" the complement of a codimension-one projective subspace of RP3(real projective space) is identifiable in a geodesic-structure manner with an affine 3-space so that the group of projective transformations acting on it is identical with the group of affine transformations of the affine 3-space.we call this set an ' affine patch ' .conversely , a natural completion of an affine 3-space is identified with RP3 in a geodesic preserving manner ".
what does 'geodesic preserving manner' mean? I know it means that we can embed affine 3-space in RP3 by a map which preserves geodesics , but how does this map do this?