Tracing points around a curve/ellipse Sorry if this has been asked before but my maths days are long behind me. 
What I want to know is how to find out the coordinates along the circumference of an ellipse. 
So supposing I am at point X,Y which lies on the circumference, and I am traveling at velocity  Z. How can i work out after given time t what the new X,Y values would be. 
seems so simple but just cant think where to start. 
Thanks for the help
Aaron
 A: I don't think this has a nice elementary solution -- since the period of such a solution would be the circumference of the ellipse, something that it hard enough to compute that it has its own class of special functions associated with it.
So in practice you need to do it numerically, and then it's easy enough to program. You know (I hope) how to generate points on the ellipse without the constant-velocity requirement:
$$ u \mapsto (a\cos u, b\sin u)$$
where $u$ is a parameter and $2a$ and $2b$ are the lengths of the ellipse's major and minor axes. Your only problem is then to find the next $u$ value at each step. If you do it with small enough steps you can simply differentiate this expression to find out how far a small change in $u$ makes the point move. You get something like
$$ u(t+\Delta t) = u(t) + \frac{z\Delta t}{\sqrt{a^2\sin^2(u(t))+b^2\cos^2(u(t))}}$$
where you choose the time step $\Delta t$ by trial and error to be small enough that the speed ends up being close enough to constant for your needs.
