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I know that the use of twistur-momentum variables makes manifest the arising of certain poles in scattering amplitudes: if the sum of external momenta $P_I = p_i + p_{i+1} + ... + p_j$ is going on-shell, i.e. $P_I^2 = 0$, then the twistors $Z_i, Z_{i+1} , Z_{j}, Z_{j+1}$ are becoming planars.

How does it translate, in momentum twistor space, that a non-consecutive subset of the external momenta are going on-shell? Is there any simple picture?

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