An Analysis of Triangulation in Geometrically Noisy Environments using Mathematics

Abstract

This paper uses mathematics to analyze the challenges of geometrically noisy environments on triangulation. Given widely accepted algorithmic triangulation methods, such as O (n ln n) or a simpler O (n^3) method, we can mathematically prove that triangulation of any two dimensional polygonal region is possible, albeit impractical in some cases. Further, we consider the implications of environments in which a z-axis is present, as seen in cellular triangulation. In many of the cases where consideration of the z-axis is necessary, we recognize the absence of a fixed or known point of origin and consider methods of addressing this challenge.