Shape interrogation for computer aided design and manufacturing:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2002
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | 3-540-42454-7 |
| Physical Description: | XVI, 408 S. graph. Darst. |
| ISBN: | 3540424547 |
Staff View
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| 245 | 1 | 0 | |a Shape interrogation for computer aided design and manufacturing |c Nicholas M. Patrikalakis ; Takashi Maekawa |
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Record in the Search Index
| _version_ | 1804128722709643264 |
|---|---|
| adam_text | NICHOLAS M. PATRIKALAKIS TAKASHI MAEKAWA SHAPE INTERROGATION FOR
COMPUTER AIDED DESIGN AND MANUFACTURING WITH 165 FIGURES, 8 IN COLOR
SPRINGER CONTENTS 1. REPRESENTATION OF CURVES AND SURFACES 1 1.1
ANALYTIC REPRESENTATION OF CURVES 1 1.1.1 PLANE CURVES 1 1.1.2 SPACE
CURVES 3 1.2 ANALYTIC REPRESENTATION OF SURFACES 4 1.3 BEZIER CURVES AND
SURFACES 6 1.3.1 BERNSTEIN POLYNOMIALS 6 1.3.2 ARITHMETIC OPERATIONS OF
POLYNOMIALS IN BERNSTEIN FORM 7 1.3.3 NUMERICAL CONDITION OF POLYNOMIALS
IN BERNSTEIN FORM . 9 1.3.4 DEFINITION OF BEZIER CURVE AND ITS
PROPERTIES 12 1.3.5 ALGORITHMS FOR BEZIER CURVES 13 1.3.6 BEZIER
SURFACES 18 1.4 B-SPLINE CURVES AND SURFACES 20 1.4.1 B-SPLINES 20 1.4.2
B-SPLINE CURVE 21 1.4.3 ALGORITHMS FOR B-SPLINE CURVES 24 1.4.4 B-SPLINE
SURFACE 29 1.5 GENERALIZATION OF B-SPLINE TO NURBS 30 2. DIFFERENTIAL
GEOMETRY OF CURVES 35 2.1 ARC LENGTH AND TANGENT VECTOR 35 2.2 PRINCIPAL
NORMAL AND CURVATURE 39 2.3 BINORMAL VECTOR AND TORSION 43 2.4
FRENET-SERRET FORMULAE 47 3. DIFFERENTIAL GEOMETRY OF SURFACES 49 3.1
TANGENT PLANE AND SURFACE NORMAL 49 3.2 FIRST FUNDAMENTAL FORM /
(METRIC) 52 3.3 SECOND FUNDAMENTAL FORM // (CURVATURE) 55 3.4 PRINCIPAL
CURVATURES 59 3.5 GAUSSIAN AND MEAN CURVATURES 64 3.5.1 EXPLICIT
SURFACES 64 3.5.2 IMPLICIT SURFACES 65 3.6 EULER S THEOREM AND DUPIN S
INDICATRIX 68 XII CONTENTS 4. NONLINEAR POLYNOMIAL SOLVERS AND
ROBUSTNESS ISSUES 73 4.1 INTRODUCTION 73 4.2 LOCAL SOLUTION METHODS 74
4.3 CLASSIFICATION OF GLOBAL SOLUTION METHODS 76 4.3.1 ALGEBRAIC AND
HYBRID TECHNIQUES 76 4.3.2 HOMOTOPY (CONTINUATION) METHODS 78 4.3.3
SUBDIVISION METHODS 78 4.4 PROJECTED POLYHEDRON ALGORITHM 78 4.5
AUXILIARY VARIABLE METHOD FOR NONLINEAR SYSTEMS WITH SQUARE ROOTS OF
POLYNOMIALS 88 4.6 ROBUSTNESS ISSUES 90 4.7 INTERVAL ARITHMETIC 92 4.8
ROUNDED INTERVAL ARITHMETIC AND ITS IMPLEMENTATION 95 4.8.1 DOUBLE
PRECISION FLOATING POINT ARITHMETIC 95 4.8.2 EXTRACTING THE EXPONENT
FROM THE BINARY REPRESENTATION 98 4.8.3 COMPARISON OF TWO DIFFERENT
UNIT*IN*THE*LAST*PLACE IMPLEMENTATIONS 101 4.8.4 HARDWARE ROUNDING FOR
ROUNDED INTERVAL ARITHMETIC . . . 102 4.8.5 IMPLEMENTATION OF ROUNDED
INTERVAL ARITHMETIC 103 4.9 INTERVAL PROJECTED POLYHEDRON ALGORITHM 105
4.9.1 FORMULATION OF THE GOVERNING POLYNOMIAL EQUATIONS ... 105 4.9.2
COMPARISON OF SOFTWARE AND HARDWARE ROUNDING 106 5. INTERSECTION
PROBLEMS 109 5.1 OVERVIEW OF INTERSECTION PROBLEMS 109 5.2 INTERSECTION
PROBLEM CLASSIFICATION ILL 5.2.1 CLASSIFICATION BY DIMENSION 112 5.2.2
CLASSIFICATION BY TYPE OF GEOMETRY 112 5.2.3 CLASSIFICATION BY NUMBER
SYSTEM 114 5.3 POINT/POINT INTERSECTION 114 5.4 POINT/CURVE INTERSECTION
114 5.4.1 POINT/IMPLICIT ALGEBRAIC CURVE INTERSECTION 114 5.4.2
POINT/RATIONAL POLYNOMIAL PARAMETRIC CURVE INTERSECTION 117 5.4.3
POINT/PROCEDURAL PARAMETRIC CURVE INTERSECTION 121 5.5 POINT/SURFACE
INTERSECTION 121 5.5.1 POINT/IMPLICIT ALGEBRAIC SURFACE INTERSECTION 121
5.5.2 POINT/RATIONAL POLYNOMIAL PARAMETRIC SURFACE INTERSEC- TION 122
5.5.3 POINT/PROCEDURAL PARAMETRIC SURFACE INTERSECTION 125 5.6
CURVE/CURVE INTERSECTION 126 5.6.1 RATIONAL POLYNOMIAL
PARAMETRIC/IMPLICIT ALGEBRAIC CURVE INTERSECTION (CASE D3) 126 5.6.2
RATIONAL POLYNOMIAL PARAMETRIC/RATIONAL POLYNOMIAL PARAMETRIC CURVE
INTERSECTION (CASE DL) 130 CONTENTS XIII 5.6.3 RATIONAL POLYNOMIAL
PARAMETRIC/PROCEDURAL PARAME- TRIC AND PROCEDURAL PARAMETRIC/PROCEDURAL
PARAMETRIC CURVE INTERSECTIONS (CASES D2 AND D5) 131 5.6.4 PROCEDURAL
PARAMETRIC/IMPLICIT ALGEBRAIC CURVE INTER- SECTION (CASE D6) 133 5.6.5
IMPLICIT ALGEBRAIC/IMPLICIT ALGEBRAIC CURVE INTERSECTION (CASE D8) 133
5.7 CURVE/SURFACE INTERSECTION 134 5.7.1 RATIONAL POLYNOMIAL PARAMETRIC
CURVE/IMPLICIT ALGE- BRAIC SURFACE INTERSECTION (CASE E3) 135 5.7.2
RATIONAL POLYNOMIAL PARAMETRIC CURVE/RATIONAL POLY- NOMIAL PARAMETRIC
SURFACE INTERSECTION (CASE EL) 135 5.7.3 RATIONAL POLYNOMIAL
PARAMETRIC/PROCEDURAL PARAME- TRIC AND PROCEDURAL PARAMETRIC/PROCEDURAL
PARAMETRIC CURVE/SURFACE INTERSECTIONS (CASES E2/E6) 136 5.7.4
PROCEDURAL PARAMETRIC CURVE/IMPLICIT ALGEBRAIC SUR- FACE INTERSECTION
(CASE E7) 136 5.7.5 IMPLICIT ALGEBRAIC CURVE/IMPLICIT ALGEBRAIC SURFACE
IN- TERSECTION (CASE ELL) 137 5.7.6 IMPLICIT ALGEBRAIC CURVE/RATIONAL
POLYNOMIAL PARAME- TRIC SURFACE INTERSECTION (CASE E9) 137 5.8
SURFACE/SURFACE INTERSECTIONS 137 5.8.1 RATIONAL POLYNOMIAL
PARAMETRIC/IMPLICIT ALGEBRAIC SUR- FACE INTERSECTION (CASE F3) 138 5.8.2
RATIONAL POLYNOMIAL PARAMETRIC/RATIONAL POLYNOMIAL PARAMETRIC SURFACE
INTERSECTION (CASE FL) 147 5.8.3 IMPLICIT ALGEBRAIC/IMPLICIT ALGEBRAIC
SURFACE INTERSEC- TION (CASE F8) 151 5.9 OVERLAPPING OF CURVES AND
SURFACES 155 5.10 SELF-INTERSECTION OF CURVES AND SURFACES 157 5.11
SUMMARY 159 6. DIFFERENTIAL GEOMETRY OF INTERSECTION CURVES 161 6.1
INTRODUCTION 161 6.2 MORE DIFFERENTIAL GEOMETRY OF CURVES 162 6.3
TRANSVERSAL INTERSECTION CURVE 164 6.3.1 TANGENTIAL DIRECTION 164 6.3.2
CURVATURE AND CURVATURE VECTOR 165 6.3.3 TORSION AND THIRD ORDER
DERIVATIVE VECTOR 167 6.3.4 HIGHER ORDER DERIVATIVE VECTOR 168 6.4
INTERSECTION CURVE AT TANGENTIAL INTERSECTION POINTS 170 6.4.1
TANGENTIAL DIRECTION 171 6.4.2 CURVATURE AND CURVATURE VECTOR 173 6.4.3
THIRD AND HIGHER ORDER DERIVATIVE VECTOR 176 6.5 EXAMPLES 177 XIV
CONTENTS 6.5.1 TRANSVERSAL INTERSECTION OF PARAMETRIC-IMPLICIT SURFACES
177 6.5.2 TANGENTIAL INTERSECTION OF IMPLICIT-IMPLICIT SURFACES . . .
179 7. DISTANCE FUNCTIONS 181 7.1 INTRODUCTION 181 7.2 PROBLEM
FORMULATION 182 7.2.1 DEFINITION OF THE DISTANCES BETWEEN TWO POINT SETS
.... 182 7.2.2 GEOMETRIC INTERPRETATION OF STATIONARITY OF DISTANCE
FUNCTION 184 7.3 MORE ABOUT STATIONARY POINTS 185 7.3.1 CLASSIFICATION
OF STATIONARY POINTS 185 7.3.2 NONISOLATED STATIONARY POINTS 190 7.4
EXAMPLES 192 8. CURVE AND SURFACE INTERROGATION 195 8.1 CLASSIFICATION
OF INTERROGATION METHODS 195 8.1.1 ZEROTH-ORDER INTERROGATION METHODS
196 8.1.2 FIRST-ORDER INTERROGATION METHODS 197 8.1.3 SECOND-ORDER
INTERROGATION METHODS 200 8.1.4 THIRD-ORDER INTERROGATION METHODS 205
8.1.5 FOURTH-ORDER INTERROGATION METHODS 208 8.2 STATIONARY POINTS OF
CURVATURE OF FREE-FORM PARAMETRIC SURFACES210 8.2.1 GAUSSIAN CURVATURE
210 8.2.2 MEAN CURVATURE 213 8.2.3 PRINCIPAL CURVATURES 214 8.3
STATIONARY POINTS OF CURVATURE OF EXPLICIT SURFACES 215 8.4 STATIONARY
POINTS OF CURVATURE OF IMPLICIT SURFACES 221 8.5 CONTOURING CONSTANT
CURVATURE 223 8.5.1 CONTOURING LEVELS 223 8.5.2 FINDING STARTING POINTS
223 8.5.3 MATHEMATICAL FORMULATION OF CONTOURING 225 8.5.4 EXAMPLES 227
9. UMBILICS AND LINES OF CURVATURE 231 9.1 INTRODUCTION 231 9.2 LINES OF
CURVATURE NEAR UMBILICS 232 9.3 CONVERSION TO MONGE FORM 237 9.4
INTEGRATION OF LINES OF CURVATURE 242 9.5 LOCAL EXTREMA OF PRINCIPAL
CURVATURES AT UMBILICS 244 9.6 PERTURBATION OF GENERIC UMBILICS 250 9.7
INFLECTION LINES OF DEVELOPABLE SURFACES 256 9.7.1 DIFFERENTIAL GEOMETRY
OF DEVELOPABLE SURFACES 256 9.7.2 LINES OF CURVATURE NEAR INFLECTION
LINES 262 CONTENTS XV 10. GEODESIES 265 10.1 INTRODUCTION 265 10.2
GEODESIC EQUATION 266 10.2.1 PARAMETRIC SURFACES 266 10.2.2 IMPLICIT
SURFACES 270 10.3 TWO POINT BOUNDARY VALUE PROBLEM 272 10.3.1
INTRODUCTION 272 10.3.2 SHOOTING METHOD 273 10.3.3 RELAXATION METHOD 274
10.4 INITIAL APPROXIMATION 275 10.4.1 LINEAR APPROXIMATION 275 10.4.2
CIRCULAR ARC APPROXIMATION 277 10.5 SHORTEST PATH BETWEEN A POINT AND A
CURVE 278 10.6 NUMERICAL APPLICATIONS 281 10.6.1 GEODESIC PATH BETWEEN
TWO POINTS 281 10.6.2 GEODESIC PATH BETWEEN A POINT AND A CURVE 282 10.7
GEODESIC OFFSETS 284 10.8 GEODESIES ON DEVELOPABLE SURFACES 287 11.
OFFSET CURVES AND SURFACES 293 11.1 INTRODUCTION 293 11.1.1 BACKGROUND
AND MOTIVATION 293 11.1.2 NC MACHINING 293 11.1.3 MEDIAL AXIS 299 11.1.4
TOLERANCE REGION 306 11.2 PLANAR OFFSET CURVES 307 11.2.1 DIFFERENTIAL
GEOMETRY 307 11.2.2 CLASSIFICATION OF SINGULARITIES 308 11.2.3
COMPUTATION OF SINGULARITIES 311 11.2.4 APPROXIMATIONS 312 11.3 OFFSET
SURFACES 316 11.3.1 DIFFERENTIAL GEOMETRY 316 11.3.2 SINGULARITIES OF
OFFSET SURFACES 318 11.3.3 SELF-INTERSECTION OF OFFSETS OF IMPLICIT
QUADRATIC SURFACES 319 11.3.4 SELF-INTERSECTION OF OFFSETS OF EXPLICIT
QUADRATIC SURFACES 328 11.3.5 SELF-INTERSECTION OF OFFSETS OF POLYNOMIAL
PARAMETRIC SURFACE PATCHES 335 11.3.6 TRACING OF SELF-INTERSECTION
CURVES 343 11.3.7 APPROXIMATIONS 345 11.4 PYTHAGOREAN HODOGRAPH 349
11.4.1 CURVES 349 11.4.2 SURFACES 351 11.5 GENERAL OFFSETS 352 11.6 PIPE
SURFACES 353 11.6.1 INTRODUCTION 353 XVI CONTENTS 11.6.2 LOCAL
SELF-INTERSECTION OF PIPE SURFACES 355 11.6.3 GLOBAL SELF-INTERSECTION
OF PIPE SURFACES 356 PROBLEMS 367 A. COLOR PLATES 377 REFERENCES 381
INDEX 405
|
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| author_facet | Patrikalakis, Nicholas M. Maekawa, Takashi |
| author_role | aut aut |
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| dewey-ones | 670 - Manufacturing |
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| dewey-tens | 670 - Manufacturing |
| discipline | Technik Werkstoffwissenschaften / Fertigungstechnik |
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| id | DE-604.BV013883807 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:53:46Z |
| institution | BVB |
| isbn | 3540424547 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009498604 |
| oclc_num | 248480397 |
| open_access_boolean | |
| owner | DE-M347 DE-634 DE-83 |
| owner_facet | DE-M347 DE-634 DE-83 |
| physical | XVI, 408 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| spelling | Patrikalakis, Nicholas M. Verfasser aut Shape interrogation for computer aided design and manufacturing Nicholas M. Patrikalakis ; Takashi Maekawa Berlin [u.a.] Springer 2002 XVI, 408 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier 3-540-42454-7 Freiformfläche - Geometrische Modellierung - Differentialgeometrie Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Freiformfläche (DE-588)4198736-6 gnd rswk-swf Geometrische Modellierung (DE-588)4156717-1 gnd rswk-swf Freiformfläche (DE-588)4198736-6 s Geometrische Modellierung (DE-588)4156717-1 s Differentialgeometrie (DE-588)4012248-7 s DE-604 Maekawa, Takashi Verfasser aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009498604&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Patrikalakis, Nicholas M. Maekawa, Takashi Shape interrogation for computer aided design and manufacturing Freiformfläche - Geometrische Modellierung - Differentialgeometrie Differentialgeometrie (DE-588)4012248-7 gnd Freiformfläche (DE-588)4198736-6 gnd Geometrische Modellierung (DE-588)4156717-1 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4198736-6 (DE-588)4156717-1 |
| title | Shape interrogation for computer aided design and manufacturing |
| title_auth | Shape interrogation for computer aided design and manufacturing |
| title_exact_search | Shape interrogation for computer aided design and manufacturing |
| title_full | Shape interrogation for computer aided design and manufacturing Nicholas M. Patrikalakis ; Takashi Maekawa |
| title_fullStr | Shape interrogation for computer aided design and manufacturing Nicholas M. Patrikalakis ; Takashi Maekawa |
| title_full_unstemmed | Shape interrogation for computer aided design and manufacturing Nicholas M. Patrikalakis ; Takashi Maekawa |
| title_short | Shape interrogation for computer aided design and manufacturing |
| title_sort | shape interrogation for computer aided design and manufacturing |
| topic | Freiformfläche - Geometrische Modellierung - Differentialgeometrie Differentialgeometrie (DE-588)4012248-7 gnd Freiformfläche (DE-588)4198736-6 gnd Geometrische Modellierung (DE-588)4156717-1 gnd |
| topic_facet | Freiformfläche - Geometrische Modellierung - Differentialgeometrie Differentialgeometrie Freiformfläche Geometrische Modellierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009498604&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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