Geometric algebra with applications in engineering:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2009
|
| Schriftenreihe: | Geometry and computing
4 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 385 S. Ill., graph. Darst. |
| ISBN: | 9783540890676 |
Internformat
MARC
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| 100 | 1 | |a Perwass, Christian B. U. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometric algebra with applications in engineering |c Christian Perwass |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2009 | |
| 300 | |a XIV, 385 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Geometry and computing |v 4 | |
| 650 | 4 | |a Geometrische Algebra | |
| 650 | 4 | |a Clifford algebras | |
| 650 | 0 | 7 | |a Geometrische Algebra |0 (DE-588)4156707-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Geometrische Algebra |0 (DE-588)4156707-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-540-89068-3 |
| 830 | 0 | |a Geometry and computing |v 4 |w (DE-604)BV022959018 |9 4 | |
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Datensatz im Suchindex
| _version_ | 1804138617726042112 |
|---|---|
| adam_text | CONTENTS INTRODUCTION 1 1.1 HISTORY 3 1.2 GEOMETRY 5 1.3 OUTLOOK 6 1.4
OVERVIEW OF THIS TEXT 8 1.4.1 CLUCALC 9 1.4.2 ALGEBRA 9 1.4.3 GEOMETRIES
10 1.4.4 NUMERICS 10 1.4.5 UNCERTAIN GEOMETRIE ENTITIES AND OPERATORS 13
1.4.6 THE INVERSION CAMERA MODEL 13 1.4.7 MONOCULAR POSE ESTIMATION 14
1.4.8 VERSOR PUNCTIONS 14 1.4.9 RANDOM VARIABLE SPACE 15 1.5 OVERVIEW OF
GEOMETRIE ALGEBRA 15 1.5.1 BASICS OF THE ALGEBRA 16 1.5.2 GENERAL
VECTORS 17 1.5.3 GEOMETRY 19 1.5.4 TRANSFORMATIONS 21 1.5.5
OUTERMORPHISM 23 LEARNING GEOMETRIE ALGEBRA WITH CLUCALC 25 2.1
BACKGROUND 26 2.2 THE SOFTWARE 27 2.2.1 EDITOR WINDOW 28 2.2.2
VISUALIZATION WINDOW 29 2.2.3 OUTPUT WINDOW 29 2.2.4 COMMAND LINE
PARAMETERS 30 2.3 THE SCRIPTING LANGUAGE 30 2.3.1 BASICS 30 2.3.2
VISUALIZING GEOMETRY 32 BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/990736318 DIGITALISIERT DURCH 3.6.3 TENSOR
REPRESENTATION 103 X CONTENTS 2.3.3 USER INTERACTION 39 2.3.4 ANIMATION
40 2.3.5 ANNOTATING GRAPHICS 42 2.3.6 MULTIVECTOR CALCULATIONS 45 2.4
SUMMARY 48 PART I THEORY 3 ALGEBRA 51 3.1 BASICS 52 3.1.1 AXIOMS 52
3.1.2 BASIC PROPERTIES 54 3.1.3 ALGEBRAIC BASIS 56 3.1.4 INVOLUTIONS 59
3.1.5 DUALITY 60 3.1.6 INNER AND OUTER PRODUCT 61 3.2 BLADES 64 3.2.1
GEOMETRIE PRODUCT 64 3.2.2 OUTER PRODUCT 66 3.2.3 SCALAR PRODUCT 68
3.2.4 REVERSE 69 3.2.5 CONJUGATE 69 3.2.6 NORM 70 3.2.7 INNER PRODUCT 72
3.2.8 DUALITY 79 3.2.9 INVERSE 81 3.2.10 PROJECTION 82 3.2.11 REJECTION
83 3.2.12 MEET AND JOIN 84 3.2.13 REGRESSIVE PRODUCT 89 3.3 VERSORS 89
3.3.1 DEFINITIONS 90 3.3.2 PROPERTIES 91 3.4 LINEAR FUNCTIONS 93 3.4.1
DETERMINANT 94 3.4.2 DETERMINANT PRODUCT 96 3.4.3 INVERSE 96 3.4.4
SUMMARY 96 3.5 RECIPROCAL BASES 97 3.5.1 DEFINITION 98 3.5.2 EXAMPLE 98
3.6 DIFFERENTIATION 99 3.6.1 VECTOR DERIVATIVE 99 3.6.2 MULTIVECTOR
DIFFERENTIATION 101 CONTENTS 3.7 ALGORITHMS 104 3.7.1 BASIS
ORTHOGONALIZATION 105 3.7.2 FACTORIZATION OF BLADES 105 3.7.3 EVALUATION
OF THE JOIN 106 3.7.4 VERSOR FACTORIZATION 107 3.8 RELATED ALGEBRAS 109
3.8.1 GIBBS S VECTOR ALGEBRA 109 3.8.2 COMPLEX NUMBERS 110 3.8.3
QUATERNIONS 111 3.8.4 GRASSMANN ALGEBRA 114 3.8.5 GRASSMANN-CAYLEY
ALGEBRA 115 GEOMETRIES 119 4.1 EUCLIDEAN SPACE 121 4.1.1 OUTER-PRODUCT
REPRESENTATIONS 122 4.1.2 GEOMETRIE INTERPRETATION OF THE INNER PRODUCT
123 4.1.3 INNER PRODUCT REPRESENTATION 124 4.1.4 REFLECTIONS 127 4.1.5
ROTATIONS 130 4.1.6 MEAN ROTOR 133 4.2 PROJECTIVE SPACE 134 4.2.1
DEFINITION 134 4.2.2 OUTER-PRODUCT REPRESENTATIONS 138 4.2.3
INNER-PRODUCT REPRESENTATIONS 140 4.2.4 REFLECTIONS IN PROJECTIVE SPACE
142 4.2.5 ROTATIONS IN PROJECTIVE SPACE 143 4.3 CONFORMAL SPACE 145
4.3.1 STEREOGRAPHIC EMBEDDING OF EUCLIDEAN SPACE 146 4.3.2
HOMOGENIZATION OF STEREOGRAPHIC EMBEDDING 147 4.3.3 GEOMETRIE ALGEBRA ON
R N+1 1 150 4.3.4 INNER-PRODUCT REPRESENTATIONS IN G 4 1 152 4.3.5
OUTER-PRODUCT REPRESENTATIONS IN G 4 1 158 4.3.6 SUMMARY OF
REPRESENTATIONS 161 4.3.7 STRATIFICATION OF SPACES 161 4.3.8 REFLECTIONS
IN G N+11 16 CONTENTS 4.4.3 THE GEOMETRIE ALGEBRA G 6 183 4.4.4 ROTATION
OPERATOR 184 4.4.5 ANALYSIS OF CONICS 186 4.4.6 INTERSECTING LINES AND
CONICS 189 4.4.7 INTERSECTION OF CONICS 190 4.5 CONFORMAL CONIC SPACE
193 4.5.1 THE VECTOR SPACE 193 4.5.2 THE GEOMETRIE ALGEBRA G 53 194
NUMERICS 197 5.1 TENSOR REPRESENTATION 198 5.1.1 COMPONENT VECTORS 199
5.1.2 EXAMPLE: GEOMETRIE PRODUCT IN G2 200 5.1.3 SUBSPACE PROJECTION 201
5.1.4 EXAMPLE: REDUCED GEOMETRIE PRODUCT 202 5.1.5 CHANGE OF BASIS 203
5.2 SOLVING LINEAR GEOMETRIE ALGEBRA EQUATIONS 203 5.2.1 INVERSE OF A
MULTIVECTOR 204 5.2.2 VERSOR EQUATION 205 5.2.3 EXAMPLE: INVERSE OF A
MULTIVECTOR IN G2 207 5.3 RANDOM MULTIVECTORS 208 5.3.1 DEFINITION 208
5.3.2 FIRST-ORDER ERROR PROPAGATION 210 5.3.3 BILINEAR FUNCTIONS 212
5.3.4 SUMMARY 214 5.4 VALIDITY OF ERROR PROPAGATION 215 5.4.1
NON-GAUSSIVITY 215 5.4.2 ERROR PROPAGATION BIAS 217 5.4.3 CONCLUSIONS
220 5.5 UNCERTAINTY IN PROJECTIVE SPACE 221 5.5.1 MAPPING 221 5.5.2
RANDOM HOMOGENEOUS VECTORS 223 5.5.3 CONDITIONING 224 5.6 UNCERTAINTY IN
CONFORMAL SPACE 228 5.6.1 BLADES AND OPERATORS 230 5.7 UNCERTAINTY IN
CONIC SPACE 233 5.8 THE GAUSS-MARKOV MODEL 234 5.8.1 LINEARIZATION 235
5.8.2 CONSTRAINTS ON PARAMETERS ALONE 236 5.8. CONTENTS XIII 5.9.3
DERIVATION OF THE COVARIANCE MATRIX SAP,AP 244 5.9.4 NUMERICAL
EVALUATION 246 5.9.5 GENERALIZATION 248 5.10 APPLYING THE GAUSS-MARKOV
AND GAUSS-HELMERT MODELS .... 248 5.10.1 ITERATIVE APPLICATION OF
GAUSS-HELMERT METHOD 249 PART II APPLICATIONS 6 UNCERTAIN GEOMETRIE
ENTITIES AND OPERATORS 255 6.1 CONSTRUCTION 255 6.1.1 GEOMETRIE ENTITIES
IN CONFORMAL SPACE 256 6.1.2 GEOMETRIE ENTITIES IN CONIC SPACE 258 6.1.3
OPERATORS IN CONFORMAL SPACE 259 6.2 ESTIMATION 263 6.2.1 ESTIMATION OF
GEOMETRIE ENTITIES 263 6.2.2 VERSOR EQUATION 265 6.2.3 PROJECTIVE VERSOR
EQUATION 267 6.2.4 CONSTRAINT METRICS 268 6.2.5 ESTIMATION OF A 3D
CIRCLE 272 6.2.6 ESTIMATION OF A GENERAL ROTOR 274 6.3 HYPOTHESIS
TESTING 275 7 THE INVERSION CAMERA MODEL 277 7.1 THE PINHOLE CAMERA
MODEL 279 7.2 DEFINITION OF THE INVERSION CAMERA MODEL 281 7.3 FROM
PINHOLE TO LENS 282 7.3.1 MATHEMATICAL FORMULATION 283 7.3.2
RELATIONSHIP BETWEEN FOCAL LENGTH AND LENS DISTORTION288 7.4 FISHEYE
LENSES 293 7.5 CATADIOPTRIC CAMERA 294 7.6 EXTENSIONS 296 8 MONOCULAR
POSE ESTIMATION 299 8.1 INITIAL POSE 301 8.2 FORMULATION OF THE PROBLEM
IN CGA 305 8.3 SOLUTION METHOD 307 8.3.1 TENSOR FORM 308 8.3. 381 XIV
CONTENTS 9 VERSOR FUNCTIONS 325 9.1 COUPLED MOTORS 326 9.1.1 CYCLOIDAL
CURVES 326 9.1.2 FOURIER SERIES 327 9.1.3 SPACE CURVES 330 9.2
PYTHAGOREAN-HODOGRAPH CURVES 330 9.2.1 RELATION TO VERSOR EQUATION 332
9.2.2 PYTHAGOREAN-HODOGRAPH CURVES 333 9.2.3 RELATION BETWEEN THE
ROTATION AND REFLECTION FORMS . 336 9.2.4 PYTHAGOREAN-HODOGRAPH QUINTIC
HERMITE INTERPOLATION 339 9.2.5 DEGREES OF FREEDOM 340 9.2.6 CURVES OF
CONSTANT LENGTH 342 9.2.7 PYTHAGOREAN-HODOGRAPH CURVES IN R N 347 9.2.8
SUMMARY 347 9.2.9 PROOF OF LEMMA 9.5 348 10 RANDOM-VARIABLE SPACE 351
10.1 A RANDOM-VARIABLE VECTOR SPACE 352 10.1.1 PROBABILITY SPACE 352
10.1.2 CONTINUOUS RANDOM VARIABLES 352 10.1.3 MULTIPLE RANDOM VARIABLES
354 10.2 A HUBERT SPACE OF RANDOM VARIABLES 356 10.2.1 THE NORM 356
10.2.2 THE SCALAR PRODUCT 357 10.2.3 THE DIRAC DELTA DISTRIBUTION 358
10.3 GEOMETRIE ALGEBRA OVER RANDOM VARIABLES 360 10.3.1 THE NORM 361
10.3.2 GENERAL PROPERTIES 362 10.3.3 CORRELATION 363 10.3.4 NORMAL
RANDOM VARIABLES 365 NOTATION 369 REFERENCES 371 INDEX
|
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| discipline | Maschinenbau / Maschinenwesen Physik Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:31:02Z |
| institution | BVB |
| isbn | 9783540890676 |
| language | English |
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| physical | XIV, 385 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Geometry and computing |
| series2 | Geometry and computing |
| spelling | Perwass, Christian B. U. Verfasser aut Geometric algebra with applications in engineering Christian Perwass Berlin [u.a.] Springer 2009 XIV, 385 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Geometry and computing 4 Geometrische Algebra Clifford algebras Geometrische Algebra (DE-588)4156707-9 gnd rswk-swf Geometrische Algebra (DE-588)4156707-9 s DE-604 Erscheint auch als Online-Ausgabe 978-3-540-89068-3 Geometry and computing 4 (DE-604)BV022959018 4 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017117478&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Perwass, Christian B. U. Geometric algebra with applications in engineering Geometry and computing Geometrische Algebra Clifford algebras Geometrische Algebra (DE-588)4156707-9 gnd |
| subject_GND | (DE-588)4156707-9 |
| title | Geometric algebra with applications in engineering |
| title_auth | Geometric algebra with applications in engineering |
| title_exact_search | Geometric algebra with applications in engineering |
| title_full | Geometric algebra with applications in engineering Christian Perwass |
| title_fullStr | Geometric algebra with applications in engineering Christian Perwass |
| title_full_unstemmed | Geometric algebra with applications in engineering Christian Perwass |
| title_short | Geometric algebra with applications in engineering |
| title_sort | geometric algebra with applications in engineering |
| topic | Geometrische Algebra Clifford algebras Geometrische Algebra (DE-588)4156707-9 gnd |
| topic_facet | Geometrische Algebra Clifford algebras |
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