In a previous article, the authors described an algorithm to determine
whether a finite metric polyhedral complex satisfied various local
curvature conditions such as being locally CAT(0). The proof made
use of Tarski's theorem about the decidability of first order
sentences over the reals in an essential way, and thus it was not
immediately applicable to a specific finite complex. In this article,
we describe an algorithm restricted to 3-dimensional complexes which
uses only elementary 3-dimensional geometry. After describing the
procedure, we include several examples involving Euclidean tetrahedra
which were run using an implementation of the algorithm in GAP.