Duality Between Lines and Points

In Computational Geometry, there are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. There is a common generalisation of all these notions. Most interesting properties of various notions of duality are also valid for this generalisation. However, there are two properties, which cannot simultaneously be true. It is also shown that either dual mapping can be its own inverse or it can preserve relative order (but not both). Generalisation of notion of duality to higher dimensions is also discussed. An elementary and very intuitive treatment of relationship between arrangements (in Computational Geometry) in d+1 dimensions and searching for k-nearest neighbour in d-dimensions is also given.