The efficient navigational queries supported by the succinct representations of mosaic and slicing floorplans, as well as plane bipolar orientations, have significant implications in various practical applications. In the realm of computer-aided design (CAD), these representations can facilitate rapid querying of spatial relationships between rectangular objects, which is crucial for tasks such as block placement in integrated circuit design. The ability to quickly determine adjacency or retrieve neighboring objects enhances the efficiency of layout optimization processes. Additionally, in graph drawing and visualization, the efficient navigational capabilities can improve the rendering of complex structures, allowing for dynamic adjustments and interactive exploration of graph properties. Furthermore, in the context of data structures and algorithms, these succinct representations can serve as a foundation for developing more advanced data management systems that require efficient spatial queries, thereby broadening their applicability in fields such as geographic information systems (GIS) and robotics.