Reflection curve on a surface

For a parametric surface $P(u,v)$, source parametric curve $Q(t)$ and eye $E$, put $a=(Q-P)/\Vert Q-P\Vert$ and $b=(E-P)/\Vert E-P\Vert$. The visible reflection locus satisfies $(a+b)\cdot P_u=(a+b)\cdot P_v=0$, with the source and eye on the reflecting side. Rank two of the resulting Jacobian matrix gives a locally one-dimensional locus in $(u,v,t)$ by the implicit function theorem.

// Target: analysis.bigb