A directional sensor network (DSN) consists of directional sensors instead of the omnidirectional ones in the conventional wireless sensor networks. The sensing coverage of a DSN depends on the directionality and size-specific sensing angle of the sensors. The conditions are dissimilar from those of omnidirectional sensor networks for researches, especially on the sensing coverage. For coverage problem in DSNs, the geometric structures of Voronoi diagram and Delaunay triangulation have not drawn the attention of researchers. This study utilised Voronoi diagram and Delaunay triangulation and proposed four basic distributed and localised sensor direction adjustment algorithms with the characteristics of these two geometric structures to explore the field coverage improvement in DSNs. The simulation results and comparisons of coverage performance of the proposed four basic algorithms are provided. They can give the clarity of the performance results and have a reference value for future advanced studies on various coverage issues in DSNs.