LEADER 05438nam 22006854a 450 001 9910953570703321 005 20251116191456.0 010 $a1-281-03630-7 010 $a9786611036300 010 $a0-08-053340-X 035 $a(CKB)1000000000358193 035 $a(EBL)311448 035 $a(OCoLC)476098639 035 $a(SSID)ssj0000167294 035 $a(PQKBManifestationID)12036612 035 $a(PQKBTitleCode)TC0000167294 035 $a(PQKBWorkID)10170067 035 $a(PQKB)10834975 035 $a(Au-PeEL)EBL311448 035 $a(CaPaEBR)ebr10190088 035 $a(CaONFJC)MIL103630 035 $a(CaSebORM)9780444511041 035 $a(MiAaPQ)EBC311448 035 $a(PPN)18384419X 035 $a(EXLCZ)991000000000358193 100 $a20020418d2002 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aHandbook of computer aided geometric design /$fedited by Gerald Farin, Josef Hoschek, Myung-Soo Kim 205 $a1st ed. 210 $aAmsterdam ;$aBoston, Mass. $cElsevier$d2002 215 $a1 online resource (849 p.) 300 $aDescription based upon print version of record. 311 08$a0-444-51104-0 320 $aIncludes bibliographical references and index. 327 $aFront Cover; Handbook of Computer Aided Geometric Design; Copyright Page; Preface; Contents; Contributors; Chapter 1. A History of Curves and Surfaces in CAGD; 1.1. INTRODUCTION; 1.2. EARLY DEVELOPMENTS; 1.3. DE CASTELJAU AND BE?ZIER; 1.4. PARAMETRIC CURVES; 1.5. RECTANGULAR SURFACES; 1.6. B-SPLINE CURVES AND NURBS; 1.7. TRIANGULAR PATCHES; 1.8. SUBDIVISION SURFACES; 1.9. SCIENTIFIC APPLICATIONS; 1.10. SHAPE; 1.11. INFLUENCES AND APPLICATIONS; Chapter 2. Geometric Fundamentals; 2.1. AFFINE FUNDAMENTALS; 2.2. CONIC SECTIONS AND QUADRICS; 2.3. THE EUCLIDEAN SPACE; 2.4. PROJECTIVE FUNDAMENTALS 327 $a2.5. DUALITY2.6. OSCULATING CURVES AND SURFACES; 2.7. DIFFERENTIAL FUNDAMENTALS; Chapter 3. Geometries for CAGD; 3.1. CURVES AND SURFACES IN PROJECTIVE GEOMETRY; 3.2. SPHERE GEOMETRIES; 3.3. LINE GEOMETRY; 3.4. APPROXIMATION IN SPACES OF GEOMETRIC OBJECTS; 3.5. NON-EUCLIDEAN GEOMETRIES; Chapter 4. Be?zier Techniques; 4.1. WHY BE?ZIER TECHNIQUES?; 4.2. BE?ZIER CURVES; 4.3. RECTANGULAR BE?ZIER PATCHES; 4.4. TRIANGULAR BE?ZIER PATCHES; Chapter 5. Rational Techniques; 5.1. INTRODUCTION; 5.2. RATIONAL BE?ZIER CURVES; 5.3. RATIONAL B-SPLINE CURVES; 5.4. GEOMETRIC CONTINUITY FOR RATIONAL CURVES 327 $a5.5. RATIONAL CURVE APPROXIMATION AND INTERPOLATION5.6. RATIONAL BE?ZIER SURFACES; 5.7. RATIONAL B-SPLINE SURFACES; 5.8. GEOMETRIC CONTINUITY FOR RATIONAL PATCHES; 5.9. INTERPOLATION AND APPROXIMATION ALGORITHMS; 5.10. RATIONAL SURFACE CONSTRUCTIONS; 5.11. CONCLUDING REMARKS; Chapter 6. Spline Basics; 6.1. PIECEWISE POLYNOMIALS; 6.2. B-SPLINES DEFINED; 6.3. SUPPORT AND POSITIVITY; 6.4. SPLINE SPACES DEFINED; 6.5. SPECIFIC KNOT SEQUENCES; 6.6. THE POLYNOMIALS IN THE SPLINE SPACE: MARSDEN'S IDENTITY; 6.7. THE PIECEWISE POLYNOMIALS IN THE SPLINE SPACE; 6.8. DUAL FUNCTIONALS AND BLOSSOMS 327 $a6.9. GOOD CONDITION6.10. CONVEX HULL; 6.11. DIFFERENTIATION AND INTEGRATION; 6.12. EVALUATION; 6.13. SPLINE FUNCTIONS VS SPLINE CURVES; 6.14. KNOT INSERTION; 6.15. VARIATION DIMINUTION AND SHAPE PRESERVATION: SCHOENBERG'S OPERATOR; 6.16. ZEROS OF A SPLINE, COUNTING MULTIPLICITY; 6.17. SPLINE INTERPOLATION: SCHOENBERG-WHITNEY; 6.18. SMOOTHING SPLINE; 6.19. LEAST-SQUARES SPLINE APPROXIMATION; 6.20. BACKGROUND; Chapter 7. Curve and Surface Constructions; 7.1. INTRODUCTION; 7.2. POLYNOMIAL CURVE METHODS; 7.3. C2 CUBIC SPLINE INTERPOLATION; 7.4. POLYNOMIAL SURFACE METHODS 327 $a7.5. C2 BICUBIC SPLINE INTERPOLATION7.6. VOLUME DEFORMATIONS; Chapter 8. Geometric Continuity; 8.1. MOTIVATING EXAMPLES; 8.2. GEOMETRIC CONTINUITY OF PARAMETRIC CURVES/SURFACES; 8.3. EQUIVALENT AND ALTERNATIVE DEFINITIONS; 8.4. CONSTRUCTIONS; 8.5. ADDITIONAL LITERATURE; Chapter 9. Splines on Surfaces; 9.1. INTRODUCTION; 9.2. SCALAR SPLINES ON SMOOTH SURFACES; 9.3. ALTERNATIVE METHODS FOR FUNCTIONS ON SURFACES; Chapter 10. Box Splines; 10.1. BOX SPLINES; 10.2. BOX SPLINE SURFACES; 10.3. HALF-BOX SPLINES; 10.4. HALF-BOX SPLINE SURFACES; Chapter 11. Finite Element Approximation with Splines 327 $a11.1. INTRODUCTION 330 $aThis book provides a comprehensive coverage of the fields Geometric Modeling, Computer-Aided Design, and Scientific Visualization, or Computer-Aided Geometric Design. Leading international experts have contributed, thus creating a one-of-a-kind collection of authoritative articles. There are chapters outlining basic theory in tutorial style, as well as application-oriented articles. Aspects which are covered include: Historical outline Curve and surface methods Scientific Visualization Implicit methods Reverse engineering. This book is meant to be a reference te 606 $aComputer graphics 606 $aComputer-aided design 615 0$aComputer graphics. 615 0$aComputer-aided design. 676 $a006.6 701 $aFarin$b Gerald E$030395 701 $aHoschek$b Josef$029650 701 $aKim$b Myung-Soo$051281 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910953570703321 996 $aHandbook of computer aided geometric design$94456903 997 $aUNINA