Abstract
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.
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