Having come into possession of a clear plastic cube, I decided to create a physical model of it.
The first step was to place the picture plane so as to divide the cube in half, so that the distance from the ground plane to the centerpoint, one half the cube's height, would equal the distance from the viewpoint to the picture plane.
I cut the picture plane out of an old CD jewel box, inscribed the horizon line, vertical center line, and circle of view on it, and mounted it at the halfway point.
On the facing side of the same piece, I made a line from the middle of the bottom edge to the centerpoint, representing the viewer's eye height and viewpoint.
I made a rectangular opening in a square sheet of paper to mask off part of the picture plane, leaving a window to reveal the space on the far side. Note that the center of the picture window is not the same as the center of vision.
The window could be any arbitrary size, shape, or position in the plane, although usually the center of vision (the main vanishing point) is somewhere near the center of the picture.
The space behind the window is defined by two inclined planes at 45˚, meeting at the horizon and inscribed with a grid of orthogonals and diagonals.
Figuring out how to plot this grid was a puzzle, and led to some interesting insights into the wider subject of space division in a rectangle, so I'll address that in a separate installment. Basically, the inclined planes mimic the appearance of infinite ground and sky planes receding to the horizon, but contained in the half-cube opposite the viewpoint.
I tried to get a photo from as close as possible to the actual viewpoint. It should give the impression of looking into 3D space (on a really gloomy, depressing day in some sort of post-apocalyptic dystopia).
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