### Computing an Algorithm to Detect Three-Dimensional Objects in Space

#### Abstract

The motivation behind this research is to find a new strategy for data clustering, based on the iterative extraction of control points. A control point is a point used to maximize the distance to other existing control points that have already been recursively defined. Previous work in 2D data has been able to theoretically prove the consistency/equivalence between control points and vertices of data shaped in a polygon based on the theory of ellipsis. In a higher dimensional space, the theoretical justification of the consistency between control points and vertices is hard. Thus, I propose to generate a large set of simulated data to experimentally justify their consistency. The research consists of two parts. Firstly, the generation of simulated 3D data. To do this, we will generate a set of 3D points in a pyramid shape, but we will eventually expand to other 3D shapes. By being able to find 3 control points on a single plane, a generalized algorithm would have to be made to find the next control point. We will also add some randomness to ideal point sets the points in order to test the robustness of control point extraction with respect to noise. Secondly, we will implement the algorithm for control point extraction, then verifying the correctness on larger sets to visually verify the correctness. By doing so, we will be able to correctly identify shapes on a 3D scale, and then expand the algorithm to compensate for multidimensional objects and shapes.

#### Keywords

control point extraction; simulated data; multidimensional

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