An Introduction to Splines for Use in Computer Graphics and Geometric Modeling

As the field of computer graphics develops, techniques for modeling complex curves and surfaces are increasingly important. A major technique is the use of parametric splines in which a curve is defined by piecing together a succession of curve segments, and surfaces are defined by stitching together a mosaic of surface patches.

An Introduction to Splines for Use in Computer Graphics and Geometric Modeling discusses the use of splines from the point of view of the computer scientist. Assuming only a background in beginning calculus, the authors present the material using many examples and illustrations with the goal of building the reader's intuition. Based on courses given at the University of California, Berkeley, and the University of Waterloo, as well as numerous ACM Siggraph tutorials, the book includes the most recent advances in computer-aided geometric modeling and design to make spline modeling techniques generally accessible to the computer graphics and geometric modeling communities.

1 Introduction
2 Preliminaries
3 Hermite and Cubic Spline Interpolation
4 A Simple Approximation Technique - Uniform Cubic B-splines
5 Splines in a More General Setting
6 The One-Sided Basis
7 Divided Differences
8 General B-splines
9 B-spline Properties
10 Bezier Curves
11. Knot Insertion
12 The Oslo Algorithm
13 Parametric vs. Geometric Continuity
14 Uniformly-Shaped Beta-spline Surfaces
15 Geometric Continuity, Reparametrization, and the Chain Rule
16 Continuously-Shaped Beta-splines
17 An Explicity Formulation for Cubic Beta-splines
18 Discretely-Shaped Beta-splines
19 B-spline Representations for Beta-splines
20 Rendering and Evaluation
21 Selected Applications