Les Piegl Wayne Tiller. The NURBS Book. Second Edition with 334 Figures in 578 Parts. A) Springer

Transcription

1 Les Piegl Wayne Tiller The NURBS Book Second Edition with 334 Figures in 578 Parts A) Springer

2 CONTENTS Curve and Surface Basics 1.1 Implicit and Parametric Forms Power Basis Form of a Curve Bezier Curves Rational Bezier Curves Tensor Product Surfaces 34 Exercises 43 CHAPTER ONE B-Spline Basis Functions 2.1 Introduction Definition and Properties of B-spline Basis Functions Derivatives of B-spline Basis Functions Further Properties of the Basis Functions Computational Algorithms 67 Exercises 78 CHAPTER TWO B-spline Curves and Surfaces 3.1 Introduction The Definition and Properties of B-spline Curves The Derivatives of a B-spline Curve Definition and Properties of B-spline Surfaces Derivatives of a B-spline Surface 110 Exercises 116 CHAPTER THREE Rational B-spline Curves and Surfaces 4.1 Introduction Definition and Properties of NURBS Curves Derivatives of a NURBS Curve Definition and Properties of NURBS Surfaces Derivatives of a NURBS Surface 136 Exercises 138 CHAPTER FOUR

3 xii Contents Fundamental Geometric Algorithms 5.1 Introduction Knot Insertion Knot Refinement Knot Removal Degree Elevation Degree Reduction 212 Exercises 227 CHAPTER FIVE Advanced Geometric Algorithms 6.1 Point Inversion and Projection for Curves and Surfaces Surface Tangent Vector Inversion Transformations and Projections of Curves and Surfaces Reparameterization of NURBS Curves and Surfaces Curve and Surface Reversal Conversion Between B-spline and Piecewise Power Basis Forms. 265 Exercises 279 CHAPTER SIX Conies and Circles 7.1 Introduction Various Forms for Representing Conies The Quadratic Rational Bezier Arc Infinite Control Points Construction of Circles Construction of Conies Conic Type Classification and Form Conversion Higher Order Circles 326 Exercises 330 CHAPTER SEVEN Construction of Common Surfaces 8.1 Introduction Bilinear Surfaces The General Cylinder The Ruled Surface The Surface of Revolution Nonuniform Scaling of Surfaces A Three-sided Spherical Surface 351 CHAPTER EIGHT Curve and Surface Fitting 9.1 Introduction Global Interpolation Global Curve Interpolation to Point Data Global Curve Interpolation with End Derivatives Specified Cubic Spline Curve Interpolation 371 CHAPTER NINE

4 Contents xiii Global Curve Interpolation with First Derivatives Specified Global Surface Interpolation Local Interpolation Local Curve Interpolation Preliminaries Local Parabolic Curve Interpolation Local Rational Quadratic Curve Interpolation Local Cubic Curve Interpolation Local Bicubic Surface Interpolation Global Approximation Least Squares Curve Approximation Weighted and Constrained Least Squares Curve Fitting Least Squares Surface Approximation Approximation to Within a Specified Accuracy Local Approximation Local Rational Quadratic Curve Approximation Local Nonrational Cubic Curve Approximation 441 Exercises 452 Advanced Surface Construction Techniques 10.1 Introduction Swung Surfaces Skinned Surfaces Swept Surfaces Interpolation of a Bidirectional Curve Network Coons Surfaces 496 CHAPTER TEN Shape Modification Tools 11.1 Introduction Control Point Repositioning Weight Modification Modification of One Curve Weight Modification of Two Neighboring Curve Weights Modification of One Surface Weight Shape Operators Warping Flattening Bending Constraint-based Curve and Surface Shaping Constraint-based Curve Modification Constraint-based Surface Modification 562 CHAPTER ELEVEN Standards and Data Exchange 12.1 Introduction Knot Vectors Nurbs Within the Standards 580 CHAPTER TWELVE

5 xiv Contents IGES STEP PHIGS Data Exchange to and from a NURBS System 586 B-spline Programming Concepts 13.1 Introduction Data Types and Portability Data Structures Memory Allocation Error Control Utility Routines Arithmetic Routines Example Programs Additional Structures System Structure 626 CHAPTER THIRTEEN References 629 Index 641