Fourier Series: Smoothing Curves

By smoothing a curve its shape becomes more favorable, eye pleasing. Of course, it has more applications and benefits depending on the topic. The following animation shows transformation of a flying eagle modeled by fitting Fourier series to its sample data with variant number of coefficients.

Smoothed fit of flying eagle by means of Fourier series.

It is interesting to see that in all levels of fitting the shape remains very smooth, fully connected with no knot.

A close up view shows as the number of coefficients increases the fitting becomes closer to the original data. In all levels, the fitting curve remains perfectly smooth.

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