A

rotation around the

edge of a

circle is often interesting in making

computer games. An

elliptic rotation may be of

similar interest.

Let

` x`^{2}/a^{2}+y^{2}/b^{2}=1 be an ellipse with given

parameters a and b. Let (x

_{0},y

_{0}) 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,

`
x`_{n}=x_{0}cos(t)-sqrt(a^{2}-x_{0}^{2})sin(t)

and

y_{n}=y_{0}cos(t)+sqrt(b^{2}-y_{0}^{2})sin(t).

I

suspect that this rotation can be accomplished with a

distance instead of an angle, but I am still working this out.