
Total Pages: 510
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1447104951

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These proceedings collect the papers accepted for presentation at the bien nial IMA Conference on the Mathematics of Surfaces, held in the University of Cambridge, 4-7 September 2000. While there are many international con ferences in this fruitful borderland of mathematics, computer graphics and engineering, this is the oldest, the most frequent and the only one to concen trate on surfaces. Contributors to this volume come from twelve different countries in Eu rope, North America and Asia. Their contributions reflect the wide diversity of present-day applications which include modelling parts of the human body for medical purposes as well as the production of cars, aircraft and engineer ing components. Some applications involve design or construction of surfaces by interpolating or approximating data given at points or on curves. Others consider the problem of 'reverse engineering'-giving a mathematical descrip tion of an already constructed object. We are particularly grateful to Pamela Bye (at the Institue of Mathemat ics and its Applications) for help in making arrangements; Stephanie Harding and Karen Barker (at Springer Verlag, London) for publishing this volume and to Kwan-Yee Kenneth Wong (Cambridge) for his heroic help with com piling the proceedings and for dealing with numerous technicalities arising from large and numerous computer files. Following this Preface is a listing of the programme committee who with the help of their colleagues did much work in refereeing the papers for these proceedings.