This app is a raster graphics editor in hyperbolic geometry using the Pointcaré disk model.
One way to open the app is this:
- Open a terminal and
cdto where the index.html file is located. - Type
python -m http.serverin the terminal (Python needs to be installed in order to do that). - Type
http://localhost:8000/in your web browser.
Now you can use the app to paint with a paintbrush of a constant hyperbolic radius and you can also draw geodesics, certain rectangles, triangles and stars. It is also possible to erase the objects on the canvas (in order to do so for lines one needs to erase one of the lines' ends) and to save the drawn image as a PNG file by clicking on the "Download" button.
General information about hyperbolic geometry and the Pointcaré disk model can be found in various media, for example here and here.
Geodesics can be constructed by using this method. For circle inversion, see the instruction on wikipedia.
The paint brush draws circles with a constant hyperbolic radius. In order to determine the euclidean equivalent to this hyperbolic radius, one can use the method presented in the answer by user "Blue" on November 4, 2016 at 11:32pm. It uses hyperbolic distance in the Pointcaré disk model.
Various parts of the app "Hyperpaint" (see here and here) by "zokalyx" were used.
Some of the app's functions involve explicit formulas, e.g. the function of drawing geodesics uses formulas derrived by using (if recalled correctly) some of the websites listed under Mathematics.
Various features could be added to the app in the future. Here are some examples:
- a fill-in function
- a function to reflect the drawn image along hyperbolic lines
- a function to draw circles (without filling)
- functions to draw other polygons
- an opportunity to save drawn images in a way that they can be edited again with the editor
- adjustment of the line thickness in such a way that its hyperbolic size is constant (currently lines are drawn with constant Euclidean thickness)