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We're inside the Mach cone of the tube, as if we were flying right behind a supersonic aircraft."
The bodies of revolution are defined by the cuts through the aircraft made by the tangent to the fore Mach cone from a distant point of the aircraft at an azimuthal angle.
Because the different radial directions around the aircraft's direction of travel are equivalent (given the "smooth flight" condition), the shock wave forms a Mach cone, similar to a vapor cone, with the aircraft at its tip.
Considering a rectangular wing, the pressure at a point P with coordinates (x,y) on the wing is only being defined by pressure disturbances originated at points within the upstream Mach cone emanating from point P. As result, the wing tips modify the flow.