ComplexMaps

A small program to visualize complex functions

This program is created in sake of better understanding how various shapes on a complex plane are transformed when complex functions are applied to them.

1. What can I do in this program?

Drawing

You can draw different kinds of shapes (curves, straight lines and ellipses by now). The kind of a shape is defined by the current mode. You can switch between the modes pressing 1,2 and 3 on the keyboard.

• 1 stands for curves
• 2 stands for straight lines
• 3 stands for ellipses
  To draw a shape, you should press the left mouse button anywhere on the screen, move the mouse around and release it. In the ellipse mode you can also regulate the width of an ellipse scrolling the mouse wheel.

Curve mode:

Line mode:

Ellipse mode:

Navigating around the plot

You can scroll the mouse wheel and resize both preimage and image.

Moreover, you can press on the spacebar and, moving your mouse around, drag both preimage and image.

Setting a custom function

You can enter a custom function in a text box on the right. All axises and your paintings will be re-mapped. However, the function must meet some syntax requirements:

1. There must not be any excessive brackets
2. There must not be 2 and more operators in a row
3. Currently the following operators are supported: + - * / ^
4. Currently the following functions are supported:
   1. sin(), or s(); cos(), or c()
   2. exp(), or e(); ln(), or log(), or l()

Ln(x):

Sin(x):

Sin(x)+1/x:

2. How can I launch this program?

Download pre-compiled executable files...

First of all, there are pre-compiled executable files, which you can download and launch if you dare.

- Linux:

Download script and run it from the command prompt (assuming that your current directory is the one containing the file):
$ ./script

- Windows:

Download script.exe and run it as an ordinary executable file.

...or compile by your own.

Moreover, you can compile executable by yourself.

- On Linux for Linux:

You have to install such libraries as libgl1-mesa-dev, freeglut3-dev and libglew-dev:
$ sudo apt-get install libgl1-mesa-dev freeglut3-dev libglew-dev
Then go to the directory of the downloaded repo and compile:
g++ script.cpp function.cpp complex.cpp line.cpp curve.cpp ellipse.cpp text.cpp -lGL -lGLU -lGLEW -lglut -lm -o script
Run the compiled output:
./script

- On Linux for Windows:

Firstly, Mingw-w64 will come in handy while compiling on Linux for Windows:
$ sudo apt-get install mingw-w64
Then, you should download freeglut for windows. Otherwise you will just run into a bunch of errors. You can find it here. Just scroll down for the freeglut 3.0.0 MSVC Package. There are two important folders: include and lib.

├-- lib
│   ├-- x64
│   ├-- ...
└ ...

If you want to compile for x32 and x64, copy everything inside of include and everything (but x64) inside of lib to /usr/i686-w64-mingw32/. Switch to the directory with downloaded repo and run the following command:

$ i686-w64-mingw32-g++ -m32 -Wall -I/usr/i686-w64-mingw32/include/GL -o script.exe script.cpp function.cpp complex.cpp curve.cpp text.cpp ellipse.cpp line.cpp -D FREEGLUT_STATIC -L/usr/i686-w64-mingw32/lib -lfreeglut_static -lopengl32 -lwinmm -lgdi32 -Wl,--subsystem,windows -static-libgcc -static-libstdc++

If you want to compile for x64, copy everything inside of include and everything inside of lib/x64 to /usr/x86_64-w64-mingw32/. Switch to the directory with downloaded repo and run the following command:

$ x86_64-w64-mingw32-g++ -m64 -Wall -I/usr/x86_64-w64-mingw32/include/GL -o script64.exe script.cpp function.cpp complex.cpp curve.cpp text.cpp ellipse.cpp line.cpp -D FREEGLUT_STATIC -L/usr/x86_64-w64-mingw32/lib -lfreeglut_static -lopengl32 -lwinmm -lgdi32 -Wl,--subsystem,windows -static-libgcc -static-libstdc++

Executable file will be generated. Launching of the executables under different systems was described in the previous paragraph.