Tessellations by connection

摘要

Let us consider a set R of points of the plane, composed of n connected components R_1,. . .,R_n. To each component R_i, we can associate the set V_i of points y of the plane that are strictly closer to R_i than to any other component of R. The Set V_i is called the influence zone of R_i .It is a generalization of the well-known concept of the Voronoi region. The influence zones transformation is the map which associates, to each set R, the set V which is the union of the Influence zones of the connected components of R. In the discrete space Z~2, with the distances d_4 and d_8, the influence Zones transformation does not preserve any topological characteristic, not even the number of connected components.