The NURBS Book /
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...
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| Online Access: |
Full text (MCPHS users only) |
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| Main Author: | |
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg,
1997
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| Edition: | Second edition. |
| Series: | Monographs in visual communication.
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| Subjects: | |
| Local Note: | ProQuest Ebook Central |
Table of Contents:
- 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
- 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
- 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
- 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
- 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
- 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
- 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 Conies
- 7.7 Conic Type Classification and Form Conversion
- 7.8 Higher Order Circles
- Exercises
- 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
- Nine Curve and Surface Fitting
- 9.1 Introduction
- 9.2 Global Interpolation
- 9.3 Local Interpolation
- 9.4 Global Approximation
- 9.5 Local Approximation
- Exercises
- 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
- Eleven Shape Modification Tools
- 11.1 Introduction
- 11.2 Control Point Repositioning
- 11.3 Weight Modification
- 11.4 Shape Operators
- 11.5 Constraint-based Curve and Surface Shaping
- Twelve Standards and Data Exchange
- 12.1 Introduction
- 12.2 Knot Vectors
- 12.3 Nurbs Within the Standards
- 12.4 Data Exchange to and from a NURBS System
- 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.
