Computational line geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2001
|
| Series: | Mathematics and visualization
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009405663&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Literaturverzeichnis Seite [547]-555 Hier auch später erschienene, unveränderete Nachdrucke |
| Physical Description: | IX, 563 S. Ill., graph. Darst. |
| ISBN: | 3540420584 9783540420583 9783642040177 |
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MARC
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| 245 | 1 | 0 | |a Computational line geometry |c Helmut Pottmann ; Johannes Wallner |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2001 | |
| 300 | |a IX, 563 S. |b Ill., graph. Darst. | ||
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| 500 | |a Literaturverzeichnis Seite [547]-555 | ||
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| 650 | 4 | |a Liniengeometrie | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Line geometry |x Data processing | |
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Record in the Search Index
| _version_ | 1819328724859879424 |
|---|---|
| adam_text | HELMUT POTTMANN JOHANNES WALLNER COMPUTATIONAL LINE GEOMETRY WITH 264
FIGURES, 17 IN COLOR SPRINGER TABLE OF CONTENTS PREFACE V TABLE OF
CONTENTS VII 1. FUNDAMENTALS 1 1.1 REAL PROJECTIVE GEOMETRY 1 1.1.1 THE
REAL PROJECTIVE PLANE 1 1.1.2 N-DIMENSIONAL PROJECTIVE SPACE 6 1.1.3
PROJECTIVE MAPPINGS 11 1.1.4 PROJECTIVITIES, CROSS RATIO AND HARMONIC
POSITION 20 1.1.5 POLARITIES AND QUADRICS 28 1.1.6 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 PLUCKER COORDINATES 133 2.1.2 N COMPUTING WITH
PLUCKER COORDINATES 137 2.1.3 THE KLEIN QUADRIC 141 2.2 THE GRASSMANN
ALGEBRA 144 2.3 THE STUDY SPHERE 154 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 5.4.1 DISCRETE MODELS AND DIFFERENCE GEOMETRY 282 5.4.2
INTERPOLATION AND APPROXIMATION ALGORITHMS 291 5.4.3 VARIATIONAL DESIGN
296 5.4.4 OFFSET SURFACES AND THEIR APPLICATIONS 303 5.4.5 INTERSECTION
OF RULED SURFACES 309 COLOR PLATES 311 6. DEVELOPABLE SURFACES 327 6.1
DIFFERENTIAL GEOMETRY OF DEVELOPABLE SURFACES 327 6.2 DUAL
REPRESENTATION 334 6.2.1 DIFFERENTIAL GEOMETRY OF THE DUAL SURFACE 334
6.2.2 DEVELOPABLE BEZIER AND B-SPLINE SURFACES 343 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 8.1 LINEAR LINE MAPPINGS AND
VISUALIZATION OF THE KLEIN MODEL 497 8.1.1 LINEAR LINE MAPPINGS INTO P 2
498 8.1.2 LINEAR LINE MAPPINGS INTO P 3 511 8.1.3 VISUALIZATION OF THE
KLEIN IMAGE 519 8.2 KINEMATIC MAPPINGS 522 8.2.1 QUATERNIONS 523 8.2.2
THE SPHERICAL KINEMATIC MAPPING 527 8.2.3 OTHER KINEMATIC MAPPINGS 535
8.3 MOTION DESIGN 538 REFERENCES 547 LIST OF SYMBOLS 556 INDEX 557
|
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| author | Pottmann, Helmut 1959- Wallner, Johannes 1971- |
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| 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 | Mathematik |
| format | Book |
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| id | DE-604.BV013757601 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:53:03Z |
| institution | BVB |
| isbn | 3540420584 9783540420583 9783642040177 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009405663 |
| oclc_num | 248098513 |
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| owner_facet | DE-739 DE-703 DE-384 DE-M347 DE-706 DE-824 DE-526 DE-634 DE-83 DE-11 DE-521 |
| physical | IX, 563 S. Ill., graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Springer |
| record_format | marc |
| series2 | Mathematics and visualization |
| spellingShingle | Pottmann, Helmut 1959- Wallner, Johannes 1971- Computational line geometry Liniengeometrie Datenverarbeitung Line geometry Data processing 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 Datenverarbeitung Line geometry Data processing Liniengeometrie (DE-588)4167754-7 gnd |
| topic_facet | Liniengeometrie Datenverarbeitung Line geometry Data processing |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009405663&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pottmannhelmut computationallinegeometry AT wallnerjohannes computationallinegeometry |