Cost-optimal parallel B-spline interpolations

Authors:
Kuo-Liang Chung;Ferng-Ching Lin;Wen-Chin Chen
Affiliations:
Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan 10764, R.O.C.;Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan 10764, R.O.C;Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan 10764, R.O.C.
Venue:
ICS '90 Proceedings of the 4th international conference on Supercomputing
Year:
1990

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Abstract

We show how to transform the B-spline curve and surface fitting problems into suffix computations of continued fractions. Then a parallel substitution scheme is introduced to compute the suffix values on a newly proposed mesh-of-unshuffle network. The derived parallel algorithm allows the curve interpolation through n points to be solved in O(logn) time using &THgr;(n/log n processors and allows the surface interpolation through m × n points to be solved in O(log m log n) time using &THgr;(mn/(log m log n)) processors. Both interpolation algorithms are cost-optimal for their respective problems. Besides, the surface fitting problem can be even faster solved in O(log m + log n) time if &THgr;(mn) processors are used in the network.