Integrating over a neighborhood subdomain

Hello, as part of a larger problem I want to solve an integral over a circle with radius R for each node, the circle should be centered at each nodes (x,y) coordinates, so every node would have a circular neighborhood consisting of the nodes within a adistance R. Doing this for a circle with a fixed center would be fairly straightforward by using a function which is 1 within the neighborhood and 0 outside it however how could one do this when the circle has a changing center, or is there a better way than trying to define a function?