THIS IS A PROOF OF CONCEPT, EXPECT MANY FEATURES TO BE MISSING, AND BUGS TO OCCUR

What it does

Let's assume we have a function f and f(1 + i) = 0.5 + 0.5i.

We could place an image onto the complex plane, and move the pixel which is over the 1 + i point to the 0.5 + 0.5i point.

This way, we can get an intuition of what this function does: we can see which zones go where, or wether it moves the image, rotates it, does both, zooms out...

See below for imaged examples.

Function example

This is the most basic function example: do nothing.

#include <complex.h> // get library to do complex number computation
// see https://www.gnu.org/software/libc/manual/html_node/Complex-Numbers.html for documentation

// f is the function we will draw
// it takes a complex number c as input : the origin point
// it must return a complex number: the destination point
complex double f(complex double c)
{ // edit below
    return c; // return the same position, unchanged
}

Using a function

This project provides a web UI through which you can create a use functions. A live demo can be found here. You have to register, so you can create your own functions, you can then create a function, compile it, and use it.

Parameters

The render page provides multiple options:

• inputRange: a complex range which represents where the image is placed on the complex plane before transformation. It is the equivalent of xMin and xMax for a real function.
• outputRange: a complex range which represents the part of the complex plane after transformation which is displayed. It is the equivalent of yMin and yMax for a real function.
• outputDimension: width and height of the output image.
• samplingFactor: a float which represents the number of points moved per pixel in the output image.
• handleCollisions: whether or color blending should occur when multiple point land on the same pixel. Render is slightly slower when enabled, but often yields a much better result.

A complex range is a string of the following format: {%f%fi;%f%fi} with %f being a + or a - followed by at least one digit, which may be followed by a . and at least one digit.

License

This poject is published under a GPL v3 license.

See LICENSE.

Example of results

• Source image:
• f(a + ib) = a + 0.5 + 0.5i:
• f(a + ib) = (a + ib) * 1.41:
• f(a + ib) = (a + ib) * i * 0.75:
• Riemann's zeta function:

Reporting a bug

If you think you have found a bug, you can help us fixing it faster by opening a github issue and providing the following informations:

Browser: <browser name> <browser version>
Email: <email used to register>
Page: <url of the page(s) on which the bug occured>
Function (if relevant): <source code of the function you used>

## What happened:

## What should have happened:

Feature request

If you would like a feature to be included in this project, feel free to open an issue, and describe the missing feature.

Contributing

There are many ways you can contribute to this project, even without knowing how to code.

• You know about web design, css and stuff like that? Our UI is terrible, you can open pull requests to improve it or get in touch, so we can talk :)
• You know about color blending and alpha blending? I'm terrible at it, and I must have done things wrong, and I'd love to learn more about how I should do this!
• You know about IT security? This project is about compiling untrusted code and user authentication! It's likely I've done things wrong or left an obvious XSS.
• You know about math? I'm sure you can make rendering faster, or maybe you have idea of pretty functions we can showcase in this README?
• You speak english better than me? I'm french, I must have made many mistakes, open a pull request and improve this README.
• You're a C/GO/JS developer? Find //todos and fix them, implement your own features , or get in touch!
• You're crazy? Go ahead and comment my code. Just kidding, I'll do it, but I first wanted to get a working proof of concept before doing things the proper way!
• You've got an extra server? Mine is super slow, compiling functions can take up to a minute, with a faster one, this could go under 20 seconds!

And if you think you can contribute to this project, open a PR, an issue, or get in touch!