LAST EDITED ON Feb-02-01 AT 00:18 AM (EST)If I may modify my previous post, the situation is probably a little more complex than that.
Instead of saying "Right, this is what you do," I should have said "You are within your rights to do that." Yours may not be the only possible definition of the reflection in a curve. The well known "reflection" in a circle is inversion.
Two points P and Q are inversions of each other in a circle with center O and radius r iff the three points O, P, Q are colinear and OP·OQ = r2.