  A graph is 1-planar if it can be drawn in the plane so that each edge is
crossed at most once. However, there are 1-planar graphs which do not admit a
straight-line 1-planar drawing. We show that every 1-planar graph has a
straight-line drawing with a two-coloring of the edges, so that edges of the
same color do not cross. Hence, 1-planar graphs have geometric thickness two.
In addition, each edge is crossed by edges with a common vertex if it is
crossed more than twice. The drawings use high precision arithmetic with
numbers with O(n log n) digits and can be computed in linear time from a
1-planar drawing
