Multibeam sonar systems have become essential tools for seafloor mapping and characterization. However, optimal survey planning for multibeam systems remains unresolved, particularly in regions with complex and irregular bathymetry. Practical exploration of these terrains requires the use of adaptive path planning strategies. The proposed method is novel, combining spatial analytic geometry with genetic algorithms (GA). Multibeam coverage's 2D and geometric parameters are analyzed for simplified 3D cases, based on geometric relationships derived through mathematical modeling. Next, measured bathymetric data are used to generate 3D seafloor models. The GA structure automatically optimizes competing possibilities. This method enables effective and comprehensive multibeam mapping of challenging seabed terrains and can be applied to sonar and radar technologies for adaptive survey planning in non-uniform environments.