The complement of a codimension-one projective subspace of $\mathbb{R}\mathbf{P}^{3}$ is identifiable in a geodesic structure preserving 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.

In the above sentence what does the "geodesic structure preserving manner" part mean?