Fourier Drawing Animation

A highly optimized and generalized Manim project that creates mesmerizing epicycle animations from any image using Fourier transforms.

Features

• ✅ Multi-format support: Works with SVG, PNG, and JPG images
• ✅ Highly configurable: All settings in one easy-to-edit config file
• ✅ Optimized performance: Efficient FFT-based calculations
• ✅ Clean architecture: Modular, well-documented code
• ✅ Flexible visualization: Toggle circles, arrows, and customize colors

Quick Start

1. Installation

Ensure you have the required dependencies:

pip install manim pillow scipy svgpathtools

For PNG/JPG to SVG conversion (optional):

# Install ImageMagick and Potrace
# Windows: Download from official websites
# Linux: sudo apt-get install imagemagick potrace
# Mac: brew install imagemagick potrace

2. Basic Usage

1. Configure your animation in config.py:

   IMAGE_PATH = 'images/your_image.svg'  # or .png, .jpg
   N_VECTORS = 300                        # Number of epicycles
   NUM_SAMPLES = 10000                    # Sampling resolution
   ANIMATION_DURATION = 50.0              # Animation length in seconds

2. Run the animation:

   # Quick preview (low quality)
   manim -pql fourier_drawing.py FourierDrawing
   
   # High quality render
   manim -pqh fourier_drawing.py FourierDrawing
   
   # 4K quality
   manim -pqk fourier_drawing.py FourierDrawing

Configuration Options

All settings are in config.py:

Image Settings

• IMAGE_PATH: Path to your image file (SVG, PNG, or JPG)

Fourier Settings

• N_VECTORS: Number of epicycles (100-500 recommended)
• NUM_SAMPLES: Sampling resolution (1000-10000 recommended)

Animation Settings

• ANIMATION_DURATION: Duration in seconds for one complete cycle
• PAUSE_AT_END: Pause duration after completing the drawing

Visual Settings

• DRAW_CIRCLES: Show/hide rotating circles
• DRAW_ARROWS: Show/hide rotating vectors
• SHOW_TRACER_DOT: Show/hide the drawing point
• Various color and style options

Project Structure

d:/Python/Manim/
├── config.py                 # Main configuration file
├── fourier_drawing.py        # Main animation script
├── helpers/
│   ├── fourier_calc.py      # Fourier transform calculations
│   └── complex_to_np.py     # Utility functions
├── images/
│   ├── vectorize.py         # PNG/JPG to SVG converter
│   └── [your images]
└── media/                   # Rendered videos (created automatically)

Converting Images

For PNG/JPG Images

The script automatically handles PNG/JPG files by detecting edges. For better results, you can convert them to SVG first:

cd images
python vectorize.py your_image.jpg output.svg

Then update config.py:

IMAGE_PATH = 'images/output.svg'

Tips for Best Results

1. Start small: Begin with N_VECTORS=100 and NUM_SAMPLES=1000 for quick tests
2. Simple images work best: High-contrast, simple shapes produce cleaner results
3. Adjust duration: Longer durations (50-100s) look smoother but take longer to render
4. Quality vs. Speed:
   • More vectors = more detail but slower rendering
   • More samples = smoother paths but slower preprocessing

Performance Guide

Setting	Fast	Balanced	High Quality
N_VECTORS	50-100	200-300	500-1000
NUM_SAMPLES	1000-2000	5000-10000	10000-20000
Render time	<1 min	2-5 min	10+ min

Troubleshooting

"No module named 'PIL'"

pip install pillow

"No module named 'svgpathtools'"

pip install svgpathtools

Image not loading

• Check the file path in config.py
• Ensure the image file exists
• Try using an absolute path

Animation cuts off early

• Increase ANIMATION_DURATION in config.py
• Ensure PAUSE_AT_END is set to a positive value

Poor quality output

• Increase NUM_SAMPLES for smoother paths
• Increase N_VECTORS for more detail
• Use higher render quality: -pqh or -pqk

Examples

See the images/ directory for example images and their settings:

1. Simple logo (N_VECTORS=100, NUM_SAMPLES=2000, Duration=20s)
2. Complex drawing (N_VECTORS=500, NUM_SAMPLES=10000, Duration=60s)

License

This project is open source and available for educational purposes.

Credits

Built with:

• Manim Community
• NumPy, SciPy
• svgpathtools
• Pillow (PIL)