  A single-vertex origami is a piece of paper with straight-line rays called
creases emanating from a fold vertex placed in its interior or on its boundary.
The Single-Vertex Origami Flattening problem asks whether it is always possible
to reconfigure the creased paper from any configuration compatible with the
metric, to a flat, non-overlapping position, in such a way that the paper is
not torn, stretched and, for rigid origami, not bent anywhere except along the
given creases.
  Streinu and Whiteley showed how to reduce the problem to the carpenter's rule
problem for spherical polygons. Using spherical expansive motions, they solved
the cases of open < \pi and closed <= 2\pi spherical polygons. Here, we solve
the case of open polygons with total length between [\pi, 2\pi), which requires
non-expansive motions. Our motion planning algorithm works in a finite number
of discrete steps, for which we give precise bounds depending on both the
number of links and the angle deficit.
