Computer Aided Geometric Design of Line Constructs

[+] Author and Article Information
B. Ravani, J. W. Wang

Computer Integrated Design and Manufacturing Laboratory, Department of Mechanical Engineering, University of California-Davis, Davis, CA 95616

J. Mech. Des 113(4), 363-371 (Dec 01, 1991) (9 pages) doi:10.1115/1.2912791 History: Received April 01, 1990; Revised August 01, 1990; Online June 02, 2008


This paper develops a mathematical foundation for Computer Aided Design (CAD) of sculptured shapes based on line geometry. First, a new representation is presented for a line based on Plücker coordinates that would allow specification of a line segment (rather than an infinite line) in an elegant manner and suitable for computational purposes. Then, methods are presented for geometric design of shape patches (here referred to as line constructs) by interpolating or approximating a set of control lines (rather than control points) using ruled surfaces, line congruences, and line complexes. The methods presented are general and allow utilization of different basis functions such as Bézier, Cardinal, and B-spline bases. As Computer Aided Manufacturing (CAM) application of the theory, methods are developed for generation of offsets of ruled surfaces useful in Numerical Control (NC) milling and tool motion generation in the Wire Cut Electric Discharge Machining (EDM) operation.

Copyright © 1991 by The American Society of Mechanical Engineers
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