Timeline for How to smootly interpolate between möbius transformations?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 19, 2009 at 20:15 | comment | added | hyperlogic | Thanks Greg. I eventually got it to work. When $\theta > \frac{\pi}{2}$ I use $\theta - \pi$ instead. Thanks for your help! | |
| Nov 19, 2009 at 20:14 | vote | accept | hyperlogic | ||
| Nov 18, 2009 at 5:17 | comment | added | Greg Kuperberg | Actually what you should do, as a consistency check, is compute the fixed point of the rotation matrix and mark it as a dot in a draft version of the game. The fixed point is determined by the eigenvectors of the matrix. In the hyperbolic case, you should mark the unique invariant line, the line that connects the two fixed points on the boundary; again these fixed points are eigenvectors. That will help you see the intended motion. | |
| Nov 18, 2009 at 5:14 | comment | added | Greg Kuperberg | (1) If you replace $M$ by $-M$, then $\theta$ goes to $\theta \pm \pi$. If this is interpreted properly, then keeping the total rotation $|2\theta|$ below $\pi$ is inevitable. (2) If it's done properly, then the rotation point shouldn't be at the same spot of the tile in different cases, nor even inside or near the tile at all. In the hyperbolic case, there shouldn't be any true rotation, but an off-center hyperbolic motion might well look like a rotation. | |
| Nov 18, 2009 at 4:57 | comment | added | hyperlogic | I'm attempting to implement your description, but I'm seeing a couple problems. 1) negating M has no effect, the rotation still takes the long way around. Maybe I've misunderstood what you mean by negation? 2) the tiles rotate about one of their corners rather then about their centers. | |
| Nov 15, 2009 at 6:04 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |