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RESEARCH PAPERS

Geometric Design and Fabrication of Developable Bezier and B-spline Surfaces

[+] Author and Article Information
R. M. C. Bodduluri

Accuray Incorporated, Santa Clara, CA

B. Ravani

Department of Mechanical Engineering, University of California, Davis, Davis, CA

J. Mech. Des 116(4), 1042-1048 (Dec 01, 1994) (7 pages) doi:10.1115/1.2919485 History: Received February 01, 1992; Revised May 01, 1994; Online June 02, 2008

Abstract

In this paper we study Computer Aided Geometric Design (CAGD) and Manufacturing (CAM) of developable surfaces. We develop a direct representation of developable surfaces in terms of plane geometry. It uses control planes to determine a surface which is a Bezier or a B-spline interpolation of the control planes. In the Bezier case, a de Casteljau type construction method is presented for geometric design of developable Bezier surfaces. In the B-spline case, de Boor type construction for the geometric design of the developable surface and Boehm type knot insertion algorithm are presented. In the area of manufacturing or fabrication of developable surfaces, we present simple methods for both development of a surface into a plane and bending of a flat plane into a desired developable surface. The approach presented uses plane and line geometries and eliminates the need for solving differential equations of Riccatti type used in previous methods. The results are illustrated using an example generated by a CAD/CAM system implemented based on the theory presented.

Copyright © 1994 by The American Society of Mechanical Engineers
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