Simple Fun Fourier Drawing Programm

Note

This is oringinally a program for the Functional Programming Competition and is under refactor
see details about the competition here: Link
see original source here: Link

Inspiration

• 3Blue1Brwon's amazing video told us that Fourier Series can draw anything
• In the form of Integral, the series will approach the oringinal image as the number of terms rise

• The Mathematical Pinciple behind the image is so amazing that I decide to present this simple fun programm that draws anything

Data Format

• prepare your data in the following json format, where each object of series represents a term of fourier series

{
    "series": [
        {
            "number" : 0,
            "real" : 1,
            "imag" : 2 
        }
    ]
}

• number represents exactly n in the form, which should be a Integer, and controls how fast the vector spins
• real and imag represent the complex constant Cn in the form, control the starting position and length of the vector
• Then put them in one directory without other files. Each file will be transformed to a closed curve. In order to draw a image with multiple curves, you'll need the same amount of json files.

Example

• this image of haskell logo is generated using data from the data directory

Usage

Build the Binary

• clone the repository and run cabal-build
• make sure to run cabal update once if it is newly installed

git clone https://github.com/HE7086/Fourier.git
cd Fourier
cabal build

• you can find the binary inside dist folder

CLI Flags

short	long	description
-g	--gif	generate gif files
-p	--png	generate png files
-c	--combined	combine the images afterwards
-o PATH	--output PATH	specify output path
-i PATH	--input PATH	specify input path/file
-v	--version	print version message
-h	--help	print help message

• by default help messages will be printed

Example

• generate gifs from all the files in a directory

cabal run -- Fourier --gif --input ./data --output ./out --combined

• generate one png from a file

cabal run -- Fourier --png --input ./data/1.json --output ./out

• run with threaded mode (significantly increase performance on multicore cpus)

cabal run -- Fourier --png --input ./data/1.json --output ./out +RTS -N

Customization

• In the file src/Settings.hs are several option that can be customized easily
  • width, height : the height and width of the generated image
  • white, black : the standard pixel color
  • pixelArt : the function that dertermines color and by default draws black
  • pointCount : the number of points to be painted
  • gifStep : how many pixels will be rendered each frame
    • warning : terrible runtime if set too small
  • filename : the name of outputed image
  • scaleFactor : how much the final image will be scaled
• These customization options will be merged into cli flags in the future

TODO list

• optimize performance
• adjustable line thickness
• adjustable fore-/background color
• coordinates converter: convert coordinates to forms