Fourier Circle Drawing

Turn any image into an animated Fourier epicycle drawing — rotating circles that trace your image's contours using the Discrete Fourier Transform.

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Demo

Input image	Fourier animation

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What is this?

This tool uses the Discrete Fourier Transform (DFT) to decompose the contours of an image into a set of rotating circles (epicycles). When the circles spin together at different frequencies and radii, their combined tip traces the original shape — just like how any periodic signal can be reconstructed from sine waves.

Inspired by 3Blue1Brown's Fourier series videos.

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Features

• Load any image (PNG / JPG / BMP) — the app auto-extracts its contours
• Real-time preview of the Fourier reconstruction inside the GUI
• Interactive animation rendered with Pygame showing all the spinning epicircles
• Detail Level slider (0–100 %) controls how many Fourier coefficients are used
  • 0 % = abstract / minimal → 100 % = maximum fidelity
• Scale slider (10–500 %) zooms the preview and animation
• Precise parameter input via spinboxes (type a value or use ↑↓ keys)
• Save Preview as PNG — export the current static preview with one click
• Auto GIF recording — every animation is automatically recorded; click Download GIF Recording to save it to the recordings/ folder
• Screenshot shortcut — press S in the animation window → saved to screenshots/ with a timestamp

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Requirements

Python 3.8+

pip install -r requirements.txt

Package	Purpose
opencv-python	Image → SVG contour extraction
numpy	FFT computation
pyqt5	Main GUI window
pygame	Animated epicycle rendering
Pillow	GIF recording

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Quick Start

# 1. Install dependencies
pip install -r requirements.txt

# 2. Launch the GUI
python main.py

Step-by-step

1. Click ① Load Image — choose any PNG or JPG
2. Click ② Generate Preview — the app converts the image to SVG contours and runs the FFT
3. Adjust Detail Level and Scale to taste
4. Click Save Preview as PNG to export the static result
5. Click ③ Start Animation — watch the epicircles draw your image!
6. When the animation window closes, click Download GIF Recording to save the GIF to recordings/

Animation window controls

Key	Effect
S	Save screenshot → screenshots/fourier_YYYYMMDD_HHMMSS.png
ESC	Exit the animation

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CLI usage

# GUI with a specific starting detail level (0–300 coefficients)
python main.py --gui --coeffs 150

# Run animation directly on an SVG file
python main.py --svg path/to/file.svg --coeffs 100 --scale 1.2

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How it works

Image (PNG/JPG)
    │
    ▼  OpenCV: threshold + findContours
SVG paths  (series of (x, y) points per stroke)
    │
    ▼  NumPy FFT  →  low-pass filter (keep N coefficients)
Fourier coefficients  [amplitude, frequency, phase]
    │
    ▼  IFFT reconstruction  /  real-time synthesis
Animated epicircles  →  traces the original shape

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Project structure

Fourier_drawing/
├── main.py          # Entry point — GUI + CLI
├── fft.py           # FFT processing + Pygame animation + GIF recording
├── SVG.py           # Bitmap → SVG contour converter
├── requirements.txt
├── icon.png         # App icon
├── images/          # Intermediate files (temp SVG, demo assets)
├── recordings/      # Auto-saved GIF recordings
└── screenshots/     # Auto-saved animation screenshots

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References

• 3Blue1Brown — But what is a Fourier series?
• Fourier series interactive demo (jezzamon.com)
• FourierCircleDrawing (ruanluyu)

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License

MIT