Originally the classical Laguerre plane was defined as the geometry of the oriented lines and circles in the real euclidean plane. Like a projective plane, a Laguerre plane is a type of incidence structure, defined in terms of sets of elements and an incidence relationship between them. The most important objects of a Laguerre plane are generally called points, generators and circles, with the circles and generators being sets of points. Perhaps the most straightforward model of a Laguerre plane uses the unit cylinder S_1*R in R3. The set of points, P consists of the points on this cylinder, the set of circles, C consists of the circles and ovals formed by intersections of the cylinder with any non-vertical planes and the set of generators, G consists of the generators of the cylinder. Points are incident with circles and generators in the standard way.
