Error-Free Interpolation of Parametric Surfaces

[+] Author and Article Information
J. G. Gan

Nanyang Technological University, Singapore

T. C. Woo

University of Michigan, 1205 Beal Ave., Ann Arbor, MI 48109-2117

J. Eng. Ind 114(3), 271-276 (Aug 01, 1992) (6 pages) doi:10.1115/1.2899791 History: Received December 01, 1989; Revised February 01, 1991; Online April 08, 2008


A Digital Differential analyzer (DDA) is a cost effective implementation for interpolating parametric curves and surfaces. However, the problems of register overflow and integer round-off have prevented it from being adopted by industry. Contrary to intuition, an increase in register capacity is shown to have no bearing on the register overflow problem. It is shown that there is a minimum number of interpolation steps K l below which register overflow occurs. Correspondingly, it is also shown that there exists a maximum number of interpolation steps K u above which the accumulation of integer round-off errors exceeds the acceptable limit. But, when K l >K u , conflict arises. A solution is given to resolve the possible conflict and to yield an error-free interpolation of curves and surfaces.

Copyright © 1992 by The American Society of Mechanical Engineers
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