Subdivision surfaces:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Schriftenreihe: | Geometry and computing
3 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 183 - 197 |
| Beschreibung: | XVI, 204 S. graph. Darst. 24 cm |
| ISBN: | 9783540764052 9783540764069 |
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 |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XVI, 204 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Geometry and computing |v 3 | |
| 500 | |a Literaturverz. S. 183 - 197 | ||
| 650 | 4 | |a Geometry, Differential | |
| 650 | 0 | 7 | |a Geometrische Modellierung |0 (DE-588)4156717-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Freiformfläche |0 (DE-588)4198736-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spline |0 (DE-588)4182391-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Unterteilungsalgorithmus |0 (DE-588)4753239-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Freiformfläche |0 (DE-588)4198736-6 |D s |
| 689 | 0 | 2 | |a Spline |0 (DE-588)4182391-6 |D s |
| 689 | 0 | 3 | |a Unterteilungsalgorithmus |0 (DE-588)4753239-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Reif, Ulrich |e Verfasser |0 (DE-588)113715129 |4 aut | |
| 830 | 0 | |a Geometry and computing |v 3 |w (DE-604)BV022959018 |9 3 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016608079 | ||
Datensatz im Suchindex
| _version_ | 1804137820517826560 |
|---|---|
| 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
xii Contents
5 C^-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 C|-Algorithms................................140
7.4 A Framework for C^-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
List of Definitions, Theorems,
Examples and Lemmas
2.1 Definition
2.2 Theorem
2.3 Theorem
2.4 Definition
2.5 Theorem
2.6 Example
2.7 Example
2.8 Definition
2.9 Definition
2.10 Example
2.11 Definition
2.12 Definition
2.13 Theorem
2.14 Theorem
2.15 Example
2.16 Definition
2.17 Lemma
2.18 Lemma
2.19 Theorem
2.20 Lemma
3.1 Definition
3.2 Definition
3.3 Definition
3.4 Lemma
3.5 Lemma
3.6 Definition
3.7 Lemma
3.8 Definition
3.9 Definition
3.10 Example
Regular surface, Gauss map.......................... 18
Invariance of n..................................... 18
Invariance of principal curvatures and directions ........ 20
Embedded Weingarten map W ....................... 20
Invariance of W.................................... 22
Euler form........................................ 22
Geometric and analytic smoothness................... 23
Cq -function, almost regular.......................... 24
Normal continuity.................................. 24
Multi-sheeted surface............................... 25
Single-sheetedness................................. 25
Crfc-surface........................................ 26
Normal continuity and single-sheetedness imply C ..... 27
Convergence of W implies C$........................ 28
Computing W..................................... 29
Winding number................................... 32
Persistence of winding number....................... 33
Number of preimages............................... 34
Injectivity of an almost regular function................ 34
Winding number via arguments....................... 36
Spline............................................ 43
Embedding........................................ 44
Cfc-spline......................................... 44
Derivatives at knot lines............................. 45
Smoothness of xDx................................. 46
Regular surface.................................... 47
Forced singularities................................. 48
Ordinary and extraordinary knot...................... 49
Cq-spline — Definition 2.8™......................... 49
Fractional power embedding......................... 50
3.11 Definition
3.12 Definition
3.13 Theorem
3.14 Example
3.15 Theorem
4.1 Definition
4.2 Definition
4.3 Definition
4.4 Theorem
4.5 Theorem
4.6 Definition
4.7 Theorem
4.8 Theorem
4.9 Definition
4.10 Theorem
4.11 Definition
4.12 Definition
4.13 Theorem
4.14 Example
4.15 Definition
4.16 Definition
4.17 Lemma
4.18 Example
4.19 Definition
4.20 Theorem
4.21 Example
4.22 Lemma
4.23 Example
4.24 Definition
4.25 Lemma
4.26 Theorem
4.27 Definition
4.28 Theorem
5.1 Definition
5.2 Definition
5.3 Definition
5.4 Definition
5.5 Definition
5.6 Theorem
5.7 Definition
List of Definitions, Theorems, Examples and Lemmas
Normal continuity and single-sheetedness —
Definitions 2.9™, 2.1 Us............................. 51
C^-spline surface — Definition 2.12™................. 51
Conditions for C - and Cf-spline surfaces —
Theorems 2.13/27, 2.14™............................. 52
Gradients near the central knot....................... 52
Single-sheetedness via winding number................ 53
Refined domain.................................... 58
Segment and ring .................................. 60
Spline in subdivision form........................... 62
Smoothness conditions for segments .................. 62
From Cfc-rings to Cq-splines......................... 63
Local almost regularity.............................. 63
Normal continuity of subdivision surfaces.............. 64
Single-sheetedness of subdivision surfaces............. 64
Generating rings................................... 65
Affine invariance of rings............................ 66
Subdivision algorithm, preliminary.................... 67
Generating spline .................................. 68
Properties of generating splines....................... 69
Usefulness of overcomplete systems of
generating rings.................................... 70
Equivalence of sequences............................ 71
Eigenrings and eigencoefficients...................... 74
Dominant eigenvalue and consistency................. 75
Large dominant eigenvalue permits consistency......... 76
Ineffective eigenvector.............................. 76
Removal of ineffective eigenvectors................... 77
Removal of ineffective eigenvectors................... 77
Linear independence of eigenrings.................... 78
Linear dependence of eigenrings...................... 78
Eigensplines....................................... 78
Linear independence of eigensplines .................. 78
Unique dominant eigenvalue......................... 79
Subdivision algorithm, final.......................... 80
Cq -subdivision algorithm yields Cg-spline............. 80
Generic initial data................................. 84
C^ -subdivision algorithm ........................... 84
Standard algorithm, subdominant eigenvalue A.......... 84
Characteristic ring ip and spline , standard ............ 85
Regularity of %[ .................................... 87
Regularity of ip and normal continuity, standard......... 87
Winding number of rf ............................... 88
List of Definitions, Theorems, Examples and Lemmas xv
5.8 Theorem Winding number of ip and single-sheetedness,
standard.......................................... 88
5.9 Definition Standard C -algorithm.............................. 89
5.10 Definition Characteristic ring, general .......................... 92
5.11 Theorem Regularity of xp and normal continuity, general.......... 93
5.12 Theorem Winding number of tp and single-sheetedness, general ... 93
5.13 Definition Shift invariance.................................... 96
5.14 Example Catmull-Clark algorithm in circulant form............. 97
5.15 Definition Fourier index......................................100
5.16 Theorem Shift invariant algorithms............................100
5.17 Definition Characteristic ring, complex .........................101
5.18 Theorem Winding number of i/ and Fourier index...............101
5.19 Definition Characteristic ring, normalized.......................103
5.20 Example Flip symmetry.....................................103
5.21 Definition Symmetry.........................................104
5.22 Theorem Symmetry requires real subdominant eigenvalues........104
5.23 Theorem Symmetry of the characteristic ring...................105
5.24 Theorem Conditions for symmetric Cf -algorithms...............105
5.25 Theorem More conditions for symmetric Cf -algorithms..........107
6.1 Theorem C?-variants of Catmull-Clark........................114
6.2 Theorem C -variants of Doo-Sabin subdivision.................119
6.3 Theorem Simplest subdivision is C ...........................122
7.1 Definition Algorithm of type (X,fJ,,£)...........................127
7.2 Definition Central ring and central spline........................128
7.3 Lemma Asymptotic expansion of fundamental forms............129
7.4 Theorem Asymptotic expansion of Wm........................130
7.5 Lemma Generically, W / 0 ................................132
7.6 Theorem Curvature integrability..............................132
7.7 Definition P-periodicity......................................135
7.8 Definition Sign-type.........................................135
7.9 Theorem Central surface and sign-type ........................135
7.10 Theorem Fourier index and sign-type..........................136
7.11 Definition Limit-type........................................136
7.12 Theorem Central surface and limit-type........................136
7.13 Definition Average-type......................................138
7.14 Theorem Central surface and average-type......................138
7.15 Theorem Necessity of/x A2................................141
7.16 Theorem Cf -criterion.......................................143
7.17 Definition (^-algorithm ....................................143
7.18 Lemma Degree estimate for ip ..............................143
7.19 Theorem Degree estimate for C -algorithms..................144
7.20 Definition Reparametrization Hm..............................145
7.21 Definition Quadratic precision.................................146
7.22 Lemma
7.23 Theorem
7.24 Theorem
7.25 Definition
7.26 Theorem
8.1 Definition
8.2 Theorem
8.3 Example
8.4 Lemma
8.5 Theorem
8.6 Example
8.7 Definition
8.8 Theorem
8.9 Example
8.10 Example
List of Definitions, Theorems, Examples and Lemmas
Quadratic precision yields correct spectrum ............146
Quadratic precision suggests C^ -algorithm.............147
The PTER-framework works.........................149
Guided C^ J-subdivision............................152
Guided C r -subdivision works.......................153
Proxy spline.......................................159
Parametric distance to a proxy spline..................161
Characteristic proxy spline...........................162
Boundedness of ckF.................................164
Geometric distance to proxy spline....................166
Hausdorff distance of Catmull-Clark control net........168
Local linear dependence.............................169
Local linear dependence.............................170
Local linear dependence for the Catmull-Clark
algorithm.........................................171
Global linear dependence for the Catmull-Clark
algorithm.........................................173
|
| adam_txt |
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
xii Contents
5 C^-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 C|-Algorithms.140
7.4 A Framework for C^-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
List of Definitions, Theorems,
Examples and Lemmas
2.1 Definition
2.2 Theorem
2.3 Theorem
2.4 Definition
2.5 Theorem
2.6 Example
2.7 Example
2.8 Definition
2.9 Definition
2.10 Example
2.11 Definition
2.12 Definition
2.13 Theorem
2.14 Theorem
2.15 Example
2.16 Definition
2.17 Lemma
2.18 Lemma
2.19 Theorem
2.20 Lemma
3.1 Definition
3.2 Definition
3.3 Definition
3.4 Lemma
3.5 Lemma
3.6 Definition
3.7 Lemma
3.8 Definition
3.9 Definition
3.10 Example
Regular surface, Gauss map. 18
Invariance of n. 18
Invariance of principal curvatures and directions . 20
Embedded Weingarten map W . 20
Invariance of W. 22
Euler form. 22
Geometric and analytic smoothness. 23
Cq -function, almost regular. 24
Normal continuity. 24
Multi-sheeted surface. 25
Single-sheetedness. 25
Crfc-surface. 26
Normal continuity and single-sheetedness imply C\. 27
Convergence of W implies C$. 28
Computing W. 29
Winding number. 32
Persistence of winding number. 33
Number of preimages. 34
Injectivity of an almost regular function. 34
Winding number via arguments. 36
Spline. 43
Embedding. 44
Cfc-spline. 44
Derivatives at knot lines. 45
Smoothness of xDx. 46
Regular surface. 47
Forced singularities. 48
Ordinary and extraordinary knot. 49
Cq-spline — Definition 2.8™. 49
Fractional power embedding. 50
3.11 Definition
3.12 Definition
3.13 Theorem
3.14 Example
3.15 Theorem
4.1 Definition
4.2 Definition
4.3 Definition
4.4 Theorem
4.5 Theorem
4.6 Definition
4.7 Theorem
4.8 Theorem
4.9 Definition
4.10 Theorem
4.11 Definition
4.12 Definition
4.13 Theorem
4.14 Example
4.15 Definition
4.16 Definition
4.17 Lemma
4.18 Example
4.19 Definition
4.20 Theorem
4.21 Example
4.22 Lemma
4.23 Example
4.24 Definition
4.25 Lemma
4.26 Theorem
4.27 Definition
4.28 Theorem
5.1 Definition
5.2 Definition
5.3 Definition
5.4 Definition
5.5 Definition
5.6 Theorem
5.7 Definition
List of Definitions, Theorems, Examples and Lemmas
Normal continuity and single-sheetedness —
Definitions 2.9™, 2.1 Us. 51
C^-spline surface — Definition 2.12™. 51
Conditions for C\- and Cf-spline surfaces —
Theorems 2.13/27, 2.14™. 52
Gradients near the central knot. 52
Single-sheetedness via winding number. 53
Refined domain. 58
Segment and ring . 60
Spline in subdivision form. 62
Smoothness conditions for segments . 62
From Cfc-rings to Cq-splines. 63
Local almost regularity. 63
Normal continuity of subdivision surfaces. 64
Single-sheetedness of subdivision surfaces. 64
Generating rings. 65
Affine invariance of rings. 66
Subdivision algorithm, preliminary. 67
Generating spline . 68
Properties of generating splines. 69
Usefulness of overcomplete systems of
generating rings. 70
Equivalence of sequences. 71
Eigenrings and eigencoefficients. 74
Dominant eigenvalue and consistency. 75
Large dominant eigenvalue permits consistency. 76
Ineffective eigenvector. 76
Removal of ineffective eigenvectors. 77
Removal of ineffective eigenvectors. 77
Linear independence of eigenrings. 78
Linear dependence of eigenrings. 78
Eigensplines. 78
Linear independence of eigensplines . 78
Unique dominant eigenvalue. 79
Subdivision algorithm, final. 80
Cq -subdivision algorithm yields Cg-spline. 80
Generic initial data. 84
C^ -subdivision algorithm . 84
Standard algorithm, subdominant eigenvalue A. 84
Characteristic ring ip and spline \, standard . 85
Regularity of %[ . 87
Regularity of ip and normal continuity, standard. 87
Winding number of rf . 88
List of Definitions, Theorems, Examples and Lemmas xv
5.8 Theorem Winding number of ip and single-sheetedness,
standard. 88
5.9 Definition Standard C\-algorithm. 89
5.10 Definition Characteristic ring, general . 92
5.11 Theorem Regularity of xp and normal continuity, general. 93
5.12 Theorem Winding number of tp and single-sheetedness, general . 93
5.13 Definition Shift invariance. 96
5.14 Example Catmull-Clark algorithm in circulant form. 97
5.15 Definition Fourier index.100
5.16 Theorem Shift invariant algorithms.100
5.17 Definition Characteristic ring, complex .101
5.18 Theorem Winding number of i/ and Fourier index.101
5.19 Definition Characteristic ring, normalized.103
5.20 Example Flip symmetry.103
5.21 Definition Symmetry.104
5.22 Theorem Symmetry requires real subdominant eigenvalues.104
5.23 Theorem Symmetry of the characteristic ring.105
5.24 Theorem Conditions for symmetric Cf -algorithms.105
5.25 Theorem More conditions for symmetric Cf -algorithms.107
6.1 Theorem C?-variants of Catmull-Clark.114
6.2 Theorem C\ -variants of Doo-Sabin subdivision.119
6.3 Theorem Simplest subdivision is C\.122
7.1 Definition Algorithm of type (X,fJ,,£).127
7.2 Definition Central ring and central spline.128
7.3 Lemma Asymptotic expansion of fundamental forms.129
7.4 Theorem Asymptotic expansion of Wm.130
7.5 Lemma Generically, W / 0 .132
7.6 Theorem Curvature integrability.132
7.7 Definition 'P-periodicity.135
7.8 Definition Sign-type.135
7.9 Theorem Central surface and sign-type .135
7.10 Theorem Fourier index and sign-type.136
7.11 Definition Limit-type.136
7.12 Theorem Central surface and limit-type.136
7.13 Definition Average-type.138
7.14 Theorem Central surface and average-type.138
7.15 Theorem Necessity of/x A2.141
7.16 Theorem Cf -criterion.143
7.17 Definition (^-algorithm .143
7.18 Lemma Degree estimate for ip .143
7.19 Theorem Degree estimate for C\''-algorithms.144
7.20 Definition Reparametrization Hm.145
7.21 Definition Quadratic precision.146
7.22 Lemma
7.23 Theorem
7.24 Theorem
7.25 Definition
7.26 Theorem
8.1 Definition
8.2 Theorem
8.3 Example
8.4 Lemma
8.5 Theorem
8.6 Example
8.7 Definition
8.8 Theorem
8.9 Example
8.10 Example
List of Definitions, Theorems, Examples and Lemmas
Quadratic precision yields correct spectrum .146
Quadratic precision suggests C^ -algorithm.147
The PTER-framework works.149
Guided C^'J-subdivision.152
Guided C\'r -subdivision works.153
Proxy spline.159
Parametric distance to a proxy spline.161
Characteristic proxy spline.162
Boundedness of ckF.164
Geometric distance to proxy spline.166
Hausdorff distance of Catmull-Clark control net.168
Local linear dependence.169
Local linear dependence.170
Local linear dependence for the Catmull-Clark
algorithm.171
Global linear dependence for the Catmull-Clark
algorithm.173 |
| any_adam_object | 1 |
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| author | Peters, Jörg Reif, Ulrich |
| author_GND | (DE-588)113715129 |
| author_facet | Peters, Jörg Reif, Ulrich |
| author_role | aut aut |
| author_sort | Peters, Jörg |
| author_variant | j p jp u r ur |
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| ctrlnum | (OCoLC)212432109 (DE-599)DNB98862737X |
| dewey-full | 516.00285 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.00285 516.36 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV023425717 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:32:45Z |
| indexdate | 2024-07-09T21:18:22Z |
| institution | BVB |
| isbn | 9783540764052 9783540764069 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016608079 |
| oclc_num | 212432109 |
| open_access_boolean | |
| owner | DE-824 DE-703 DE-20 DE-188 |
| owner_facet | DE-824 DE-703 DE-20 DE-188 |
| physical | XVI, 204 S. graph. Darst. 24 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Geometry and computing |
| series2 | Geometry and computing |
| spelling | Peters, Jörg Verfasser aut Subdivision surfaces Jörg Peters ; Ulrich Reif Berlin [u.a.] Springer 2008 XVI, 204 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Geometry and computing 3 Literaturverz. S. 183 - 197 Geometry, Differential Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Freiformfläche (DE-588)4198736-6 gnd rswk-swf Spline (DE-588)4182391-6 gnd rswk-swf Unterteilungsalgorithmus (DE-588)4753239-7 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 DE-604 Reif, Ulrich Verfasser (DE-588)113715129 aut Geometry and computing 3 (DE-604)BV022959018 3 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016608079&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Peters, Jörg Reif, Ulrich Subdivision surfaces Geometry and computing Geometry, Differential Geometrische Modellierung (DE-588)4156717-1 gnd Freiformfläche (DE-588)4198736-6 gnd Spline (DE-588)4182391-6 gnd Unterteilungsalgorithmus (DE-588)4753239-7 gnd |
| subject_GND | (DE-588)4156717-1 (DE-588)4198736-6 (DE-588)4182391-6 (DE-588)4753239-7 |
| title | Subdivision surfaces |
| title_auth | Subdivision surfaces |
| title_exact_search | Subdivision surfaces |
| title_exact_search_txtP | 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 | Geometry, Differential Geometrische Modellierung (DE-588)4156717-1 gnd Freiformfläche (DE-588)4198736-6 gnd Spline (DE-588)4182391-6 gnd Unterteilungsalgorithmus (DE-588)4753239-7 gnd |
| topic_facet | Geometry, Differential Geometrische Modellierung Freiformfläche Spline Unterteilungsalgorithmus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016608079&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 |