Dr. Hesham A. Hegazi

Comparison of least squares techniques for fitting of single patch Conic surfaces in reverse engineering

Abstract

Reverse engineering can transform real existing parts into engineering geometric models for the redesign process of parts. Creating geometric models of existing objects for which no such models are available is also invaluable as a design and development tool. The pseudo inverse least square approach was used for fitting the captured data to get their geometric models.  The new geometric model is exported to CAD/CAM software for implementing any design changes and for getting CNC codes for production. This paper presents a comparison between different least squares techniques. These techniques are used in this paper for evaluating the coefficients of the Cartesian equations of conic surfaces. Gauss-Jordan and full pivoting techniques are compared for different cases of fitting a cylinder, a cone and a sphere. Visual BASIC programming language was used for creating the fitting software. Both techniques succeed in solving the general fitting cases; yet for some singular cases, full pivoting technique leads to the desired solution, while Gauss-Jordan failed.

Keywords: Reverse engineering, Conics, Least squares, Eigen vectors, Surface fitting.

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