Fourier Series of Shapes

In ACLib curves and shapes can easily be fitted by a Fourier series. The complexity of shapes does not matter; however, the curve is assumed to be one. ACLib’s Sample function can sample any curve by the given length or the total number of points.

The process applies to the given point set. Examples here are based on the point set of Alghalandis Computing logo.

Alghalandis Computing official logo as point samples.

Feeding the above input to FFPoint function results in the following. Here, the number coefficients of Fourier series is set to vary from 5 to 45, showing different quality of fitness. Note that once the Fourier series was found, the function can be sampled at any rate, e.g., a 250 samples per curve are shown below.

Fitted Fourier series with variant number of coefficients.

And the quality of fitting can also easily be set.


Variant number of coefficients from 5 to 45 enhance the fitness of the Fourier series to the model. Once the Fourier series was found, the function can be utilized in various forms. For example, the sampling of the function by 250 equal steps, shown here. The resulting curve is simply node to node straight line connection.

Variation from 5 to 45.

And here are more examples.

Fourier Series fitting to “hope for justice”.

Read more on Justice Cases at Public.


Fourier Series fitting to elephant shape.

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