The NURBs Book

Les Piegl, Wayne Tiller

Springer, 1997 - Computers - 646 pages

The NURBS book covers all aspects of non-uniform rational B-splines necessary to design geometry in a computer aided environment. Basic B-spline features, curve and surface algorithms, and state-of-the-art geometry tools are all discussed. Detailed code for design algorithms and computational tricks are covered too, in a lucid, easy-to-understand style, with a minimum of mathematics and using numerous worked examples. The book is a must for students, researchers, and implementors whose work involves the use of splines. "Some years ago a few researchers joked about NURBS, saying that the acronym really stands for Nobody Understands Rational B-Splines write the authors in their foreword; they formulate the aim of changing NURBS to EURBS, that is, Everybody ... . There is no doubt that they have achieved this goal. ... ... I highly recommend the book to anyone who is interested in a detailed description of NURBS. It is extremely helpful for students, teachers and designers of geometric modelling systems. ..." - H. Pottmann, Computer Aided Design, 1996

What people are saying

Review: The Nurbs Book

User Review  - Austin - Goodreads

This is one of those books that seems to preclude the writing of any further books on the topic. It is the resource on the subject of NURBS, bar none. I cannot overstate the utility of this book to me ...

Review: The Nurbs Book

User Review  - Greg - Goodreads

This taught me everything I needed to be able to understand and use non-uniform rational bsplines for my work. I didn't need quite all the detail in the book - I'm not designing a nurbs library, just ...

Contents

• Curve and Surface Basics: 1
• 12 Power Basis Form of a Curve: 5
• 13 Bezier Curves: 9
• 14 Rational Bezier Curves: 25
• 15 Tensor Product Surfaces: 34
• EXERCISES: 43
• BSpline Basis Functions: 47
• 22 Definition and Properties of Bspline Basis Functions: 50
• 23 Derivatives of Bspline Basis Functions The derivative of a basis function is given by: 59
• 24 Further Properties of the Basis Functions: 63
• 25 Computational Algorithms: 67
• EXERCISES: 78
• Bspline Curves and Surfaces: 81
• 33 The Derivatives of a Bspline Curve: 91
• 34 Definition and Properties of Bspline Surfaces: 100
• 35 Derivatives of a Bspline Surface: 110
• EXERCISES: 116
• Rational Bspline Curves and Surfaces: 117
• 43 Derivatives of a NURBS Curve: 125
• 44 Definition and Properties of NURBS Surfaces: 128
• 45 Derivatives of a NURBS Surface: 136
• EXERCISES: 138
• Fundamental Geometric Algorithms: 141
• 53 Knot Refinement: 161
• 54 Knot Removal: 178
• 55 Degree Elevation: 187
• 56 Degree Reduction: 211
• EXERCISES: 226
• Advanced Geometric Algorithms: 228
• 62 Surface Tangent Vector Inversion: 234
• 63 Transformations and Projections of Curves and Surfaces: 235
• 64 Reparameterization of NURBS Curves and Surfaces: 240
• 65 Curve and Surface Reversal: 262
• 66 Conversion Between Bspline and Piecewise Power Basis Forms: 264
• EXERCISES: 278
• 73 The Quadratic Rational Bezier Arc: 290
• 74 Infinite Control Points: 294
• 75 Construction of Circles: 297
• 76 Construction of Conies: 309
• 77 Conic Type Classification and Form Conversion: 319
• 78 Higher Order Circles: 325
• EXERCISES: 329
• 83 The General Cylinder: 333
• 84 The Ruled Surface: 336
• 85 The Surface of Revolution: 339
• 86 Nonuniform Scaling of Surfaces: 347
• 87 A Threesided Spherical Surface: 350
• Curve and Surface Fitting: 360
• 92 Global Interpolation: 363
• 922 GLOBAL CURVE INTERPOLATION WITH END DERIVATIVES SPECIFIED: 369
• 923 CUBIC SPLINE CURVE INTERPOLATION: 370
• 924 GLOBAL CURVE INTERPOLATION WITH FIRST DERIVATIVES SPECIFIED: 372
• 925 GLOBAL SURFACE INTERPOLATION: 375
• 93 Local Interpolation: 381
• 932 LOCAL PARABOLIC CURVE INTERPOLATION: 387
• 933 LOCAL RATIONAL QUADRATIC CURVE INTERPOLATION: 391
• 934 LOCAL CUBIC CURVE INTERPOLATION: 394
• 935 LOCAL BICUBIC SURFACE INTERPOLATION: 398
• 94 Global Approximation: 404
• 941 LEAST SQUARES CURVE APPROXIMATION: 406
• 942 WEIGHTED AND CONSTRAINED LEAST SQUARES CURVE FITTING: 412
• 943 LEAST SQUARES SURFACE APPROXIMATION: 418
• 944 APPROXIMATION TO WITHIN A SPECIFIED ACCURACY: 423
• 95 Local Approximation: 436
• 951 LOCAL RATIONAL QUADRATIC CURVE APPROXIMATION: 437
• 952 LOCAL NONRATIONAL CUBIC CURVE APPROXIMATION: 440
• EXERCISES: 451
• 103 Skinned Surfaces: 456
• 104 Swept Surfaces: 471
• 105 Interpolation of a Bidirectional Curve Network: 484
• 106 Coons Surfaces: 495
• 112 Control Point Repositioning: 510
• 113 Weight Modification: 517
• 1131 MODIFICATION OF ONE CURVE WEIGHT: 519
• 1132 MODIFICATION OF TWO NEIGHBORING CURVE WEIGHTS: 525
• 1133 MODIFICATION OF ONE SURFACE WEIGHT: 530
• 114 Shape Operators: 532
• 1142 FLATTENING: 541
• 1143 BENDING: 546
• 115 Constraintbased Curve and Surface Shaping: 554
• 1152 CONSTRAINTBASED SURFACE MODIFICATION: 561
• 123 NURBS Within the Standards: 579
• l232 STEP: 582
• 1233 PHIGS: 584
• 124 Data Exchange to and from a NURBS System: 585
• 132 Data Types and Portability: 593
• 133 Data Structures: 595
• 134 Memory Allocation: 600
• 135 Error Control: 606
• 136 Utility Routines: 612
• 137 Arithmetic Routines: 615
• 138 Example Programs: 617
• 139 Additional Structures: 622
• 1310 System Structure: 625
• REFERENCES: 628

Bibliographic information

• Title: The NURBs Book; Monographs in visual communications
• Authors: Les Piegl, Wayne Tiller
• Edition: 2, illustrated
• Publisher: Springer, 1997
• ISBN: 3540615458, 9783540615453
• Length: 646 pages
• Subjects: Computers / CAD-CAM; Computers / Computer Graphics