Interactive exploration of the Möbius transformations, by dragging the four p...
- 2016-01-12 00:19:51+0000 - Updated: 2016-01-12 00:19:51+0000
Interactive exploration of the Möbius transformations, by dragging the four parameters a, b, c and d around on the complex plane.

http://timhutton.github.io/mobius-transforms/

### timhutton/mobius-transforms

Shared with: Public, Roice Nelson
- 2016-01-12 18:03:26+0000
Very nice!  Interesting how the movements are sometimes intuitive, but often not (esp. when c and d are in general positions).  I had a couple thoughts for additions:

- I'm not sure what a good UI would be, but it'd be nice to provide a way to send points to infinity.

- A Möbius transformation can be defined by picking any 3 points and sending them to any other 3 points.  So another mode of this applet could be to drag around 3 points and graph the transformation that sends them to 3 canonical points (say 0, 1, and infinity).

Of course since you've posted your code, there is no excuse to not go experiment with these suggestions myself :)
- 2016-01-12 18:29:57+0000
Yes, I hope to find time to add those sorts of options. Also a way to limit the transforms to those for the Poincare disk which was my real goal. Maybe the 3-points suggestion would suffice for that.

I was inspired by the mouse dragging for translation of the hyperbolic plane in your MagicTile program. So I'm working my way through Visual Complex Analysis, as suggested from a comment in your code.
- 2016-01-12 20:11:10+0000
Cool, that's a great book, and where I learned the concepts needed to make MagicTile.  I'd like to reread it.

Let me know if you run into any specific questions about the hyperbolic panning.  The panning code there was derived from what Don Hatch did here (his code is available):

www.plunk.org/~hatch/HyperbolicApplet/

I recall isometries of the hyperbolic plane do amount to moving around 3 points on the disk boundary, though the MagicTile code doesn't end up calculating the Möbius transformations that way.
- 2016-01-12 20:14:01+0000