A scanning range measuring laser gives very useful sensor feedback for many robot operations. Plane surfaces and, say, tree trunks are the most useful geometric primitives. However, most of the angular resolution is carried by range discontinuities. This thesis is a study of properties of range discontinuities and their use in robot navigation. We nd algorithms for computing the locations: and determine whether it is a front or back discontinuity. The thesis also involves test-driving, calculations and simulations. The MICA (Mobile Internet Connected Assistant) wheelchair is used as test platform. Some applications use other means of nding the range, a range camera for example.