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Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces

Ronald N. Goldman and Tom Lyche, Editors

"Knot insertion and deletion algorithms are the two fundamental procedures used to understand, analyze, and render B-spline curves and surfaces. Papers cover blossoming, algorithms for progressive curves, factored knot insertion, knot insertion algorithms, conversion between B-spline bases using the generalized Oslo algorithm, how much the size of the B-spline coefficients can be reduced by inserting one knot, and the envelope approach to a sketching editor for hierarchial free-form curve design and modification." -- SciTech Book News, June 1993.

New approaches to knot insertion and deletion are presented in this unique, detailed approach to understanding, analyzing, and rendering B-spline curves and surfaces. Computer scientists, mechanical engineers, and programmers and analysts involved in CAD and CAGD will find innovative, practical applications using the blossoming approach to knot insertion, factored knot insertion, and knot deletion, as well as comparisons of many knot insertion algorithms. This book also serves as an excellent reference guide for graduate students involved in computer aided geometric design.


Chapter 1: An Introduction to Blossoming, Phillip J. Barry; Chapter 2: Algorithms for Progressive Curves: Extending B-Spline and Blossoming Techniques to the Monomial, Power, and Newton Dual Bases, Phillip J. Barry and Ronald N. Goldman; Chapter 3: Factored Knot Insertion, Phillip J. Barry and Ronald N. Goldman; Chapter 4: Knot Insertion Algorithms, Phillip J. Barry and Ronald N. Goldman; Chapter 5: Conversion Between B-Spline Bases Using the Generalized Oslo Algorithm, Tom Lyche, Knut Morken, and Kyrre Strom; Chapter 6: How Much Can the Size of the B-Spline Coefficients be Reduced by Inserting One Knot?, Tom Lyche and Knut Morken; Chapter 7: An Envelope Approach to a Sketching Editor for Hierarchical Free-form Curve Design and Modification; Michael J. Banks, Elaine Cohen, and Timothy I. Mueller; Index.

1993 / xiii + 197 pages / Softcover / ISBN-13: 978-0-898713-06-0 / ISBN-10: 0-89871-306-4 /
List Price $88.00 / SIAM Member Price $61.60 / Order Code OT36
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