A user can selectively engage some part or all of the haptic display of a haptic interface device to produce an enhanced interaction with an environment with which the user interacts using the haptic interface device. Further, the haptic interface device can be implemented so that the part of the haptic display that is engaged can be engaged to varying degree. The degree of engagement with the haptic display (together with whether part or all of the haptic display is engaged) determines the manner in which the haptic display is experienced by the user. The selective engagement with the haptic display is enabled by adding a haptic clutch model to the underlying haptic model used to produce the haptic display, the haptic clutch model engaging some part or all of the haptic model in response to user input. The addition of a haptic clutch model to the haptic model used to produce a haptic display provides a richer user interaction than is provided by a haptic display produced by the haptic model alone.