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Bibliographic Details
Main Authors:	Pottmann, Helmut 1959- (Author), Wallner, Johannes 1971- (Author)
Format:	Book
Language:	English
Published:	Heidelberg [u.a.] Springer 2010
Series:	Mathematics and Visualization
Subjects:	Liniengeometrie
Links:	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
Physical Description:	IX, 563 S. graph. Darst.
ISBN:	9783642040177

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Record in the Search Index

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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
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dewey-ones	516 - Geometry
dewey-raw	516.183
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dewey-sort	3516.183
dewey-tens	510 - Mathematics
discipline	Informatik Mathematik
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physical	IX, 563 S. graph. Darst.
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publisher	Springer
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series2	Mathematics and Visualization
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
work_keys_str_mv	AT pottmannhelmut computationallinegeometry AT wallnerjohannes computationallinegeometry

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