Table of Contents
The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling
Chapter 1: P. Bézier: How a Simple System Was Born
Chapter 2: Introductory Material
Chapter 3: Linear Interpolation
3.2 Piecewise Linear Interpolation
3.5 Barycentric Coordinates in the Plane
Chapter 4: The de Casteljau Algorithm
4.2 The de Casteljau Algorithm
4.3 Some Properties of Bézier Curves
Chapter 5: The Bernstein Form of a Bézier Curve
5.2 Properties of Bézier Curves
5.3 The Derivatives of a Bézier Curve
5.4 Domain Changes and Subdivision
5.7 The Matrix Form of a Bézier Curve
Chapter 6: Bézier Curve Topics
6.3 The Variation Diminishing Property
6.8 The Bézier Form of a Bézier Curve
6.9 The Weierstrass Approximation Theorem
6.10 Formulas for Bernstein Polynomials
Chapter 7: Polynomial Curve Constructions
7.4 Limits of Lagrange Interpolation
7.5 Cubic Hermite Interpolation
7.6 Quintic Hermite Interpolation
7.7 Point-Normal Interpolation
7.8 Least Squares Approximation
7.10 Designing with Bézier Curves
7.11 The Newton Form and Forward Differencing
Chapter 9: Constructing Spline Curves
9.2 Least Squares Approximation
9.4 C2 Cubic Spline Interpolation
9.8 C1 Piecewise Cubic Interpolation
Chapter 10: W. Boehm: Differential Geometry I
10.1 Parametric Curves and Arc Length
Chapter 11: Geometric Continuity
11.3 The γ, v, and β Formulations
11.5 Interpolating G2 Cubic Splines
11.6 Higher-Order Geometric Continuity
12.1 Projective Maps of the Real Line
12.2 Conics as Rational Quadratics
Chapter 13: Rational Bézier and B-Spline Curves
13.2 The de Casteljau Algorithm
13.5 Reparametrization and Degree Elevation
13.7 Rational Cubic B-Spline Curves
13.8 Interpolation with Rational Cubics
13.9 Rational B-Splines of Arbitrary Degree
Chapter 14: Tensor Product Patches
14.2 The Direct de Casteljau Algorithm
14.3 The Tensor Product Approach
14.11 The Matrix Form of a Bézier Patch
Chapter 15: Constructing Polynomial Patches
15.4 Tensor Product Interpolation
15.9 A Problem with Unstructured Data
Chapter 16: Composite Surfaces
16.1 Smoothness and Subdivision
16.2 Tensor Product B-Spline Surfaces
16.4 Bicubic Spline Interpolation
16.6 Rational Bézier and B-Spline Surfaces
16.9 CONS and Trimmed Surfaces
17.1 The de Casteljau Algorithm
Chapter 18: Practical Aspects of Bézier Triangles
18.1 Rational Bézier Triangles
18.4 Cubic and Quintic Interpolants
18.5 The Clough–Tocher Interpolant
18.6 The Powell–Sabin Interpolant
Chapter 19: W. Boehm: Differential Geometry II
19.1 Parametric Surfaces and Arc Element
19.3 The Curvature of a Surface Curve
19.6 Gaussian and Mean Curvature
19.9 Asymptotic Lines and Conjugate Directions
19.10 Ruled Surfaces and Developables
Chapter 20: Geometric Continuity for Surfaces
20.5 “Filling in” Rectangular Patches
20.6 “Filling in” Triangular Patches
Chapter 21: Surfaces with Arbitrary Topology
21.1 Recursive Subdivision Curves
21.3 Catmull–Clark Subdivision
21.7 Interpolating Subdivision Surfaces
22.1 Coons Patches: Bilinearly Blended
22.2 Coons Patches: Partially Bicubically Blended
22.3 Coons Patches: Bicubically Blended
23.2 Curve and Surface Smoothing
Chapter 24: Evaluation of Some Methods
24.1 Bézier Curves or B-Spline Curves?
24.2 Spline Curves or B-Spline Curves?
24.3 The Monomial or the Bézier Form?
24.4 The B-Spline or the Hermite Form?
24.5 Triangular or Rectangular Patches?