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

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Morgan Kaufmann, Sep 15, 1995 - Computers - 476 pages
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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.

 

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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

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