An Introduction to Splines for Use in Computer Graphics and Geometric ModelingAs 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. |
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Contents
Introduction | 1 |
Preliminaries | 8 |
A Simple Approximation Technique Uniform Cubic Bsplines | 19 |
Splines in a More General Setting | 67 |
The OneSided Basis | 101 |
Divided Differences | 133 |
General Bsplines | 145 |
Bspline Properties | 173 |
UniformlyShaped Betasplines | 301 |
Geometric Continuity Reparametrization and | 315 |
ContinuouslyShaped Beta splines | 321 |
An Explicit Formulation for Cubic Betasplines | 343 |
DiscretelyShaped Betasplines | 357 |
Bspline Representations for Betasplines | 371 |
Rendering and Evaluation | 383 |
Selected Applications | 421 |
Bezier Curves | 211 |
Knot Insertion | 247 |
The Oslo Algorithm | 261 |
Parametric vs Geometric Continuity | 293 |
455 | |
467 | |