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We introduce a procedure to adapt local interpolations to represent spatial fields as they are measured by a mobile sensor network. The scheme incorporates new sensor (synchronous) measurements in a similar fashion to a Kalman filter-like recursion. We derive necessary conditions that allow the distributed computation of the recursion and present an algorithm that makes use of agreement rules that satisfy them. We show how the nearest neighbor interpolation scheme is compatible with the motion coordination algorithm for region coverage proposed in. Finally, we illustrate the performance of the algorithms in simulation.