This paper proposes a distributed coverage control strategy for quadcopters equipped with downward-facing cameras that prevents the appearance of unmonitored areas in between the quadcopters' fields of view (FOVs). We derive a necessary and sufficient condition for eliminating any unsurveilled area that may arise in between the FOVs among a trio of quadcopters by utilizing a power diagram, i.e. a weighted Voronoi diagram defined by radii of FOVs. Because this condition can be described as logically combined constraints, we leverage nonsmooth control barrier functions (NCBFs) to prevent the appearance of unmonitored areas among a team's FOV. We then investigate the symmetric properties of the proposed NCBFs to develop a distributed algorithm. The proposed algorithm can support the switching of the NCBFs caused by changes of the quadcopters composing trios. The existence of the control input satisfying NCBF conditions is analyzed by employing the characteristics of the power diagram. The proposed framework is synthesized with a coverage control law that maximizes the monitoring quality while reducing overlaps of FOVs. The proposed method is demonstrated in simulation and experiment.