The Klein Disk

Below is an applet with drawing tools for the Klein Disk model of elliptic geometry.
(Be patient; the applet takes a few seconds to load.)
Use the "disk" menu (1st tool from the right) to access the tools of elliptic geometry in this model.

Caveat Emptor (Buyer Beware):

This applet is a work in progress! Some known bugs and features are described below.

Known bugs and features:

• This applet uses stereographic projection to represent elliptic geometry, and can therefore be used to model either double elliptic geometry (spherical geometry) or single elliptic geometry (the Klein Disk).
• To work in spherical geometry, interpret the interior of the disk as the northern hemisphere, and the exterior of the disk as the southern hemisphere.
• To work in the Klein Disk, ignore the points in the exterior (except possibly as part of constructions).
• Elliptic distances are given assuming spherical geometry. (The sphere is assumed to have unit radius.)
  To determine distance in the Klein Disk, distances d greater than π/2 should be replaced by π/2−d.
• The elliptic line tools do not work for (parts of) diameters. Use Euclidean tools instead.
• The elliptic angle tool does not work if one side is (part of) a diameter. Use Euclidean tools for angles at the origin.
  (There is currently no way to measure an elliptic angle when just one of its sides is along a diameter.)
• Known bug: The elliptic angle tool is only reliable for small triangles.
  This issue is likely related to whether or not any of the lines used in the underlying construction become diameters. So it can be triggered by moving points around, and is not always fixed by returning them to their original location. You can check whether this bug is in effect by verifying that the angle sums in your triangles are greater than 180°.

Acknowledgment: The underlying applet Klein.ggb was written by Tevian Dray in 2016, and may be used under a by-nc-nd Creative Commons license.