# PIECEWISE LINEAR APPROXIMATION OF SMOOTH, FLAT CURVES BY THE SECANT METHOD

I.P. Kryvoruchko

Èlektron. model. 2022, 44(5):51-60

https://doi.org/10.15407/emodel.44.05.051

### ABSTRACT

The approximation of smooth lines by a piecewise linear function is relevant in many applications, where this representation can significantly simplify the technological process without a significant loss in quality indicators. An improved method of dividing or representing a smooth curve by a piecewise linear line is proposed, which, in comparison with dividing by the "chord" method, reduces the degree of difference between the approximated and approximating curves for the selected number of segments. The essence of the method consists in the successive point-by-point calculation of the deviation between the approximated line, given analytically, and the straight line segment until the condition of equality of this deviation of the specified tolerance value is met. The next step is to correct the point of intersection of these lines by moving it along the ordinate axis by an amount equal to part of the tolerance in the direction determined by the convexity (concavity) of the original curve. The proposed method of piecewise linear approximation is supposed to be used to implement the sinusoidal motion of the carriage with the sensors in the vibro-calibration system.

### KEYWORDS

piecewise linear approximation, secant method, chord method.

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