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the nurbs book 2nd.pdf

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    COVER
    Forword
    Preface
    Contents
    Chapter ONE Curve and Surface Basics
    1.1 Implicit and Parametric Forms
    1.2 Power Basis Form of a Curve
    1.3 Bézier Curves
    1.4 Rational Bézier Curves
    1.5 Tensor Product Surfaces
    Exercises
    Chapter TWO B-Spline Basis Functions
    2.1 Introduction
    2.2 Definition and Properties of B-spline Basis Functions
    2.3 Derivatives of B-spline Basis Functions
    2.4 Further Properties of the Basis Functions
    2.5 Computational Algorithms
    Exercises
    Chapter THREE B-spline Curves and Surfaces
    3.1 Introduction
    3.2 The Definition and Properties of B-spline Curves
    3.3 The Derivatives of a B-spline Curve
    3.4 Definition and Properties of B-spline Surfaces
    3.5 Derivatives of a B-spline Surface
    Exercises
    Chapter FOUR Rational B-spline Curves and Surfaces
    4.1 Introduction
    4.2 Definition and Properties of NURBS Curves
    4.3 Derivatives of a NURBS Curve
    4.4 Definition and Properties of NURBS Surfaces
    4.5 Derivatives of a NURBS Surface
    Exercises
    Chapter FIVE Fundamental Geometric Algorithms
    5.1 Introduction
    5.2 Knot Insertion
    5.3 Knot Refinement
    5.4 Knot Removal
    5.5 Degree Elevation
    5.6 Degree Reduction
    Exercises
    Chapter SIX Advanced Geometric Algorithms
    6.1 Point Inversion and Projection for Curves and Surfaces
    6.2 Surface Tangent Vector Inversion
    6.3 Transformations and Projections of Curves and Surfaces
    6.4 Reparameterization of NURBS Curves and Surfaces
    6.5 Curve and Surface Reversal
    6.6 Conversion Between B-spline and Piecewise Power Basis Forms
    Exercises
    Chapter SEVEN Conics and Circles
    7.1 Introduction
    7.2 Various Forms for Representing Conics
    7.3 The Quadratic Rational Bézier Arc
    7.4 Infinite Control Points
    7.5 Construction of Circles
    7.6 Construction of Conics
    7.7 Conic Type Classification and Form Conversion
    7.8 Higher Order Circles
    Exercises
    Chapter EIGHT Construction of Common Surfaces
    8.1 Introduction
    8.2 Bilinear Surfaces
    8.3 The General Cylinder
    8.4 The Ruled Surface
    8.5 The Surface of Revolution
    8.6 Nonuniform Scaling of Surfaces
    8.7 A Three-sided Spherical Surface
    Chapter NINE Curve and Surface Fitting
    9.1 Introduction
    9.2 Global Interpolation
    9.2.1 GLOBAL CURVE INTERPOLATION TO POINT DATA
    9.2.2 GLOBAL CURVE INTERPOLATION WITH END DERIVATIVES SPECIFIED
    9.2.3 CUBIC SPLINE CURVE INTERPOLATION
    9.2.4 GLOBAL CURVE INTERPOLATION WITH FIRST DERIVATIVES SPECIFIED
    9.2.5 GLOBAL SURFACE INTERPOLATION
    9.3 Local Interpolation
    9.3.1 LOCAL CURVE INTERPOLATION PRELIMINARIES
    9.3.2 LOCAL PARABOLIC CURVE INTERPOLATION
    9.3.3 LOCAL RATIONAL QUADRATIC CURVE INTERPOLATION
    9.3.4 LOCAL CUBIC CURVE INTERPOLATION
    9.3.5 LOCAL BICUBIC SURFACE INTERPOLATION
    9.4 Global Approximation
    9.4.1 LEAST SQUARES CURVE APPROXIMATION
    9.4.2 WEIGHTED AND CONSTRAINED LEAST SQUARES CURVE FITTING
    9.4.3 LEAST SQUARES SURFACE APPROXIMATION
    9.4.4 APPROXIMATION TO WITHIN ASPECIFIED ACCURACY
    9.5 Local Approximation
    9.5.1 LOCAL RATIONAL QUADRATIC CURVE APPROXIMATION
    9.5.2 LOCAL NONRATIONAL CUBIC CURVE APPROXIMATION
    Exercises
    Chapter TEN Advanced Surface Construction Techniques
    10.1 Introduction
    10.2 Swung Surfaces
    10.3 Skinned Surfaces
    10.4 Swept Surfaces
    10.5 Interpolation of a Bidirectional Curve Network
    10.6 Coons Surfaces
    Chapter ELEVEN Shape Modification Tools
    11.1 Introduction
    11.2 Control Point Repositioning
    11.3 Weight Modification
    11.3.1 MODIFICATION OF ONE CURVE WEIGHT
    11.3.2 MODIFICATION OF TWO NEIGHBORING CURVE WEIGHTS
    11.3.3 MODIFICATION OF ONE SURFACE WEIGHT
    11.4 Shape Operators
    11.4.1 WARPING
    11.4.2 FLATTENING
    11.4.3 BENDING
    11.5 Constraint-based Curve and Surface Shaping
    11.5.1 CONSTRAINT-BASED CURVE MODIFICATION
    11.5.2 CONSTRAINT-BASED SURFACE MODIFICATION
    Chapter TWELVE Standards and Data Exchange
    12.1 Introduction
    12.2 Knot Vectors
    12.3 NURBS Within the Standards
    12.3.1 IGES
    12.3.2 STEP
    12.3.3 PRIGS
    12.4 Data Exchange to and from a NURBS System
    Chapter THIRTEEN B-spline Programming Concepts
    13.1 Introduction
    13.2 Data Types and Portability
    13.3 Data Structures
    13.4 Memory Allocation
    13.5 Error Control
    13.6 Utility Routines
    13.7 Arithmetic Routines
    13.8 Example Programs
    13.9 Additional Structures
    13.10 System Structure
    References
    Index
    Springer Berlin Heidelberg New York Barcelona Budapest Hong Kong London Milan Paris Singapore Tokyo
    Les Piegl Wayne Tiller The NURBS Book Second Edition with 334 Figures in 578 Parts Springer
    Prof. Dr. Les Piegl University of South Florida Department of Computer Science and Engineering Fowler Avenue, ENG uS Tampa, FL 33620-5399, USA Dr. Wayne Tiller GeomWare, Inc. 3036 Ridgetop Road Tyler, TX75703-89o6, USA ISBN 3-540-61545-8 2nd ed. Springer-Verlag Berlin Heidelberg New York ISBN 3-540-55069-0 1st ed. Springer-Verlag Berlin Heidelberg New York Cip data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Piegl, Les: The NURBS book I Les Piegl; Wayne Tiller.- 2. ed.- Berlin ; Heidelberg; New York; Barcelona; Budapest; Hong Kong; London; Milan; Paris; Tokyo: Springer, 1997 (Monographs in visual communications) ISBN 3-540-61545-8 NE: Tiller, Wayne This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfllm or in other ways, and storage in data banks. Duplication of this publication or parts thereofis permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Verlag. Violations are liable for prosecution act under German Copyright Law. © Springer-Verlag Berlin Heidelberg 1995 and 1997 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: Design & Production, Heidelberg Typsesetting: Nancy A. Rogers, NAR Assoc., Annapolis, MD, using TEX SPIN: 10691934 33/3020-5 4 3 2- Printed on acid -free paper
    To the memory of my mother Anna, and to my father Janos L.P. To my grandmother, Fern Melrose Bost, and to the memories of my grandparents, James Raney Bost, Pearl Weeks Tiller, and Albert Carroll Tiller W.T.
    FOREWORD Until recently B-spline curves and surfaces (NURBS) were principally of interest to the computer aided design community, where they have become the standard for curve and surface description. Today we are seeing expanded use of NURBS in modeling objects for the visual arts, including the film and entertainment industries, art, and sculpture. NURBS are now also being used for modeling scenes for virtual reality applications. These applications are expected to increase. Consequently, it is quite appropriate for The NURBS Book to be part of the Monographs in Visual Communication Series. B-spline curves and surfaces have been an enduring element throughout my pro fessional life. The first edition of Mathematical Elements for Computer Graphics, published in 1972, was the first computer aided design/interactive computer graph ics textbook to contain material on B-splines. That material was obtained through the good graces of Bill Gordon and Louie Knapp while they were at Syracuse University. A paper of mine, presented during the Summer of 1977 at a Society of Naval Architects and Marine Engineers meeting on computer aided ship surface design, was arguably the first to examine the use of B-spline curves for ship design. For many, B-splines, rational B-splines, and NURBS have been a bit mysterious. Consequently, for the last several years a thorough, detailed, clearly written, and easily understood book on B-splines and rational B-splines has been needed. Thus, it was with considerable anticipation that I awaited Les Piegl and Wayne Tiller's book. I was not disappointed: They have elegantly and fully satisfied that need with The .NURBS Book. In developing the material for the book, they draw from their considerable academic and industrial experience with NURBS to present this rather complex subject in a straightforward manner: Their presentation style is clear and detailed. The necessary mathematics is presented with considerable attention to detail and more than adequate rigor. The algorithms (many of which are in C-like pseudocode) are well thought out and meticulously prepared. In the interests of accuracy, each and every illustration in the book was computer generated - a monumental task. They have created a book of lasting value. B-spline curves and surfaces grew out of the pioneering work of Pierre Bezier in the early 1970s. Perhaps one can consider B-spline curves and surfaces the children of Bezier curves and surfaces, and nonuniform rational B-splines, or NURBS, the grand children. The timing is about right; they have certainly come of age. Finally, it is only appropriate to acknowledge my pleasure in working with both Les Piegl and Wayne Tiller to bring this project to fruition. David F. Rogers Series Editor Monographs in Visual Communication
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