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Geometry and Computing #6: Analysis and Design of Univariate Subdivision Schemes

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Geometry and Computing #6: Analysis and Design of Univariate Subdivision Schemes Cover

 

Synopses & Reviews

Publisher Comments:

This book covers the theory of subdivision curves in detail, which is a prerequisite for that of subdivision surfaces. The book reports on the currently known ways of analysing a subdivision scheme (i.e. measuring criteria which might be important for the application of a scheme to a given context). It then goes on to consider how those analyses can be used in reverse to design a scheme best matching the particular criteria for a given application. The book is presented in an accessible fashion, even for those whose mathematics is a tool to be used, not a way of life. It should provide the reader with a full and deep understanding of the state-of-the-art in subdivision analysis, and separate sections on mathematical techniques provide revision for those needing it. The book will be of great interest to those starting to do research in CAD/CAE. It will also appeal to those lecturing in this subject and industrial workers implementing these methods. The author has spent his professional life on the numerical representation of shape and his book fills a need for a book covering the fundamental ideas in the simplest possible context, that of curves.

Synopsis:

This book covers the theory of subdivision curves in detail, which is a prerequisite for that of subdivision surfaces. It then considers how those analyses can be used in reverse to design a scheme best matching the particular criteria for a given application.

About the Author

The author has spent his professional life on the numerical representation of shape.

Table of Contents

Introduction.- Part I. Prependices: Functions and Curves; Differences; B-Splines; Eigenfactorisation; Enclosures; Hölder Continuity; Matrix Norms; Joint Spectral Radius; Radix Notation; z-transforms.- Part II. Dramatis Personae : An Introduction to some Regularly-Appearing Characters.- Part III. Analyses: Support; Enclosure; Continuity 1 - at Support Ends; Continuity 2 - Eigenanalysis; Continuity 3 - Difference Schemes; Continuity 4 - Difference Eigenanalysis; Continuity 5 - The Joint Spectral Radius; What Converges; Reproduction of Polynomials; Artifacts; Summary of Analysis Results.- Part IV. Design: The Design Space; Linear Subspaces of the Design Space; Non-Linear Conditions; Non-Stationary Schemes; Geometry Sensitive Schemes.- Part V. Implementation: Making Polygons; Rendering; Interrogation; End Conditions; Modifying the Original Polygon.- Part VI. Appendices: Proofs; Historical Notes; Solutions to Exercises; Coda.- References.- Index.

Product Details

ISBN:
9783642136474
Author:
Sabin, Malcolm
Publisher:
Springer
Subject:
Graphic Methods
Subject:
CAD
Subject:
Computer graphics
Subject:
Splines.
Subject:
subdivision schemes
Subject:
Visualization
Subject:
Computer-Aided Engineering (CAD, CAE) and Design
Subject:
Simulation and Modeling
Subject:
Numerical analysis
Subject:
Geometry
Subject:
Mathematics - General
Copyright:
Edition Description:
2010
Series:
Geometry and Computing
Series Volume:
6
Publication Date:
20100825
Binding:
HARDCOVER
Language:
English
Pages:
232
Dimensions:
235 x 155 mm 514 gr

Related Subjects

Computers and Internet » Computers Reference » Computer Simulation
Computers and Internet » Graphics » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Numeric Analysis

Geometry and Computing #6: Analysis and Design of Univariate Subdivision Schemes New Hardcover
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$67.25 In Stock
Product details 232 pages Not Avail - English 9783642136474 Reviews:
"Synopsis" by , This book covers the theory of subdivision curves in detail, which is a prerequisite for that of subdivision surfaces. It then considers how those analyses can be used in reverse to design a scheme best matching the particular criteria for a given application.
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