Rectilinear Drawing 53
density for the drawing, and Fe is the similar density cor-
responding to the erasure (so that Fi≥Fe everywhere), then
the final drawing clearly corresponds to the density function
F = Fd-Fe≥0.
A second variant of our problem is obtained if we allow
only a single uniform erasure all over the plane, i.e., modify
F≥k>0 to F — k, where F is the density function for the
given drawing and the constant k corresponds to the uniform
erasure in question.
For our later purposes it is convenient to select a certain
point O in the plane as center for a system of rectangular
coordinates x, y and of related polar coordinates r, θ. Here r
is regarded as positive or negative while θ is an angular
coordinate of period 2τr so that (r, θ) and (— r, θ+π) will
denote the same point. Thus we may regard the density F
as a function of r and θ of period 2π: F = F(r, θ), with
F( — r, 0+7r) = F{re θ~). Similarly we may specify a line I