A human-machine interface involves plural spatially-coherent visual presentation surfaces at least some of which are movable by a person. Plural windows or portholes into a virtual space, at least some of which are handheld and movable, are provided by using handheld and other display devices. Aspects of multi-dimensional spatiality of the moveable window (e.g., relative to another window) are determined and used to generate images. As one example, the moveable window can present a first person perspective “porthole” view into the virtual space, this porthole view changing based on aspects of the moveable window's spatiality in multi-dimensional space relative to a stationary window. A display can present an image of a virtual space, and an additional, moveable display can present an additional image of the same virtual space.