THE PIVOTAL TESSELLATION

Abstract

The tessellation studied here is motivated by some stereological applications of a new expression for the motion invariant density of straight lines in R3. The term 'pivotal' stems from the fact that the tessellation is constructed within a plane which is isotropic through a fixed, 'pivotal' origin. Consider either a stationary point process, or a stationary random lattice of points in that plane. Through each point event draw a straight line which is perpendicular to the axis determined by the origin and the point event. The union of all such lines (called p-lines) constitutes the mentioned tessellation. We concentrate on the pivotal tessellation based on a stationary and isotropic planar Poisson point process; we show that this tessellation is not stationary.