Cylindrical Perspective
Cylindrical Perspective maintains vertical straight lines while rendering all horizontal lines as curved. This is an eighteenth century device to create a curved panoramic view. The flat grid looks something like this, and it really only makes sense when the painting is curved. The Central Vanishing Point will end up at the centre of the curve.
It depends for its believeability on the viewer being very near the centre of the curve, or the vanishing point, and that is really only feasible if the painting is quite large. It is now mainly used in museum display: as a diorama for the background to an exhibit. In fact, all these mathematical constructs require the viewer to assume a single point of view relative to the picture. Since all of these methods are purely conventional, purely artificial, they all require the willing and active participation of the viewer. Or to put it another way, it is the viewer's belief that makes it so. In that regard, our modern reliance on a mathematical solution to Perspective is no different from the Medieval belief in a Deocentric model.
