  A distance mean function measures the average distance of points from the
elements of a given set of points (focal set) in the space. The level sets of a
distance mean function are called generalized conics. In case of infinite focal
points the average distance is typically given by integration over the focal
set. The paper contains a survey on the applications of taxicab distance mean
functions and generalized conics' theory in geometric tomography: bisection of
the focal set and reconstruction problems by coordinate X-rays. The theoretical
results are illustrated by implementations in Maple, methods and examples as
well.
