A rotation around the edge of a circle is often interesting in making computer games. An elliptic rotation may be of similar interest.

Let x2/a2+y2/b2=1 be an ellipse with given parameters a and b. Let (x0,y0) be a given point on the edge of this ellipse, and let t be a positive angle through which to rotate:
```
(0,b)       (x0,y0)
(xn,yn)    ,....onOK@@@@@@@@@@@HQme....,
,..szSZSZF'`         |         `'TUXUXux..,
,z4P'`,                           /        `'GAc,
,xw'`    `\,               |        /             `'wx,
.u'`         `\,                     /                 `'n.
,dy`             `\,           |      /                    `qb,
/7`                 `\,               /                       `A\
4y                     `\,       |    /                          \D
,I'                       `\,         /                           `U,
dp                          `\,   |  /                             qb
,j'                            `\,   /  <--angle t                  `t,
AV                               `\|/                                VA
69- - - - - - - - - - - - - - - - -.- - - - - - - - - - - - - - - - -96 (a,0)
VA                                 |                                 AV
`t,                                                                 ,j'
qb                                |                                dp
`I,                                                               ,U'
\D                               |                              4y
VA,                                                           /7`
`qb,                           |                           ,dy`
`'n.                                                   .u'`
`'xw,                      |                      ,mx'`
`'Gcc,                                     ,zzN'`
``'Tuxuxux.,         |         ,.szszszF'``
````'TTOK@@@@@@@@@@@HQTT'````
```
Then,
xn=x0cos(t)-sqrt(a2-x02)sin(t)
and
yn=y0cos(t)+sqrt(b2-y02)sin(t).

I suspect that this rotation can be accomplished with a distance instead of an angle, but I am still working this out.