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Geometry and Computing #6: Analysis and Design of Univariate Subdivision Schemes
Synopses & Reviews
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.
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