The images to be embedded in a point cloud are placed on an adjacent pair of cuboid faces. To construct the point cloud representing these two images, direct a ray from each pixel, perpendicular to the pixel's image plane, across the cuboid. The intersections of the set of rays from the image on one face with the rays from the image on the adjacent face are registered by points in the cuboid's volume. The point cloud is the set of these points of intersection. The existence of a point cloud requires that the images have a pixel at every value of the shared coordinate.
The relationship between a body and its projections is given by the Radon transform, which forms the underlying mathematical basis for computed tomography. While the Radon transform deals with bodies of a spatially varying opacity and can use a number of projection schemes, in this Demonstration a point, or more properly a voxel, is simply either opaque or transparent, and the projection is orthogonal.