In this chapter new mathematical objects, aimed to describe semantic aspects of set of non random
points, are described together with their theoretical background. They are: Topological Weighted Centroid
(TWC); Self Topological Weighted Centroid (STWC); Proximity Scalar Field; Gradient of the Scalar Field
Relative Topological Weighted Centroid (TWCi); Paths form Arithmetic Centroid to entities; Paths between
entities; Scalar Field of the trajectories. These new mathematical quantities are able to describe some important,
semantic aspect of a set of points defined in a bi-dimensional or tri-dimensional space. These quantities
can also be used also to analyze the semantic of a set of points defined in a higher dimensional space. All the
proposed quantities will be defined considering a set of N points, called entities, in a two-dimensional space,
the extension to three dimensions being elementary. As we will see, the proposed mathematical quantities are
points, curves or scalar fields.
Keywords: Topological Weighted Centroid (TWC); Self Topological Weighted Centroid (STWC); Proximity
Scalar Field; Gradient of the Scalar Field; Relative Topological Weighted Centroid (TWCi); Paths form
Arithmetic Centroid to entities; Paths between entities; Scalar Field of the trajectories.
