Agents operating in open fields, like robots, soldiers, rescue workers, or ships, may need to do qualitative reasoning with relative directions. We have introduced here a generalized framework for that purpose, with a parameterized angular zoning scheme (e.g., zoning with 60-degree or 90-degree). Such a parameterization of qualitative reasoning is a new direction, for an area that typically engages in strict propositional reasoning otherwise. We have introduced some important properties of this ontology, the general complexity results for reasoning in it, and provided a maximal tractable subclass. We have also discussed some of the special cases for some constant values of the parameter, showing when this type of reasoning is not possible, and subsuming some of the previously reported interesting results.