 Twistor incidence relation

For a fixed affine spacetime point $x$, this linear relation cuts out a two-dimensional subspace $W_x=\{(ix\pi ,\pi )\}$ of twistor space. Projectivizing gives its twistor line. For a fixed projective twistor with $\pi \ne 0$, its solutions are $x=x_0+u^A{\pi }^{A^{\prime }}$, a totally null affine alpha-plane. The compact description replaces affine solutions by the two-planes containing the fixed twistor line in the vector space.