Subdivision Surfaces:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer Berlin
2010
|
| Ausgabe: | [1. softcover version of original hardcover edition 2008] |
| Schriftenreihe: | Geometry and Computing
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | IX, 204 S. Ill., graph. Darst. |
| ISBN: | 9783642095276 3642095275 |
Internformat
MARC
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| 100 | 1 | |a Peters, Jörg |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Subdivision Surfaces |c Jörg Peters ; Ulrich Reif |
| 250 | |a [1. softcover version of original hardcover edition 2008] | ||
| 264 | 1 | |a Berlin |b Springer Berlin |c 2010 | |
| 300 | |a IX, 204 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1807955432695660544 |
|---|---|
| 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 |
| author_facet | Peters, Jörg Reif, Ulrich |
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| author_sort | Peters, Jörg |
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| building | Verbundindex |
| bvnumber | BV040895439 |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)844038738 (DE-599)DNB1008519383 |
| discipline | Mathematik |
| edition | [1. softcover version of original hardcover edition 2008] |
| format | Book |
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| id | DE-604.BV040895439 |
| illustrated | Illustrated |
| indexdate | 2024-08-21T00:37:39Z |
| institution | BVB |
| isbn | 9783642095276 3642095275 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025875141 |
| oclc_num | 844038738 |
| open_access_boolean | |
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| owner_facet | DE-739 DE-11 |
| physical | IX, 204 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer Berlin |
| record_format | marc |
| series | Geometry and Computing |
| series2 | Geometry and Computing |
| 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 |