  Let B be a subplane of PG(2,q^3) of order q that is tangent to $\ell_\infty$.
Then the tangent splash of B is defined to be the set of q^2+1 points of
$\ell_\infty$ that lie on a line of B. In the Bruck-Bose representation of
PG(2,q^3) in PG(6,q), we investigate the interaction between the ruled surface
corresponding to B and the planes corresponding to the tangent splash of B. We
then give a geometric construction of the unique order-$q$-subplane determined
by a given tangent splash and a fixed order-$q$-subline.
