Iruface

Create drawings and animations using complex fourier series to trace smooth paths (e.g. the outline of a picture).

Fourier Coefficients

The following table summarizes the process to obtain Fourier Coefficients for the outline of a photo.

Photo	Edge Detection	Find Tour (Solve TSP)	Compute Fourier Coefficients

In general, the code can be used to obtain the Fourier Coefficients of a given curve in a plane. The first two steps must be accomplished using other software (i.e. an image processing software and a TSP solving library). For the second step, binaries for the "concorde" and "libkern" TSP solvers are included under the bin directory. Additionally, tools have been implemented to interface with the TSPLIB standard for TSP problems, which allow to convert an image into a TSPLIB instance and to parametrize a curve in space based on a TSP solution (a tour).

Drawings

Using Fourier Coefficients a doodle of the original outline can be obtained. Using more coefficients results in higher fidelity of the doodle as the Fourier Series approaches the source parametric curve, thus very high order fourier expansions are not as interesting artistically (and also require more compute resources).

Order 100	Order 1000

Animations

The curve that the Fourier Series traces can be animated displaying in each timestep the contribution of each term in the series as a phasor. This allows visualizing the beautiful complexity of the Fourier Series in action.

Animation Frame	Zoomed in Frame