Oriented projective geometry: a framework for geometric computations
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston u.a.
Academic Press u.a.
1991
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 237 S. Ill., graph. Darst. |
| ISBN: | 0126720258 |
Internformat
MARC
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| 100 | 1 | |a Stolfi, Jorge |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Oriented projective geometry |b a framework for geometric computations |c Jorge Stolfi |
| 264 | 1 | |a Boston u.a. |b Academic Press u.a. |c 1991 | |
| 300 | |a VII, 237 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Géométrie projective |2 ram | |
| 650 | 7 | |a calcul géométrique |2 inriac | |
| 650 | 7 | |a géométrie algorithmique |2 inriac | |
| 650 | 7 | |a géométrie projective |2 inriac | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Geometry, Projective |x Data processing | |
| 650 | 0 | 7 | |a Projektive Geometrie |0 (DE-588)4047436-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Orientierung |g Mathematik |0 (DE-588)4172822-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algorithmische Geometrie |0 (DE-588)4130267-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Geometrische Modellierung |0 (DE-588)4156717-1 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804119609993854976 |
|---|---|
| adam_text | TABLE OF CONTENTS
Chapter 0. Introduction 1
Chapter 1. Projective geometry 3
1.1. The classic projective plane 3
1.2. Advantages of projective geometry 6
1.3. Drawbacks of classical projective geometry 8
1.4. Oriented projective geometry 10
1.5. Related work 11
Chapter 2. Oriented projective spaces 13
2.1. Models of two sided space 13
2.2. Central projection 16
Chapter 3. Flats 19
3.1. Definition 19
3.2. Points 19
3.3. Lines 20
3.4. Planes 23
3.5. Three spaces 26
3.6. Ranks 27
3.7. Incidence and independence 27
Chapter 4. Simplices and orientation 29
4.1. Simplices 29
4.2. Simplex equivalence 30
4.3. Point location relative to a simplex 34
4.4. The vector space model 37
Chapter 5. The join operation 39
5.1. The join of two points 39
5.2. The join of a point and a line 41
5.3. The join of two arbitrary flats 42
5.4. Properties of join 43
5.5. Null objects 44
5.6. Complementary flats 45
Chapter 6. The meet operation 47
6.1. The meeting point of two lines 47
6.2. The general meet operation 49
6.3. Meet in three dimensions 51
6.4. Properties of meet 53
v
vi Contents
Chapter 7. Relative orientation 59
7.1. The two sides of a line 59
7.2. Relative position of arbitrary flats 60
7.3. The separation theorem 64
7.4. The coefficients of a hyperplane 66
Chapter 8. Projective maps 67
8.1. Formal definition 68
8.2. Examples 70
8.3. Properties of projective maps 72
8.4. The matrix of a map 73
Chapter 9. General two sided spaces 77
9.1. Formal definition 77
9.2. Subspaces 78
Chapter 10. Duality 83
10.1. Duomorphisms 83
10.2. The polar complement 85
10.3. Polar complements as duomorphisms 89
10.4. Relative polar complements 91
10.5. General duomorphisms 92
10.6. The power of duality 93
Chapter 11. Generalized projective maps 95
11.1. Projective functions 95
11.2. Computer representation 101
Chapter 12. Projective frames 107
12.1. Nature of projective frames 107
12.2. Classification of frames 110
12.3. Standard frames 113
12.4. Coordinates relative to a frame 120
Chapter 13. Cross ratio 123
13.1. Cross ratio in unoriented geometry 123
13.2. Cross ratio in the oriented framework 126
Chapter 14. Convexity 131
14.1. Convexity in classical projective space 131
14.2. Convexity in oriented projective spaces 132
14.3. Properties of convex sets 134
14.4. The half space property 138
14.5. The convex hull 141
14.6. Convexity and duality 143
Contents vii
Chapter 15. Affine geometry 151
15.1. The Cartesian connection 151
15.2. Two sided affine spaces 153
Chapter 16. Vector algebra 167
16.1. Two sided vector spaces 167
16.2. Translations 168
16.3. Vector algebra 168
16.4. The two sided real line 171
16.5. Linear maps 171
Chapter 17. Euclidean geometry on the two sided plane 173
17.1. Perpendicularity 173
17.2. Two sided Euclidean spaces 177
17.3. Euclidean maps 178
17.4. Length and distance 183
17.5. Angular measure and congruence 187
17.6. Non Euclidean geometries 189
Chapter 18. Representing flats by simplices 191
18.1. The simplex representation 191
18.2. The dual simplex representation 193
18.3. The reduced simplex representation 195
Chapter 19. Pliicker coordinates 197
19.2. The canonical embedding 202
19.3. Pliicker coefficients 203
19.4. Storage efficiency 204
19.5. The Grassmann manifolds 204
Chapter 20. Formulas for Pliicker coordinates 207
20.1. Algebraic formulas 207
20.2. Formulas for computers 212
20.3. Projective maps in Pliicker coordinates 217
20.4. Directions and parallelism 221
References 223
List of symbols 225
Index 227
|
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| author | Stolfi, Jorge |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
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| dewey-search | 516/.5 |
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| discipline | Mathematik |
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| indexdate | 2024-07-09T16:28:55Z |
| institution | BVB |
| isbn | 0126720258 |
| language | English |
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| physical | VII, 237 S. Ill., graph. Darst. |
| publishDate | 1991 |
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| publisher | Academic Press u.a. |
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| spelling | Stolfi, Jorge Verfasser aut Oriented projective geometry a framework for geometric computations Jorge Stolfi Boston u.a. Academic Press u.a. 1991 VII, 237 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Géométrie projective ram calcul géométrique inriac géométrie algorithmique inriac géométrie projective inriac Datenverarbeitung Geometry, Projective Data processing Projektive Geometrie (DE-588)4047436-7 gnd rswk-swf Orientierung Mathematik (DE-588)4172822-1 gnd rswk-swf Algorithmische Geometrie (DE-588)4130267-9 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Projektive Geometrie (DE-588)4047436-7 s Algorithmische Geometrie (DE-588)4130267-9 s DE-604 Orientierung Mathematik (DE-588)4172822-1 s Geometrische Modellierung (DE-588)4156717-1 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003379011&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stolfi, Jorge Oriented projective geometry a framework for geometric computations Géométrie projective ram calcul géométrique inriac géométrie algorithmique inriac géométrie projective inriac Datenverarbeitung Geometry, Projective Data processing Projektive Geometrie (DE-588)4047436-7 gnd Orientierung Mathematik (DE-588)4172822-1 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Geometrische Modellierung (DE-588)4156717-1 gnd |
| subject_GND | (DE-588)4047436-7 (DE-588)4172822-1 (DE-588)4130267-9 (DE-588)4156717-1 |
| title | Oriented projective geometry a framework for geometric computations |
| title_auth | Oriented projective geometry a framework for geometric computations |
| title_exact_search | Oriented projective geometry a framework for geometric computations |
| title_full | Oriented projective geometry a framework for geometric computations Jorge Stolfi |
| title_fullStr | Oriented projective geometry a framework for geometric computations Jorge Stolfi |
| title_full_unstemmed | Oriented projective geometry a framework for geometric computations Jorge Stolfi |
| title_short | Oriented projective geometry |
| title_sort | oriented projective geometry a framework for geometric computations |
| title_sub | a framework for geometric computations |
| topic | Géométrie projective ram calcul géométrique inriac géométrie algorithmique inriac géométrie projective inriac Datenverarbeitung Geometry, Projective Data processing Projektive Geometrie (DE-588)4047436-7 gnd Orientierung Mathematik (DE-588)4172822-1 gnd Algorithmische Geometrie (DE-588)4130267-9 gnd Geometrische Modellierung (DE-588)4156717-1 gnd |
| topic_facet | Géométrie projective calcul géométrique géométrie algorithmique géométrie projective Datenverarbeitung Geometry, Projective Data processing Projektive Geometrie Orientierung Mathematik Algorithmische Geometrie Geometrische Modellierung |
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