We develop the framework of decentralised Navigation Functions for the case of multiple agents of arbitrary shapes and sensing areas around them moving in N-dimensional space. Unlike previous approaches utilising the Navigation Functions methodology, the construction here does not rely on diffeomorphisms, thus reducing the computational cost of the algorithm. The resulting potential field is absolutely locally computable and can be easily adapted to decentralised aircraft conflict resolution, as shown in the paper. Simulation results of multi-aircraft conflict resolution are included to support the efficacy of the complete control scheme.