So to construct drawings in cylindrical perspective we need what I would call sine curve graph paper. So far as I can establish such paper does not exist, though I am sure a computer could be persuaded to generate it. Figure 4 shows a series of sine curve segments which I plotted on ordinary graph paper using a book of mathematical tables. Remember that we are after creating the feeling of turning or spinning round. You can see on the left hand side of figure 4A that the curves are spaced at regular intervals of height and they all converge at a vanishing point on the right. I hope you can see how this framework corresponds to a picture such as View of a Room.
In the previous article I dealt with regular space division of receding lines by using a diagonal. Figure 5 shows how this principle is adapted to cylindrical perspective. First you trace some of the curves to show the horizontals of say a wall or fence. Next you turn the tracing paper round and trace a curve in the opposite direction (this acts as the diagonal) and then mark where it crosses the horizontals and where it would cross the other curves. Then plot the verticals at or below these crossing points. Which curve you use as the diagonal will affect the spacing of the receding uprights. By trial and error it is possible to plot squares. In the background drawing itself you should emphasise the curves and only indicate the uprights faintly. Otherwise the uprights tend to “strobe” as you pan across them.
I would not recommend making a whole film of cylindrical perspective shots, but as an occasional device it can overcome the technical problem in animation of imitating what is a simple pan shot in live action. Such shots also have a certain shock value; the audience realises that you have done something clever, but isn’t quite sure what you did. They are generally used as fast pan shots to follow fast action, but I would recommend that you experiment with the speed of panning. They can be equally effective as a slow panorama.
I suspect that most of you will regard cylindrical perspective as an obscure backwater of drawing and animation, but I think its possibilities have hardly been explored. If you can overcome the initial obstacle of constructing it on a grid of sine curves then you will find yourself in a world of expanded views. It is not just a matter of getting from one end of the background to the other, but of doing so in a way which approximates to human perception.
Printed in Animator Issue 24 (Winter 1988)