A Blossoming Development of Splines: Table of Contents

• Preface
• Chapter 1 Introduction and Background
  • Section 1.1 Mathematical Background
    • subSection 1.1.1 Why Affine Geometry?
    • subSection 1.1.2 Exercises
• Chapter 2 Polynomial Curves
  • Section 2.1 Implementations
  • Section 2.2 Bernstein Polynomials and B\351zier Curves
    • subSection 2.2.1 Exercises
  • Section 2.3 Blossoming
    • subSection 2.3.1 de Casteljau Revisited
    • subSection 2.3.2 Degree Raising
    • subSection 2.3.3 Functional B\351zier Curves
    • subSection 2.3.4 Exercises
    • subSection 2.3.5 Implementations
  • Section 2.4 Multilinear Blossom
    • subSection 2.4.1 Exercises
  • Section 2.5 Derivatives of B\351zier Curves
    • subSection 2.5.1 Exercises
  • Section 2.6 Continuity
    • subSection 2.6.1 Cubic Hermite Interpolation
    • subSection 2.6.2 C1 Continuity and the Blossom
    • subSection 2.6.3 C2 Continuity
    • subSection 2.6.4 Ck Continuity
    • subSection 2.6.5 Exercises
  • Section 2.7 Change of Basis
  • Section 2.8 Exercises
  • Section 2.9 Fast Evaluation
    • subSection 2.9.1 Exercises
    • subSection 2.9.2 Implementations
• Chapter 3 B-splines
  • Section 3.1 Implementations
  • Section 3.2 Knot Multiplicity
    • subSection 3.2.1 Exercises
    • subSection 3.2.2 Implementations
  • Section 3.3 Triangle Diagrams
    • subSection 3.3.1 Exercises
  • Section 3.4 Knot Insertion
    • subSection 3.4.1 Implementations
  • Section 3.5 B-spline Basis Functions
    • subSection 3.5.1 Exercises
    • subSection 3.5.2 Implementations
  • Section 3.6 Closed B-splines
  • Section 3.7 Modeling with Polynomial and Spline Curves: Direct Manipulation
    • subSection 3.7.1 Implementations
  • Section 3.8 NURBS
• Chapter 4 Surfaces
  • Section 4.1 Triangular Surface Patches
    • subSection 4.1.1 Blossoming
    • subSection 4.1.2 Exercises
    • subSection 4.1.3 Derivatives
    • subSection 4.1.4 Parametric Continuity
    • subSection 4.1.5 Surfaces above the plane
    • subSection 4.1.6 Exercises
    • subSection 4.1.7 Storing the control points
    • subSection 4.1.8 Efficient Evaluation at a Single Point
  • Section 4.2 Fast Evaluation on a Grid of Points
    • subSection 4.2.1 A Grid of Evaluation Points
    • subSection 4.2.2 Implementations
    • subSection 4.2.3 3-to-1 Subdivision
    • subSection 4.2.4 2-to-1 Subdivision
    • subSection 4.2.5 4-to-1 Subdivision
    • subSection 4.2.6 Curve Evaluation
    • subSection 4.2.7 Cracking Problems
    • subSection 4.2.8 Discussion
    • subSection 4.2.9 Exercises
  • Section 4.3 Tensor-Product Surface Patches
    • subSection 4.3.1 The Blossom of a Tensor-Product Surface
    • subSection 4.3.2 Derivatives
    • subSection 4.3.3 Continuity
    • subSection 4.3.4 Tensor-Product B-splines
    • subSection 4.3.5 Surfaces Above the Plane
    • subSection 4.3.6 Generalizing the Dimension
    • subSection 4.3.7 Storage
  • Section 4.4 Alternative Evaluation Methods for Tensor Product Surfaces
    • subSection 4.4.1 Repeated Bilinear Interpolation
    • subSection 4.4.2 Repeated Curve Evaluation: Revisited
    • subSection 4.4.3 Recursive Subdivision
    • subSection 4.4.4 Curve Evaluation
    • subSection 4.4.5 Discussion
    • subSection 4.4.6 Exercises
• Bibliography
• Index
• Biography