Computer Graphics and Geometric Modeling Using Beta-splines

Barsky, Brian A.,

ISBN 10: 3540700064 / ISBN 13: 9783540700067

Published by Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 1988

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Bibliographic Details

• Title: Computer Graphics and Geometric Modeling Using Beta-splines
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Publication Date: 1988
• Language: English
• ISBN 10: 3540700064
• ISBN 13: 9783540700067
• Binding: Hardcover
• Condition: Brand New

About this title

Synopsis

This book explains the Beta-spline representation for curves and surfaces. This topic is important for the modeling of objects delineated by free-form curved surfaces. Such models are needed in the design and manufacture of three-dimensional parts, as well as in the generation of synthetic computer images. The Beta-spline technique follows from the earlier techniques of Bézier and B-spline curves and surfaces, and forms the latest method in this field. The utility of this technique is the capability of representing complex curved surface objects using natural input specifications. The Beta-spline technique combines powerful and general mathematics with an intuitive specification method. Mathematical underpinnings are sufficiently flexible to allow the representation of a wide class of complex shapes. At the same time, description of these shapes is achieved through the use of intuitive and meaningful specification parameters. In addition to a set of points in three-space, called control vertices, shape parameters are introduced which are parameters whose values indicate the shape of the object in terms of "sharpness" or "flatness".