  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.
