Chapter - The Topological Weighted Centroid, and the Semantic of the Physical Space - Theory

The Topological Weighted Centroid, and the Semantic of the Physical Space - Theory

Pp: 69-78 (10)

* (Excluding Mailing and Handling)

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.

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.

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