  In this paper, we provide an algorithm for traversing geometric graphs which
visits all vertices, and reports every vertex and edge exactly once. To achieve
this, we combine a given geometric graph $G$ with the integer lattice, seen as
a graph, in such a way that the resulting hypothetical graph can be traversed
using the algorithm in \cite{Chavez}. To overcome the problem with hypothetical
vertices and edges, we develop an algorithm for visiting any $k$th neighborhood
of a vertex in a graph straight-line drawn in the plane using $O(\log k)$
memory. The memory needed to complete the traversal of a geometric graph then
turns out to depend on the maximum ratio of the graph distance and Euclidean
distance for pairs of distinct vertices of $G$ at Euclidean distance greater
than one and less than $2\sqrt{2}$.
