During control of a user interface via free-space motions of a hand or other suitable control object, switching between control modes can be facilitated by tracking the control object's movements relative to, and its penetration of, a virtual control construct (such as a virtual surface construct). The technology disclosed includes determining from the motion information whether a motion of the control object with respect to the virtual control construct is an engagement gesture, such as a virtual mouse click or other control device operation. The position of the virtual control construct can be updated, continuously or from time to time, based on the control object's location.