Where the lines come from
A natal chart records a moment in time, not a place: in that second the planets stand where they stand, identically for the whole Earth. What changes is something else, namely the angle at which a planet is seen from a particular point on the surface. In Kyiv at 09:30 Mars may be high in the sky, while in Los Angeles in the same second it is below the horizon. Astrocartography finds every point on Earth where a planet was exactly on the horizon or exactly on the meridian at the moment of birth and joins them into a curve. That gives four lines per planet, around forty lines on the map in total.