- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- Contributors
- Chapter 1: A History of Curves and Surfaces in CAGD
- Chapter 2: Geometric Fundamentals
- Chapter 3: Geometries for CAGD
- Chapter 4: Bézier Techniques
- Chapter 5: Rational Techniques
- 5.1 INTRODUCTION
- 5.2 RATIONAL B éZIER CURVES
- 5.3 RATIONAL B-SPLINE CURVES
- 5.4 GEOMETRIC CONTINUITY FOR RATIONAL CURVES
- 5.5 RATIONAL CURVE APPROXIMATION AND INTERPOLATION
- 5.6 RATIONAL B éZIER SURFACES
- 5.7 RATIONAL B-SPLINE SURFACES
- 5.8 GEOMETRIC CONTINUITY FOR RATIONAL PATCHES
- 5.9 INTERPOLATION AND APPROXIMATION ALGORITHMS
- 5.10 RATIONAL SURFACE CONSTRUCTIONS
- 5.11 CONCLUDING REMARKS
- Chapter 6: Spline Basics
- 6.1 PIECEWISE POLYNOMIALS
- 6.2 B-SPLINES DEFINED
- 6.3 SUPPORT AND POSITIVITY
- 6.4 SPLINE SPACES DEFINED
- 6.5 SPECIFIC KNOT SEQUENCES
- 6.6 THE POLYNOMIALS IN THE SPLINE SPACE: MARSDEN ’S IDENTITY
- 6.7 THE PIECEWISE POLYNOMIALS IN THE SPLINE SPACE
- 6.8 DUAL FUNCTIONALS AND BLOSSOMS
- 6.9 GOOD CONDITION
- 6.10 CONVEX HULL
- 6.11 DIFFERENTIATION AND INTEGRATION
- 6.12 EVALUATION
- 6.13 SPLINE FUNCTIONS VS SPLINE CURVES
- 6.14 KNOT INSERTION
- 6.15 VARIATION DIMINUTION AND SHAPE PRESERVATION: SCHOENBERG’S OPERATOR
- 6.16 ZEROS OF A SPLINE, COUNTING MULTIPLICITY
- 6.17 SPLINE INTERPOLATION: SCHOENBERG-WHITNEY
- 6.18 SMOOTHING SPLINE
- 6.19 LEAST-SQUARES SPLINE APPROXIMATION
- BACKGROUND 6.20.
- Chapter 7: Curve and Surface Constructions
- Chapter 8: Geometric Continuity
- Chapter 9: Splines on Surfaces
- Chapter 10: Box Splines
- Chapter 11: Finite Element Approximation with Splines
- Chapter 12: Subdivision Surfaces
- Chapter 13: Interrogation of Subdivision Surfaces
- Chapter 14: Multiresolution Techniques
- Chapter 15: Algebraic Methods for Computer Aided Geometric Design
- Chapter 16: Scattered Data Interpolation: Radial Basis and Other Methods
- Chapter 17: Pythagorean-Hodograph Curves
- Chapter 18: Voronoi Diagrams
- Chapter 19: The Medial Axis Transform
- Chapter 20: Solid Modeling
- Chapter 21: Parametric Modeling
- Chapter 22: Sculptured Surface NC Machining
- Chapter 23: Cyclides
- Chapter 24: Geometry Processing
- Chapter 25: Intersection Problems
- Chapter 26: Reverse Engineering
- Chapter 27: Vector and Tensor Field Visualization
- Chapter 28: Splines over Triangulations
- Chapter 29: Kinematics and Animation
- Chapter 30: Direct Rendering of Freeform Surfaces
- Chapter 31: Modeling and Processing with Quadric Surfaces
- Index
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