Holdings: Subdivision Surfaces

Subdivision Surfaces:

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Bibliographic Details
Main Authors:	Peters, Jörg (Author), Reif, Ulrich (Author)
Format:	Book
Language:	English
Published:	Berlin Springer Berlin 2010
Edition:	[1. softcover version of original hardcover edition 2008]
Series:	Geometry and Computing 3
Subjects:	Unterteilungsalgorithmus Freiformfläche Spline Geometrische Modellierung
Online Access:	Inhaltstext Inhaltsverzeichnis
Physical Description:	IX, 204 S. Ill., graph. Darst.
ISBN:	9783642095276 3642095275

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MARC


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adam_text	Contents 1 Introduction and Overview . 1 1.1 Refined Polyhedra . 1 1.2 Control Nets . 2 1.3 Splines with Singularities . 4 1.4 Focus and Scope . 6 1.5 Overview . 7 1.6 Notation . 7 1.7 Analysis in the Shift-Invariant Setting . 8 1.8 Historical Notes on Subdivision on Irregular Meshes . 11 2 Geometry Near Singularities . 15 2.1 Dot and Cross Products . 16 2.2 Regular Surfaces . 17 2.3 Surfaces with a Singular Point . 23 2.4 Criteria for Injectivity . 31 3 Generalized Splines . 39 3.1 An Alternative View of Spline Curves . 40 3.2 Continuous Bivariate Splines . 41 3.3 C^-Splines . 44 3.4 C^-Splines . 47 3.5 A Bicubic Illustration . 53 4 Subdivision Surfaces . 57 4.1 Refinability . 58 4.2 Segments and Rings . 59 4.3 Splines in Finite-Dimensional Subspaces . 65 4.4 Subdivision Algorithms . 67 4.5 Asymptotic Expansion of Sequences . 71 4.6 Jordan Decomposition . 72 4.7 The Subdivision Matrix . 75 5 Cf -Subdivision Algorithms . 83 5.1 Generic Initial Data . 84 5.2 Standard Algorithms . 84 5.3 General Algorithms . 89 5.4 Shift Invariant Algorithms . 95 5.5 Symmetric Algorithms .103 6 Case Studies of C^-Subdivision Algorithms .109 6.1 Catmull-Clark Algorithm and Variants .109 6.2 Doo-Sabin Algorithm and Variants .116 6.3 Simplest Subdivision .120 7 Shape Analysis and C% -Algorithms .125 7.1 Higher Order Asymptotic Expansions .126 7.2 Shape Assessment .134 7.3 Conditions for Cf-Algorithms .140 7.4 A Framework for Cf-Algorithms .145 7.5 Guided Subdivision .149 8 Approximation and Linear Independence .157 8.1 Proxy Splines .157 8.2 Local and Global Linear Independence .169 9 Conclusion .175 9.1 Function Spaces .176 9.2 Recursion .177 9.3 Combinatorial Structure .178 References .183 Index .199
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author	Peters, Jörg Reif, Ulrich
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spelling	Peters, Jörg Verfasser aut Subdivision Surfaces Jörg Peters ; Ulrich Reif [1. softcover version of original hardcover edition 2008] Berlin Springer Berlin 2010 IX, 204 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Geometry and Computing 3 Unterteilungsalgorithmus (DE-588)4753239-7 gnd rswk-swf Freiformfläche (DE-588)4198736-6 gnd rswk-swf Spline (DE-588)4182391-6 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 s Freiformfläche (DE-588)4198736-6 s Spline (DE-588)4182391-6 s Unterteilungsalgorithmus (DE-588)4753239-7 s 1\p DE-604 Reif, Ulrich Verfasser aut Geometry and Computing 3 (DE-604)BV022959018 3 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3614130&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025875141&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk
spellingShingle	Peters, Jörg Reif, Ulrich Subdivision Surfaces Geometry and Computing Unterteilungsalgorithmus (DE-588)4753239-7 gnd Freiformfläche (DE-588)4198736-6 gnd Spline (DE-588)4182391-6 gnd Geometrische Modellierung (DE-588)4156717-1 gnd
subject_GND	(DE-588)4753239-7 (DE-588)4198736-6 (DE-588)4182391-6 (DE-588)4156717-1
title	Subdivision Surfaces
title_auth	Subdivision Surfaces
title_exact_search	Subdivision Surfaces
title_full	Subdivision Surfaces Jörg Peters ; Ulrich Reif
title_fullStr	Subdivision Surfaces Jörg Peters ; Ulrich Reif
title_full_unstemmed	Subdivision Surfaces Jörg Peters ; Ulrich Reif
title_short	Subdivision Surfaces
title_sort	subdivision surfaces
topic	Unterteilungsalgorithmus (DE-588)4753239-7 gnd Freiformfläche (DE-588)4198736-6 gnd Spline (DE-588)4182391-6 gnd Geometrische Modellierung (DE-588)4156717-1 gnd
topic_facet	Unterteilungsalgorithmus Freiformfläche Spline Geometrische Modellierung
url	http://deposit.dnb.de/cgi-bin/dokserv?id=3614130&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025875141&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV022959018
work_keys_str_mv	AT petersjorg subdivisionsurfaces AT reifulrich subdivisionsurfaces

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