1. A three-dimensional (3D) space interface apparatus comprising: a 3D display unit configured to output a 3D virtual object; a sensing generator, including at least one processor, configured to generate a sensing signal for sensing a position and a movement of a manipulation object; a space determiner, including the at least one processor, configured to determine: a face of a user by using the sensing signal, a rendering space located between the 3D display unit and the face of the user, in which the 3D virtual object will be outputted, and a sensing space occupying a predetermined portion of the rendering space, in which the manipulation object will be sensed; and an interface, including the at least one processor, configured to verify, using the sensing signal, whether a contact between the 3D virtual object and the manipulation object has been made, and to generate a predetermined reaction corresponding to the contact when the contact has been verified as being made, wherein the interface corrects a distortion of the rendering space and the sensing space, each space varying depending on a position of the user; aggregates the corrected rendering space and the corrected sensing space; and verifies whether the contact has been made between the 3D virtual object output in the corrected rendering space and the manipulation object in the corrected sensing space.