Fourier Draw

(Updated 2021)

Graphical animation for Fourier Transfor Series Approximations of complex relations

What is this?

Imagine a moon orbiting around a fixed point at a fixed angular velocity and radius. Now imagine a moon rotating around that moon. And another moon rotating around that one, etc. etc....

Now suppose we placed a pen on the tip of the very last moon of the sequence, what kind of image would it draw?

• By applying a Complex Fourier Transform Series to the sequence, it is possible to generate the initial angles and velocities of all the moons to match arbitrary functions/relations, such as the outline of an image!

Examples:

(The scotty dog example was traced by hand, and thus has far fewer points than the other examples which were computer generated)

Original	Fourier Animation

(The following examples were computationally generated via edge detection (cv2.Canny & cv2.findContours) and thus have many more data points. The videos have been sped up to keep the gif size small)

Original	Fourier Animation

Original	Fourier Animation

Original	Fourier Animation

Installation

Prerequisites

For the smoothest experience, you'll want the following packages:

• build-essential (For building the project, includes c++11)
• clang (For compilation)
• ffmpeg (For creating the movie out of the output images)
• python3 (For the PythonAPI)
• openmp (For multithreading parallelism)

sudo apt update
sudo apt install build-essential
sudo apt install clang
sudo apt install ffmpeg
sudo apt install python3, python3-pip
sudo apt install libomp-dev

Then you should just be able to build the project with a simple make command

Additionally, for usage of the PythonAPI (required for custom images), you'll need the following packages:

• argparse
• numpy
• pandas
• matplotlib
• cv2

Usage

The simplest script to run is FourierDraw.sh which builds, runs, and animates the project from start-to-finish.

The pipeline is essentially the following

# rebuild the project
make -B

# generates many image (.ppm) files in /Out
./FourierDraw

# concatenates the images (.ppm) into a movie (.mp4)
./CreateMovie.sh # you can also add a flag to ffmpeg to generate higher quality files

If you have any custom tracefiles you'd like to use, move them to the Data/ directory as a .csv with dataX and dataY as the headers for the pixel points. Look at the existing .csv's as templates.

Custom Usage

To use arbitrary images, follow these instructions:

1. Add them to the Images/ directory as .png or .jpg files
2. Run python3 PythonAPI/get_image_traces.py to generate all the trace-csv's
   1. Optionally, run python3 PythonAPI/show_image_traces.py to show the traces plotted
3. Edit the file input and other parameters in FourierDraw.cpp to best suit the image
4. Run ./FourierDraw.sh or each of the steps independently

Tuning Params

You might be interested in tuning the number of circles that are drawing the image, number of threads, how long the simulator runs, etc. These can all be found and edited in the Params/ directory

To run with the default Params/params.ini you just run the ./FourierDraw without arguments

However, to run with a custom Params/custom_params.ini you must specify the name as the only argument, eg. ./FourierDraw custom_params.ini

The params config files can be tuned at runtime and don't require recompilation:

[Simulator]
input_image=ai_dragonscs.csv # filename of the dataset we're rendering
num_arrows=5000              # max number of 'circles' drawing the image
num_iters=200                # number of iterations the simulator runs for
num_threads=8                # number of threads being spawned to run 
updates_per_tick=20          # how fast the circles move (larger is faster)
render=true                  # whether or not to render the image

[Image]
window_x=1000 # x dimension of output image
window_y=1000 # y dimension of output image