Analysis and Design of Univariate Subdivision Schemes

• Κύριος συγγραφέας: Sabin, Malcolm (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2010.
• Σειρά: Geometry and Computing, 6
• Θέματα: Mathematics.; Computer simulation.; Computer graphics.; Computer-aided engineering.; Visualization.; Geometry.; Discrete mathematics.; Discrete Mathematics.; Simulation and Modeling.; Computer-Aided Engineering (CAD, CAE) and Design.; Computer Graphics.

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)....

Πίνακας περιεχομένων:

• Prependices
• Functions and Curves
• Differences
• B-Splines
• Eigenfactorisation
• Enclosures
• Hölder Continuity
• Matrix Norms
• Joint Spectral Radius
• Radix Notation
• z-transforms
• Dramatis Personae
• An introduction to some regularly-appearing characters
• 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
• Normalisation of Schemes
• Summary of Analysis Results
• Design
• The Design Space
• Linear Subspaces of the Design Space
• Non-linear Conditions
• Non-Stationary Schemes
• Geometry Sensitive Schemes
• Implementation
• Making Polygons
• Rendering
• Interrogation
• End Conditions
• Modifying the Original Polygon
• Appendices
• Proofs
• Historical Notes
• Solutions to Exercises
• Coda.