A method for transforming low-density configurations of rods, discs or spheres to rigidly jammed packings is described. In D dimensions, it repeats a cycle in which each particle is moved towards to the centre of the cage of the D + 1 neighbouring particles that most closely contain it. Low-density fluid configurations of discs and spheres form rigidly jammed amorphous packings with densities below the normal glass transition density. The glassy structures contain large pores and many mobile rattler particles.