  Cryo-electron microscopy is a technique in structural biology for
discovering/determining the 3D structure of small molecules. A key step in this
process is detecting common lines of intersection between unknown embedded
image planes. We intrinsically characterize such common lines in terms of the
unembedded geometric data detected in experiments. We show these common lines
form a semi-algebraic set, i.e., they are defined by polynomial equalities and
inequalities. These polynomials are low degree and, using techniques from
spherical geometry, we explicitly derive them in this paper.
