I have a closed disc $D$ \begin{equation} D=\{(x,y) \in \mathbb{R}^{2}: (x-a)^{2}+ (y-b)^{2} \leq R^{2} \} \end{equation} centred at the origin $(a,b)=(0,0)$ and with radius $R=15$ [m]. I have discretised the two-dimensional space $D$ to obtain a finite set of points $(x,y)$ using the polar coordinate system \begin{equation} x=r \cos \theta \end{equation} \begin{equation} y=r \sin \theta \end{equation} with \begin{equation} r \in \{0, 1, 2, \dots, 15 \} \ \mathrm{[m]} \end{equation} \begin{equation} \theta \in \pm \{0, 15, 30,\dots,180\} \ \mathrm{[deg]} \end{equation} I would like to be able to define a subset A which contains all of the points $(x,y)$ (i.e., the elements of $r$ and $\theta$) belonging to the set D which satisfy the condition $S>0$. Likewise, I would be able to define another set B which contains all of the points $(x,y)$ belonging to the set D which satisfy the condition $S=0$.
Am I correct in thinking that I first need to define indices for $r$ and $\theta$, e.g., $r_{i}, \ i \in \{0, 1, 2, \dots, 15 \}$? Any advice would be greatly appreciated!