I am currently working on sensor networks, where sensors are uniformly distributed in a polar coordinate system (maximum radius $R$ is set to $1$). A few of the sensors are placed equidistantly on a circle of radius $r_s$ (with $r_s < 1$).
What I want to draw are separating functions $f: R \rightarrow \theta$, such that it maximizes the margin between two neighboring "special" sensors, while also going through the origin $(0,0)$. This is easy for the case where all the special sensors are equal in their radial component, since in that case $f$ maps all radial inputs to $\frac{|\theta_i - \theta_j|}{2}$.
However, how would I best approach this problem if noise is added to the radial components of the special node placements? What comes to mind is running max margin classifiers and use the separating hyperplane, but are there simpler approaches?
Attached you can find a figure that hopefully presents my problem in a little (sorry for the bad drawing). So what I want are functions to separate one segment from the other (each special sensor "owns" a segment).