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Least Squares Fitting of Analytic Primitives on a GPU

[+] Author Affiliations
Meghashyam Panyam, Thomas R. Kurfess

Clemson University, Clemson, SC

Thomas M. Tucker

Tucker Innovations, Inc., Charlotte, NC

Paper No. ESDA2008-59203, pp. 233-240; 8 pages
doi:10.1115/ESDA2008-59203
From:
  • ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis
  • Volume 1: Advanced Energy Systems; Advanced and Digital Manufacturing; Advanced Materials; Aerospace
  • Haifa, Israel, July 7–9, 2008
  • Conference Sponsors: International
  • ISBN: 978-0-7918-4835-7 | eISBN: 0-7918-3827-7
  • Copyright © 2008 by ASME

abstract

Metrology systems take coordinate information directly from the surface of a manufactured part and generate millions of (X, Y, Z) data points. The inspection process often involves fitting analytic primitives such as sphere, cone, torus, cylinder and plane to these points which represent an object with the corresponding shape. Typically, a least squares fit of the parameters of the shape to the point set is performed. The least squares fit attempts to minimize the sum of the squares of the distances between the points and the primitive. The objective function however, cannot be solved in the closed form and numerical minimization techniques are required to obtain the solution. These techniques as applied to primitive fitting entail iteratively solving large systems of linear equations generally involving arithmetic intensive operations. The current problem in-process metrology faces is the large computational time for the analysis of these millions of streaming data points. This paper presents a framework to address the bottleneck using a Graphical Processing Unit (GPU), to optimize operations and obtain significant gain in computation time.

Copyright © 2008 by ASME
Topics: Fittings

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