by
David F. Rogers
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An Introduction to NURBS
by David F. Rogers |
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| Chapter 1 Curve and Surface Representation |
| Chapter 2 Bezier Curves |
| Chapter 3 B-spline Curves |
| Chapter 4 Rational B-spline Curves |
| Chapter 5 Bezier Surfaces |
| Chapter 6 B-spline Surfaces |
| Chapter 7 Rational B-spline Surfaces |
| Appendices |
| Preface | ||
| Chapter 1 Curve and Surface Representation | ||
| 1.1 | Introduction | |
| 1.2 | Parametric Curves | |
| Extension to Three Dimensions | ||
| Parametric Line | ||
| 1.3 | Parametric Surfaces | |
| 1.4 | Piecewise Surfaces | |
| 1.5 | Continuity | |
| Geometric Continuity | ||
| Parametric Continuity | ||
| Historical Perspective | ||
Bezier Curves: Robin Forrest
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| Chapter 2 Bezier Curves | ||
| 2.1 | Bezier Curve Definition | |
| Bezier Curve Algorithm | ||
| 2.2 | Matrix Representation of Bezier Curves | |
| 2.3 | Bezier Curve Derivatives | |
| 2.4 | Continuity Between Bezier Curves | |
| 2.5 | Increasing the Flexibility of Bezier Curves | |
| Degree Elevation | ||
| Subdivision | ||
| Historical Perspective | ||
| Biography: Pierre Bezier | ||
| B-splines: Rich Riesenfeld
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| Chapter 3 B-spline Curves | ||
| 3.1 | B-spline Curve Definition | |
| Properties of B-spline Curves | ||
| 3.2 | Convex Hull Properties of B-spline Curves | |
| 3.3 | Knot Vectors | |
| 3.4 | B-spline Basis Functions | |
| B-spline Curve Controls | ||
| 3.5 | Open B-spline Curves | |
| 3.6 | Nonuniform B-spline Curves | |
| 3.7 | Periodic B-spline Curves | |
| 3.8 | Matrix Formulation of B-spline Curves | |
| 3.9 | End Conditions for Periodic B-spline Curves | |
| Start and End Points | ||
| Start and End Point Derivatives | ||
| Controlling Start and End Points | ||
| Multiple Coincident Vertices | ||
| Pseudovertices | ||
| 3.10 | B-spline Curve Derivatives | |
| 3.11 | B-spline Curve Fitting | |
| 3.12 | Degree Elevation | |
| Algorithms | ||
| 3.13 | Degree Reduction | |
| Bezier Curve Degree Reduction | ||
| 3.14 | Knot Insertion and B-spline Curve Subdivision | |
| 3.15 | Knot Removal | |
| Pseudocode | ||
| 3.16 | Reparameterization | |
| Historical Perspective | ||
| Subdivision: Elaine Cohen, Tom Lyche and Rich Riesenfeld
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| Chapter 4 Rational B-spline Curves | ||
| 4.1 | Rational B-spline Curves (NURBS) | |
| Characteristics of NURBS | ||
| 4.2 | Rational B-spline Basis Functions and Curves | |
| Open Rational B-spline Basis Functions and Curves | ||
| Periodic Rational B-spline Basis Functions and Curves | ||
| 4.3 | Calculating Rational B-spline Curves | |
| 4.4 | Derivatives of NURBS Curves | |
| 4.5 | Conic Sections | |
| Historical Perspective | ||
| Rational B-splines: Lewis Knapp
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| Chapter 5 Bezier Surfaces | ||
| 5.1 | Mapping Parametric Surfaces | |
| 5.2 | Bezier Surface Definition and Characteristic | |
| Matrix Representation | ||
| 5.3 | Bezier Surface Derivatives | |
| 5.4 | Transforming Between Surface Descriptions | |
| Historical Perspective | ||
| Nonuniform Rational B-splines: Ken Versprill
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| Chapter 6 B-spline Surfaces | ||
| 6.1 | B-spline Surfaces | |
| 6.2 | Convex Hull Properties | |
| 6.3 | Local Control | |
| 6.4 | Calculating Open B-spline Surfaces | |
| 6.5 | Periodic B-spline Surfaces | |
| 6.6 | Matrix Formulation of B-spline Surfaces | |
| 6.7 | B-spline Surface Derivatives | |
| 6.8 | B-spline Surface Fitting | |
| 6.9 | B-spline Surface Subdivision | |
| 6.10 | Gaussian Curvature and Surface Fairness | |
| Historical Perspective | ||
| Implementation: Al Adams and Dave Rogers
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| Chapter 7 Rational B-spline Surfaces | ||
| 7.1 | Rational B-spline Surfaces (NURBS) | |
| 7.2 | Characteristics of Rational B-spline Surfaces | |
| Positive Homogeneous Weighting Factors | ||
| Negative Homogeneous Weighting Factors | ||
| Internally Nonuniform Knot Vector | ||
| Reparameterization | ||
| 7.3 | A Simple Rational B-spline Surface Algorithm | |
| 7.4 | Derivatives of Rational B-spline Surfaces | |
| 7.5 | Bilinear Surfaces | |
| 7.6 | Sweep Surfaces | |
| 7.7 | Ruled Rational B-spline Surfaces | |
| Developable Surfaces | ||
| 7.8 | Surfaces of Revolution | |
| 7.9 | Blending Surfaces | |
| 7.10 | A Fast Rational B-spline Surface Algorithm | |
| Naive Algorithms | ||
| A More Efficient Algorithm | ||
| Incremental Surface Calculation | ||
| Measure of Computational Effort
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| Appendices | ||
| A | B-spline Surface File Format | |
| B | Problems | |
| C | Algorithms
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| References | ||
| Index | ||
| About the Author | ||
| Front Cover | Back Cover | About the Author |
| Sample Worked Example | C Code |
| Reviewer Comments |
| Order |
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