Introduction To The Mathematics Of 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 : 2010-05-13

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 2010-05-13 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 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.

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.

Introduction To The Mathematics Of Computer Graphics

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Author : Nathan Carter
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-12-31

Introduction To The Mathematics Of Computer Graphics written by Nathan Carter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-31 with Mathematics categories.

This text, by an award-winning [Author];, was designed to accompany his first-year seminar in the mathematics of computer graphics. Readers learn the mathematics behind the computational aspects of space, shape, transformation, color, rendering, animation, and modeling. The software required is freely available on the Internet for Mac, Windows, and Linux. The text answers questions such as these: How do artists build up realistic shapes from geometric primitives? What computations is my computer doing when it generates a realistic image of my 3D scene? What mathematical tools can I use to animate an object through space? Why do movies always look more realistic than video games? Containing the mathematics and computing needed for making their own 3D computer-generated images and animations, the text, and the course it supports, culminates in a project in which students create a short animated movie using free software. Algebra and trigonometry are prerequisites; calculus is not, though it helps. Programming is not required. Includes optional advanced exercises for students with strong backgrounds in math or computer science. Instructors interested in exposing their liberal arts students to the beautiful mathematics behind computer graphics will find a rich resource in this text.

Mathematics Of Surfaces

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Author : Michael J. Wilson
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-09-09

Mathematics Of Surfaces written by Michael J. Wilson 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 2003-09-09 with Computers categories.

This book constitutes the refereed proceedings of the 10th IMA International Conference on the Mathematics of Surfaces, held in Leeds, UK in September 2003. The 25 revised full papers presented were carefully reviewed and selected from numerous submissions. Among the topics addressed are triangulated surface parameterization, bifurcation structures, control vertex computation, polyhedral surfaces, watermarking 3D polygonal meshed, subdivision surfaces, surface reconstruction, vector transport, shape from shading, surface height recovery, algebraic surfaces, box splines, the Plateau-Bezier problem, spline geometry, generative geometry, manifold representation, affine arithmetic, and PDE surfaces.

Mathematics Of Surfaces Xii

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Author : Ralph Martin
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-08-22

Mathematics Of Surfaces Xii written by Ralph Martin 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 2007-08-22 with Computers categories.

This book constitutes the refereed proceedings of the 12th IMA International Conference on the Mathematics of Surfaces, held in Sheffield, UK in September 2007. The 22 revised full papers presented together with 8 invited papers were carefully reviewed and selected from numerous submissions. Among the topics addressed is the applicability of various aspects of mathematics to engineering and computer science, especially in domains such as computer aided design, computer vision, and computer graphics. The papers cover a range of ideas from underlying theoretical tools to industrial uses of surfaces. Research is reported on theoretical aspects of surfaces including topology, parameterization, differential geometry, and conformal geometry, and also more practical topics such as geometric tolerances, computing shape from shading, and medial axes for industrial applications. Other specific areas of interest include subdivision schemes, solutions of differential equations on surfaces, knot insertion, surface segmentation, surface deformation, and surface fitting.

Mathematics Of Surfaces Xi

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Author : Ralph R. Martin
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-08-25

Mathematics Of Surfaces Xi written by Ralph R. Martin 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 2005-08-25 with Computers categories.

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

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Author : Roberto Cipolla
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Mathematics Of Surfaces Ix written by Roberto Cipolla 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 2012-12-06 with Technology & Engineering categories.

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.

Multiresolution Signal And Geometry Processing Filter Banks Wavelets And Subdivision Version 2013 09 26

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Author : Michael D. Adams
language : en
Publisher: Michael Adams
Release Date : 2013-09-26

Multiresolution Signal And Geometry Processing Filter Banks Wavelets And Subdivision Version 2013 09 26 written by Michael D. Adams and has been published by Michael Adams this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-26 with Electric filters categories.

This book is intended for use in the teaching of graduate and senior undergraduate courses on multiresolution signal and geometry processing in the engineering and related disciplines. It has been used for several years for teaching purposes in the Department of Electrical and Computer Engineering at the University of Victoria and has been well received by students. This book provides a comprehensive introduction to multiresolution signal and geometry processing, with a focus on both theory and applications. The book has two main components, corresponding to multiresolution processing in the contexts of: 1) signal processing and 2) geometry processing. The signal-processing component of the book studies one-dimensional and multi-dimensional multirate systems, considering multirate structures such as sampling-rate converters, filter banks, and transmultiplexers. A particularly strong emphasis is placed on filter banks. Univariate and multivariate wavelet systems are examined, with the biorthogonal and orthonormal cases both being considered. The relationship between filter banks and wavelet systems is established. Several applications of filter banks and wavelets in signal processing are covered, including signal coding, image compression, and noise reduction. For readers interested in image compression, a detailed overview of the JPEG-2000 standard is also provided. Some other applications of multirate systems are considered, such as transmultiplexers for communication systems (e.g., multicarrier modulation). The geometry-processing component of the book studies subdivision surfaces and subdivision wavelets. Some mathematical background relating to geometry processing is provided, including topics such as homogeneous coordinate transformations, manifolds, surface representations, and polygon meshes. Several subdivision schemes are examined in detail, including the Loop, Kobbelt sqrt(3), and Catmull-Clark methods. The application of subdivision surfaces in computer graphics is considered. A detailed introduction to functional analysis is provided, for those who would like a deeper understanding of the mathematics underlying wavelets and filter banks. For those who are interested in software applications of the material covered in the book, appendices are included that introduce the CGAL and OpenGL libraries. Also, an appendix on the SPL library (which was developed for use with this book) is included. Throughout the book, many worked-through examples are provided. Problem sets are also provided for each major topic covered.