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.

Comment: 26 pages, 6 figures, the paper is based on the plenary lecture presented at Meeting on Tomography and Applications (Discrete Tomography, Neuroscience and Image Reconstruction) 16th Edition, IN MEMORIAM OF CARLA PERI, 2 - 4 May 2022, Mathematics Department, Politecnico di Milano, Milano, Italy