Computational Line Geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Heidelberg [u.a.]
Springer
2010
|
| Series: | Mathematics and Visualization
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 563 S. graph. Darst. |
| ISBN: | 9783642040177 |
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MARC
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Record in the Search Index
| _version_ | 1804139919759638529 |
|---|---|
| adam_text | TABLE OF CONTENTS PREFACE V TABLE OF CONTENTS VII 1. FUNDAMENTALS 1 1.1
REAL PROJECTIVE GEOMETRY I 1.1 THE REAL PROJECTIVE PLANE 1 .2
N-DIMENSIONAL PROJECTIVE SPACE 6 .3 PROJECTIVE MAPPINGS 11 .4
PROJECTIVITIES, CROSS RATIO AND HARMONIC POSITION 20 .5 POLARITIES AND
QUADRICS 28 .6 COMPLEX EXTENSION AND THE WAY FROM PROJECTIVE TO
EUCLIDEAN GEOMETRY 54 1.2 BASIC PROJECTIVE DIFFERENTIAL GEOMETRY 68
1.2.1 CURVES 68 1.2.2 SURFACES 78 1.2.3 DUALITY 82 1.3 ELEMENTARY
CONCEPTS OF ALGEBRAIC GEOMETRY 86 1.3.1 DEFINITIONS AND ALGORITHMS 86
1.3.2 GEOMETRIC PROPERTIES OF VARIETIES IN PROJECTIVE SPACE 99 1.3.3
DUALITY 104 1.4 RATIONAL CURVES AND SURFACES IN GEOMETRIC DESIGN 105
1.4.1 RATIONAL BEZIER CURVES 105 1.4.2 DUAL BEZIER CURVES 121 1.4.3
RATIONAL BEZIER SURFACES 126 2. MODELS OF LINE SPACE 133 2.1 THE KLEIN
MODEL 133 2.1.1 PLIICKER COORDINATES 133 2.1.2 COMPUTING WITH PLIICKER
COORDINATES 137 2.1.3 THE KLEIN QUADRIC 141 2.2 THE GRASSMANN ALGEBRA
144 2.3 THE STUDY SPHERE 154 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/996064583 DIGITALISIERT DURCH VIII TABLE OF CONTENTS 3.
LINEAR COMPLEXES 159 3.1 THE STRUCTURE OF A LINEAR COMPLEX 159 3.1.1
LINEAR COMPLEXES AND NULL POLARITIES IN PROJECTIVE SPACE .. 159 3.1.2
LINEAR COMPLEXES AND HELICAL MOTIONS IN EUCLIDEAN SPACE . 163 3.1.3
LINEAR COMPLEXES IN THE KLEIN MODEL 168 3.2 LINEAR MANIFOLDS OF
COMPLEXES 171 3.2.1 PENCILS OF LINEAR LINE COMPLEXES 172 3.2.2 EUCLIDEAN
PROPERTIES OF PENCILS OF LINEAR COMPLEXES 178 3.3 REGULI AND BUNDLES OF
LINEAR COMPLEXES 181 3.4 APPLICATIONS 185 3.4.1 SPATIAL KINEMATICS 185
3.4.2 STATICS AND SCREW THEORY 191 4. APPROXIMATION IN LINE SPACE 195
4.1 FITTING LINEAR COMPLEXES 195 4.2 KINEMATIC SURFACES 202 4.3
APPROXIMATION VIA LOCAL MAPPINGS INTO EUCLIDEAN 4-SPACE 211 4.4
APPROXIMATION IN THE SET OF LINE SEGMENTS 221 5. RULED SURFACES 223 5.1
PROJECTIVE DIFFERENTIAL GEOMETRY OF RULED SURFACES 223 5.1.1
INFINITESIMAL PROPERTIES OF FIRST ORDER 225 5.1.2 INFINITESIMAL
PROPERTIES OF HIGHER ORDER 234 5.2 ALGEBRAIC RULED SURFACES 238 5.2.1
RATIONAL RULED SURFACES 242 5.2.2 THE BEZIER REPRESENTATION OF RATIONAL
RULED SURFACES 247 5.2.3 SKEW CUBIC SURFACES 252 5.3 EUCLIDEAN GEOMETRY
OF RULED SURFACES 261 5.3.1 FIRST ORDER PROPERTIES 263 5.3.2 A COMPLETE
SYSTEM OF EUCLIDEAN INVARIANTS 270 5.4 NUMERICAL GEOMETRY OF RULED
SURFACES 282 5.4. TABLE OF CONTENTS IX 6.2.3 INTERPOLATION AND
APPROXIMATION ALGORITHMS WITH DEVELOPABLE SURFACES 352 6.3 DEVELOPABLE
SURFACES OF CONSTANT SLOPE AND APPLICATIONS 358 6.3.1 BASICS 359 6.3.2
THE CYCLOGRAPHIC MAPPING AND ITS APPLICATIONS 366 6.3.3 RATIONAL
DEVELOPABLE SURFACES OF CONSTANT SLOPE AND RATIONAL
PYTHAGOREAN-HODOGRAPH CURVES 383 6.4 CONNECTING DEVELOPABLES AND
APPLICATIONS 396 6.4.1 BASICS 396 6.4.2 CONVEX HULLS AND BINDER SURFACES
400 6.4.3 GEOMETRIC TOLERANCING 405 6.4.4 TWO-DIMENSIONAL NORMED SPACES
AND MINKOWSKI OFFSETS.. 410 6.5 DEVELOPABLE SURFACES WITH CREASES 416 7.
LINE CONGRUENCES AND LINE COMPLEXES 423 7.1 LINE CONGRUENCES 423 7.1.1
PROJECTIVE DIFFERENTIAL GEOMETRY OF CONGRUENCES 423 7.1.2 RATIONAL
CONGRUENCES AND TRIVARIATE BEZIER REPRESENTATIONS 428 7.1.3 EUCLIDEAN
DIFFERENTIAL GEOMETRY OF LINE CONGRUENCES 434 7.1.4 NORMAL CONGRUENCES
AND GEOMETRICAL OPTICS 446 7.1.5 SINGULARITIES OF MOTIONS CONSTRAINED BY
CONTACTING SUR- FACES AND APPLICATIONS IN SCULPTURED SURFACE MACHINING
... 452 7.1.6 NUMERICAL GEOMETRY OF LINE CONGRUENCES 465 7.1.7
PROJECTION VIA LINE CONGRUENCES 469 7.2 LINE COMPLEXES 474 7.2.1
DIFFERENTIAL GEOMETRY OF LINE COMPLEXES 474 7.2.2 ALGEBRAIC COMPLEXES
AND CONGRUENCES 480 7.2.3 SPECIAL QUADRATIC COMPLEXES 487 8. LINEAR LINE
MAPPINGS * COMPUTATIONAL KINEMATICS 497 8.
|
| any_adam_object | 1 |
| author | Pottmann, Helmut 1959- Wallner, Johannes 1971- |
| author_GND | (DE-588)136178049 (DE-588)136178057 |
| author_facet | Pottmann, Helmut 1959- Wallner, Johannes 1971- |
| author_role | aut aut |
| author_sort | Pottmann, Helmut 1959- |
| author_variant | h p hp j w jw |
| building | Verbundindex |
| bvnumber | BV035712625 |
| classification_rvk | SK 370 ST 320 |
| ctrlnum | (OCoLC)845586320 (DE-599)DNB996064583 |
| dewey-full | 516.183 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.183 |
| dewey-search | 516.183 |
| dewey-sort | 3516.183 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV035712625 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:51:44Z |
| institution | BVB |
| isbn | 9783642040177 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017989528 |
| oclc_num | 845586320 |
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| owner | DE-20 DE-19 DE-BY-UBM |
| owner_facet | DE-20 DE-19 DE-BY-UBM |
| physical | IX, 563 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| series2 | Mathematics and Visualization |
| spelling | Pottmann, Helmut 1959- Verfasser (DE-588)136178049 aut Computational Line Geometry Helmut Pottmann ; Johannes Wallner Heidelberg [u.a.] Springer 2010 IX, 563 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and Visualization Liniengeometrie (DE-588)4167754-7 gnd rswk-swf Liniengeometrie (DE-588)4167754-7 s DE-604 Wallner, Johannes 1971- Verfasser (DE-588)136178057 aut DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017989528&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pottmann, Helmut 1959- Wallner, Johannes 1971- Computational Line Geometry Liniengeometrie (DE-588)4167754-7 gnd |
| subject_GND | (DE-588)4167754-7 |
| title | Computational Line Geometry |
| title_auth | Computational Line Geometry |
| title_exact_search | Computational Line Geometry |
| title_full | Computational Line Geometry Helmut Pottmann ; Johannes Wallner |
| title_fullStr | Computational Line Geometry Helmut Pottmann ; Johannes Wallner |
| title_full_unstemmed | Computational Line Geometry Helmut Pottmann ; Johannes Wallner |
| title_short | Computational Line Geometry |
| title_sort | computational line geometry |
| topic | Liniengeometrie (DE-588)4167754-7 gnd |
| topic_facet | Liniengeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017989528&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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