The NURBS Book

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Springer, Jan 1, 1997 - Computers - 646 pages
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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
  

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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 ... Read full review

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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
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

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
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
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Piegl la,, Tiller W. — The NURBS Book (Monographs in Visual ...
Название: The NURBS Book (Monographs in Visual Communication) Авторы: Piegl la,, Tiller W. Аннотация:. The second, revised edition of this book covers all ...
lib.mexmat.ru/ books/ 4302

The NURBS book
The NURBS book. Purchase this Book. Source. Pages: 646. Year of Publication: 1995. ISBN:3-540-55069-0. Authors. Les Piegl, Univ. of South Florida, Tampa ...
portal.acm.org/ citation.cfm?id=208469& dl=

The NUNBS Book
Welcome to the The NURBS Book, a publication of Springer-Verlag. The book covers all geometrical and algorithmic aspects of (Non-Uniform Rational B-splines) ...
www.cse.usf.edu/ ~lap/ nurbs.htm

NURBS Toolbox
For a detailed explanation of NURBS and how to manipulate them, I can strongly recommend the book by Les Piegl and Wayne Tiller called 'The NURBS Book' ISBN ...
www.aria.uklinux.net/ nurbs.php3

Infoscience: Record #25483: The Nurbs book
infoscience. subtitle. Français | English. EPFL > infoscience > Record #25483: The Nurbs book. My actions. Identification. Identification ...
infoscience.epfl.ch/ record/ 25483

DIVERSITY IN GRAPHICS RESEARCH AT USF Dr. Les A. Piegl
of the best selling text, THE NURBS BOOK, published by Springer-Verlag. Dr. Piegl has been Editor-in-Chief. of COMPUTER-AIDED DESIGN (CAD) in the last ...
www.cs.hku.hk/ seminars/ 2003/ 030226b.pdf

sciencedirect - Computer-Aided Design : Splines with Pictures and ...
While The NURBS book by Piegl and Tiller [1], reviewed in 1996 in CAD, goes into greater detail by including pieces of code, and de Boor's B-form basics [2] ...
linkinghub.elsevier.com/ retrieve/ pii/ S0010448502001094

Notes: Code is based on the Piegl Nurbs book. The NURBS Book, Les ...
The NURBS Book, Les Piegl and Wayne Tiller, Springer 1997 */ #define GNURBS_MAX_ORDER 16 // // find span - see the NURBS Book // page 68 // int findspan ...
developer.blaxxun.com/ developer/ contact/ 3d/ nurbs/ spec/ gnurbsutil.cpp

thenurbsbook
The NURBS Book by Les Piegl and Wayne Tiller. Springer-Verlag, 1997, 646 pages, 333 figures. ISBN 3-540-61545-8. Table of Contents. Curve and surface basics ...
www.piegl.com/ TheNURBSBook.html

B-SPLINES AND NURBS CURVES AND SURFACES
Piegl, L. and Tiller, W: The NURBS Book, 2nd. Edition, Springer Verlag Berlin, 1997. NURBS surfaces are included here as a particular case. However, some ...
personales.unican.es/ iglesias/ CD-CG/ Bsplines.pdf

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