I want to draw Ford circles within a "distance Estimated system" (ray marching). Therefore, given a point $(x,y)$ from $\mathbb R^2$, I need the shortest distance to any circle with center $(p/q,1/2q^2)$ in $\mathbb R^2$ with radius $(1/2q^2)$ for coprime integers $p$, $q$. It should be somehow possible to calculate (or at least approximate) with … maybe a continued fraction approximation of $x$?

uniqueclosest Ford circle to every point? $\endgroup$ – LSpice May 23 at 15:26below(x,y). Now i still need to find the bigger neighbour circles - which are also neigbours of p/q in the Farey Sequence F_q $\endgroup$ – jukzi May 23 at 18:55