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Least-Squares Fitting Algorithms of the NIST Algorithm Testing System.

Craig M Shakarji¹

¹National Institute of Standards and Technology, Gaithersburg, MD 20899-0001.

Journal of Research of the National Institute of Standards and Technology

|December 24, 2016

Summary

This study presents algorithms for fitting 3D curves and surfaces using orthogonal distance regression. These methods serve as reference software for the National Institute of Standards and Technology

Keywords:

Levenberg-Marquardt coordinate measuring machine curve fitting least-squares fitting orthogonal distance regression surface fitting

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Area of Science:

Computational Geometry
Numerical Analysis
Scientific Computing

Background:

Orthogonal distance regression is crucial for accurate 3D data fitting.
Existing methods require robust and reliable algorithms for curve and surface fitting.
The National Institute of Standards and Technology (NIST) Algorithm Testing System requires validated software.

Purpose of the Study:

To describe algorithms for fitting curves and surfaces in three dimensions.
To provide reference software for the NIST Algorithm Testing System.
To detail the underlying linear algebra, numerical analysis, and optimization techniques.

Main Methods:

Development of algorithms based on orthogonal distance regression.
Implementation of general linear algebra and numerical analysis methods.
Utilization of the Levenberg-Marquardt optimization routine for most fitting procedures.

Main Results:

Algorithms for fitting curves and surfaces to 3D point data were successfully developed.
The developed algorithms are suitable for use as reference software.
The study details the mathematical and numerical foundations of the fitting routines.

Conclusions:

The presented algorithms provide a robust approach to 3D curve and surface fitting.
The reference software contributes to the validation of algorithms within the NIST framework.
The work advances the field of geometric data fitting through reliable computational methods.