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. Technology is used to determine aspects of the spatiality of the display devices in the physical world, and use the determined spatiality to affect the images displayed on the displays. For example, determined spatiality of the movable display relative to another display can be used to provide relative spatiality of images the two displays present to enhance the user's immersive perception. The movable display can context-switch between pointer functionality and spatial functionality depending on whether it is pointing toward a stationary display.