Hyperbolic Geometry

The Hyperbolic Geometry software is a macro package for the asymptote vector graphics language. It contains various data structures and methods for drawings and calculations in the hyperbolic model known as the poincare disk.
The software is currently under development, but there are many usefull this already implemented and most of the basic compass and straightedge constructions can be done in the hyperbolic plane.


Here you can find some demos with various geometric objects ... nice to look at, but without deeper meaning.

And here is a collection of some well known euclidean compass and straightedge constructions. A few of them do also work in hyperbolic geometry, but others don't.


The main features are:

  • Points, lines, segments, rays, circles, triangles, polygons and regular N-gons
  • Intersection calculation between lines, segments, rays, circles
  • Construction methods like midpoint, angle bisector, perpendiculars, tangents, incircle, circumcircle, ...
  • Mirroring arbitrary objects at lines, segments, rays
  • Rotating arbitrary objects around points
  • Measuring of distances and angles

A more comprehensive documentation of the available objects and methods can be found in the API doc for users.

Mathematical background

As the math behind the code is not well documented yet, I just link the english wikipedia here:
Hyperbolic geometry

Download, stable version

  • Author: R. Bourquin
  • Lizenz: GNU GPL v2 or later
  • Version 0.8


A git repository can be found at: https://git.koalatux.ch/raoul/hyperbolic_geometry.git/

To get a local copy, use git clone:
git clone https://git.koalatux.ch/raoul/hyperbolic_geometry.git/