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Bezier and B-spline techniques:

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Bibliographic Details
Main Authors:	Prautzsch, Hartmut (Author), Böhm, Wolfgang 1928-2018 (Author), Paluszny, Marco (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] Springer 2002
Series:	Mathematics and visualization
Subjects:	Computer graphics Computer-aided design Spline theory > Graphic methods B-Spline Bézier-Fläche Bézier-Kurve
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009873331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	Hier auch später erschienene, unveränderte Nachdrucke
Physical Description:	XIV, 304 S. graph. Darst.
ISBN:	3540437614 9783642078422

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Record in the Search Index

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adam_text	HARTMUT PRAUTZSCH WOLFGANG BOEHM MARCO PALUSZNY BEZIER AND B-SPLINE TECHNIQUES WITH 182 FIGURES SPRINGER CONTENTS I CURVES 1 GEOMETRIC FUNDAMENTALS 1.1 AFFINE SPACES 3 1.2 AFFINE COMBINATIONS 4 1.3 AFFINE MAPS 5 1.4 PARAMETRIC CURVES AND SURFACES 6 1.5 PROBLEMS 7 2 BEZIER REPRESENTATION 2.1 BERNSTEIN POLYNOMIALS 9 2.2 BEZIER REPRESENTATION 11 2.3 THE DE CASTELJAU ALGORITHM 13 2.4 DERIVATIVES 15 2.5 SINGULAR PARAMETRIZATION 17 2.6 A TETRAHEDRAL ALGORITHM 17 2.7 INTEGRATION 19 2.8 CONVERSION TO BEZIER REPRESENTATION 20 2.9 CONVERSION TO MONOMIAL FORM 22 2.10 PROBLEMS 22 3 BEZIER TECHNIQUES 3.1 SYMMETRIC POLYNOMIALS 25 3.2 THE MAIN THEOREM 27 3.3 SUBDIVISION 27 3.4 CONVERGENCE UNDER SUBDIVISION 29 3.5 CURVE GENERATION BY SUBDIVISION 30 3.6 CURVE GENERATION BY FORWARD DIFFERENCES 32 3.7 INTERSECTIONS 32 3.8 THE VARIATION DIMINISHING PROPERTY * 34 3.9 THE SYMMETRIC POLYNOMIAL OF THE DERIVATIVE 35 3.10 SIMPLE C R JOINTS 36 X CONTENTS 3.11 DEGREE ELEVATION 37 3.12 CONVERGENCE UNDER DEGREE ELEVATION 39 3.13 PROBLEMS 40 4 INTERPOLATION AND APPROXIMATION 4.1 INTERPOLATION 43 4.2 LAGRANGE FORM 44 4.3 NEWTON FORM 47 4.4 HERMITE INTERPOLATION 48 4.5 PIECEWISE CUBIC HERMITE INTERPOLATION 49 4.6 APPROXIMATION 52 4.7 LEAST SQUARES FITTING 53 4.8 IMPROVING THE PARAMETER 55 4.9 PROBLEMS 56 5 B-SPLINE REPRESENTATION 5.1 SPLINES 59 5.2 B-SPLINES 60 5.3 A RECURSIVE DEFINITION OF B-SPLINES 61 5.4 THE DE BOOR ALGORITHM 63 5.5 THE MAIN THEOREM IN ITS GENERAL FORM 65 5.6 DERIVATIVES AND SMOOTHNESS 67 5.7 B-SPLINE PROPERTIES 68 5.8 CONVERSION TO B-SPLINE FORM 69 5.9 THE COMPLETE DE BOOR ALGORITHM 70 5.10 CONVERSIONS BETWEEN BEZIER AND B-SPLINE REPRESENTATIONS 72 5.11 B-SPLINES AS DIVIDED DIFFERENCES 73 5.12 PROBLEMS 74 6 B-SPLINE TECHNIQUES 6.1 KNOT INSERTION 77 6.2 THE OSLO ALGORITHM 79 6.3 CONVERGENCE UNDER KNOT INSERTION 80 6.4 A DEGREE ELEVATION ALGORITHM 81 6.5 A DEGREE ELEVATION FORMULA 82 6.6 CONVERGENCE UNDER DEGREE ELEVATION 83 6.7 INTERPOLATION 84 6.8 CUBIC SPLINE INTERPOLATION 86 6.9 PROBLEMS 88 CONTENTS . XI 7 SMOOTH CURVES 7.1 CONTACT OF ORDER R 91 7.2 ARC LENGTH PARAMETRIZATION 93 7.3 GAMMA-SPLINES 94 7.4 GAMMA B-SPLINES 95 7.5 NU-SPLINES 96 7.6 THE FRENET FRAME 97 7.7 FRENET FRAME CONTINUITY 98 7.8 OSCULANTS AND SYMMETRIC POLYNOMIALS 100 7.9 GEOMETRIC MEANING OF THE MAIN THEOREM 102 7.10 SPLINES WITH ARBITRARY CONNECTION MATRICES 103 7.11 KNOT INSERTION 105 7.12 BASIS SPLINES 105 7.13 PROBLEMS 106 8 UNIFORM SUBDIVISION 8.1 UNIFORM B-SPLINES 109 8.2 UNIFORM SUBDIVISION 110 8.3 REPEATED SUBDIVISION 112 8.4 THE SUBDIVISION MATRIX 114 8.5 DERIVATIVES 115 8.6 STATIONARY SUBDIVISION 115 8.7 CONVERGENCE THEOREMS 116 8.8 COMPUTING THE DIFFERENCE SCHEME 117 8.9 THE FOUR-POINT SCHEME 119 8.10 ANALYZING THE FOUR-POINT SCHEME 120 8.11 PROBLEMS 120 II SURFACES 9 TENSOR PRODUCT SURFACES 9.1 TENSOR PRODUCTS 125 9.2 TENSOR PRODUCT BEZIER SURFACES 127 9.3 TENSOR PRODUCT POLAR FORMS 130 9.4 CONVERSION TO AND FROM MONOMIAL FORM 131 9.5 THE DE CASTELJAU ALGORITHM 132 9.6 DERIVATIVES . 133 9.7 SIMPLE C R JOINTS , 135 9.8 PIECEWISE BICUBIC C 1 INTERPOLATION 135 XII CONTENTS 9.9 SURFACES OF ARBITRARY TOPOLOGY 136 9.10 SINGULAR PARAMETRIZATION 138 9.11 BICUBIC C 1 SPLINES OF ARBITRARY TOPOLOGY 139 9.12 PROBLEMS 140 10 BEZIER REPRESENTATION OF TRIANGULAR PATCHES 10.1 BERNSTEIN POLYNOMIALS 141 10.2 BEZIER SIMPLICES 143 10.3 LINEAR PRECISION 145 10.4 THE DE CASTELJAU ALGORITHM 146 10.5 DERIVATIVES 147 10.6 CONVEXITY 149 10.7 LIMITATIONS OF THE CONVEXITY PROPERTY 150 10.8 PROBLEMS 152 11 BEZIER TECHNIQUES FOR TRIANGULAR PATCHES 11.1 SYMMETRIC POLYNOMIALS 155 11.2 THE MAIN THEOREM 157 11.3 * SUBDIVISION AND REPARAMETRIZATION 158 11.4 CONVERGENCE UNDER SUBDIVISION 160 11.5 SURFACE GENERATION 160 11.6 THE SYMMETRIC POLYNOMIAL OF THE DERIVATIVE 162 11.7 SIMPLE C R JOINTS 162 11.8 DEGREE ELEVATION 164 11.9 CONVERGENCE UNDER DEGREE ELEVATION 165 11.10 CONVERSION TO TENSOR PRODUCT BEZIER REPRESENTATION 166 11.11 CONVERSION TO TRIANGULAR BEZIER REPRESENTATION 167 11.12 PROBLEMS 168 12 INTERPOLATION 12.1 TRIANGULAR HERMITE INTERPOLATION 171 12.2 THE CLOUGH-TOCHER INTERPOLANT 172 12.3 THE POWELL-SABIN INTERPOLANT 173 12.4 SURFACES OF ARBITRARY TOPOLOGY 174 12.5 SINGULAR PARAMETRIZATION 175 12.6 QUINTIC C 1 SPLINES OF ARBITRARY TOPOLOGY 176 12.7 PROBLEMS 178 13 CONSTRUCTING SMOOT H SURFACES 13.1 THE GENERAL C 1 JOINT 179 CONTENTS XIII 13.2 JOINING TWO TRIANGULAR CUBIC PATCHES 181 13.3 A TRIANGULAR G 1 INTERPOLANT 183 13.4 THE VERTEX ENCLOSURE PROBLEM 184 13.5 THE PARITY PHENOMENON 185 13.6 PROBLEMS 186 14 G K -CONSTRUCTIONS 14.1 THE GENERAL C K JOINT 189 14.2 G K JOINTS BY CROSS CURVES * 190 14.3 G K JOINTS BY THE CHAIN RULE 192 14.4 G K SURFACES OF ARBITRARY TOPOLOGY 193 14.5 SMOOTH N-SIDED PATCHES 198 14.6 MULTI-SIDED PATCHES IN THE PLANE 201 14.7 PROBLEMS 203 15 STATIONARY SUBDIVISION FOR REGULAR NETS 15.1 TENSOR PRODUCT SCHEMES 205 15.2 GENERAL STATIONARY SUBDIVISION AND MASKS 207 15.3 CONVERGENCE THEOREMS 209 15.4 INCREASING AVERAGES 211 15.5 COMPUTING THE DIFFERENCE SCHEMES 212 15.6 COMPUTING THE AVERAGING SCHEMES 214 15.7 SUBDIVISION FOR TRIANGULAR NETS 215 15.8 BOX SPLINES OVER TRIANGULAR GRIDS 218 15.9 SUBDIVISION FOR HEXAGONAL NETS * 219 15.10 HALF-BOX SPLINES OVER TRIANGULAR GRIDS 221 15.11 PROBLEMS - 222 16 STATIONARY SUBDIVISION FOR ARBITRARY NETS 16.1 THE MIDPOINT SCHEME 225 16.2 THE LIMITING SURFACE 227 16.3 THE STANDARD PARAMETRIZATION 229 16.4 THE SUBDIVISION MATRIX 230 16.5 CONTINUITY OF SUBDIVISION SURFACES 231 16.6 THE CHARACTERISTIC MAP 232 16.7 HIGHER ORDER SMOOTHNESS 232 16.8 TRIANGULAR AND HEXAGONAL NETS 234 16.9 PROBLEMS . 235 17 BOX 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 17.10 SPLINES DEFINITION OF BOX SPLINES BOX SPLINES AS SHADOWS PROPERTIES OF BOX SPLINES DERIVATIVES OF BOX SPLINES BOX SPLINE SURFACES SUBDIVISION FOR BOX SPLINE SURFACES CONVERGENCE UNDER SUBDIVISION HALF-BOX SPLINES HALF-BOX SPLINE SURFACES PROBLEMS XIV : CONTENTS III MULTIVARIATE SPLINES 239 240 242 243 244 247 249 251 253 256 18 SIMPLEX SPLINES 18.1 SHADOWS OF SIMPLICES 259 18.2 PROPERTIES OF SIMPLEX SPLINES 260 18.3 NORMALIZED SIMPLEX SPLINES 262 18.4 KNOT INSERTION 263 18.5 A RECURRENCE RELATION 265 18.6 DERIVATIVES 267 18.7 PROBLEMS 268 19 MULTIVARIATE SPLINES 19.1 GENERALIZING DE CASTELJAU S ALGORITHM 271 19.2 B-POLYNOMIALS AND B-PATCHES 273 19.3 LINEAR PRECISION 274 19.4 DERIVATIVES OF A B-PATCH 275 19.5 MULTIVARIATE B-SPLINES 277 19.6 LINEAR COMBINATIONS OF B-SPLINES 279 19.7 A RECURRENCE RELATION 280 19.8 DERIVATIVES OF A SPLINE 282 19.9 THE MAIN THEOREM 283 19.10 PROBLEMS 284 REFERENCES 287 INDEX 297
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spellingShingle	Prautzsch, Hartmut Böhm, Wolfgang 1928-2018 Paluszny, Marco Bezier and B-spline techniques Computer graphics Computer-aided design Spline theory Graphic methods B-Spline (DE-588)4384798-5 gnd Bézier-Fläche (DE-588)4293190-3 gnd Bézier-Kurve (DE-588)4308681-0 gnd
subject_GND	(DE-588)4384798-5 (DE-588)4293190-3 (DE-588)4308681-0
title	Bezier and B-spline techniques
title_auth	Bezier and B-spline techniques
title_exact_search	Bezier and B-spline techniques
title_full	Bezier and B-spline techniques Hartmut Prautzsch ; Wolfgang Boehm ; Marco Paluszny
title_fullStr	Bezier and B-spline techniques Hartmut Prautzsch ; Wolfgang Boehm ; Marco Paluszny
title_full_unstemmed	Bezier and B-spline techniques Hartmut Prautzsch ; Wolfgang Boehm ; Marco Paluszny
title_short	Bezier and B-spline techniques
title_sort	bezier and b spline techniques
topic	Computer graphics Computer-aided design Spline theory Graphic methods B-Spline (DE-588)4384798-5 gnd Bézier-Fläche (DE-588)4293190-3 gnd Bézier-Kurve (DE-588)4308681-0 gnd
topic_facet	Computer graphics Computer-aided design Spline theory Graphic methods B-Spline Bézier-Fläche Bézier-Kurve
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009873331&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT prautzschhartmut bezierandbsplinetechniques AT bohmwolfgang bezierandbsplinetechniques AT palusznymarco bezierandbsplinetechniques

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