SVG Fourier Series

Computes the Fourier series coefficients for an input SVG line art and renders it into a video or gif

sample.mp4

Installation (for Windows):

• Clone this repository (or download this repository and extract it somewhere).
• Install Python 3.9 from https://www.python.org/.
• Create a Python 3.9 virtual environment in this folder using python3 -m venv venv.
• Activate your virtual environment using cd venv/Scripts && activate.
• Install requirements listed in requirements.txt using pip install -r requirements.txt.
• (Personally, I just use PyCharm IDE for all these).

Usage

Preview

Copy your SVG line art file (e.g. yourfilename.svg) into the ./input folder, then run:

python draw.py -i input/yourfilename.svg

Render to a file

Copy your SVG line art file (e.g. yourfilename.svg) into the ./input folder, then run:

python draw.py -i input/yourfilename.svg --render --render-type mp4

Your mp4/gif will be available in the ./output folder (e.g. as yourfilename.mp4).

How does it work?

The input SVG file is traced from start to end, and its coordinates are mapped to complex numbers (x->real, y->imaginary).

The path is treated as a repeating complex signal with period of 2 Pi, and the Fourier series complex coefficients (c_0, c_1... c_n) are generated.

The complex coefficients are substituted back into the Fourier series and the resulting function is plotted across time.

For more, read the full explainer: The Fourier Series