  In this paper, we study a class of graph drawings that arise from bobbin lace
patterns. The drawings are periodic and require a combinatorial embedding with
specific properties which we outline and demonstrate can be verified in linear
time. In addition, a lace graph drawing has a topological requirement: it
contains a set of non-contractible directed cycles which must be homotopic to
$(1,0)$, that is, when drawn on a torus, each cycle wraps once around the minor
meridian axis and zero times around the major longitude axis. We provide an
algorithm for finding the two fundamental cycles of a canonical rectangular
schema in a supergraph that enforces this topological constraint. The polygonal
schema is then used to produce a straight-line drawing of the lace graph inside
a rectangular frame. We argue that such a polygonal schema always exists for
combinatorial embeddings satisfying the conditions of bobbin lace patterns, and
that we can therefore create a pattern, given a graph with a fixed
combinatorial embedding of genus one.
