Synopses & Reviews
From the reviews: "The analysis and design of subdivision schemes, by Malcolm Sabin, provides a practical approach to subdivision curve schemes based on the state of the subject mainly from the years 1972-2010 ... . The bibliography includes a fairly comprehensive list of references sorted by year of publication. ... It is appropriate for the computer science student wishing to learn about the subject, and can whet the appetite of the more mathematically inclined reader who is interested in further investigation of the subject." (Scott N. Kersey, Mathematical Reviews, Issue 2011 j)
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.