Let's say I have $n$ circles of radius $r$ that are spaced with a nearest-neighbor distance of $\delta$. (i.e. the shortest distance between any two particles is $\delta$.)
It is trivial to determine the coordinates ($x_n$,$y_n$) of the centre of these circles if they are placed along a circle. (You can simple use the rotation matrix.) Here is a schematic of these circles placed around a circle:
If I want to place these circles around an ellipse of axes $a$ and $b$, how do I determine the coordinates of the centre of each circle? Approximations are OK.