AN ALTERNATIVE METHOD TO PERFORM THE ELLIPSE FITTING TO 2D DATA

Nicolae URSU-FISCHER

Abstract


The importance of published studies of circle or ellipse fitting, performed with different methods, algebraic or geometric, is obvious considering the great number of published scientific papers and of practical usefulness in CAD routines of discovered procedures.  The work starts with a short presentation of the well known methods – the algebraic fitting and the geometric, one pointing on its advantages and drawbacks. The common fact of both methods is the use of Cartesian ellipse equation, written as conics general equation. One can remember that the ellipse may be defined as the geometrical locus of points satisfying some imposed condition. We try to use these properties in the frame of our proposed procedure of finding the ellipse that fits with high accuracy some scattered points in plane. Considering that ellipse points have the sum of distances to the two fixed points (the focuses) constant one may imagine the new method to perform the ellipse fit. As in the previous discovered methods, the least squares procedure to find the optimal solution is used. All the necessary aspects about this procedure are presented in the paper and also a lot of numerical examples, justifying the advantages of this new discovered method.


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References


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