Prototype of the Hyperbolic Tilings Applet:
Why this applet is a prototype:
This java applet does its calculations using the Klien model of the hyperbolic
plane. As a result points near the boundary are nearly indistinguishable
in the euclidean metric and have distance close to one from the center.
Computers are then forced round values close to 1, therefore if we have
a sequence of transformations of the hyperbolic plane which take two points
close to the boundary (in the euclidean metric) then back to the center
of the plane, the distance between the two points as calculated by a computer
can change drastically because of this rounding. The Klien model is especially
bad for these kind of calculations as the Klien model pushes points further
to the boundary (relative to the Poincare disk model). I plan to rewrite
the code to this applet using the Half-Plane model for calculations, which
seems to be much more appropriate and less error prone for these kinds
of constructions.
Also I need to implement the theory of Automatic Groups to avoid
redrawing edges and make the applet more effecient.
View the Code: