The key to rotating objects in perspective is the ellipse.
Figure 5A shows a circle drawn on a grid. Figure 5B shows the grid drawn in perspective (turn it on its side and you will see that it is similar to figures 1 and 2). Using the grid as a guide, it is possible to plot the circle in perspective. The circle becomes an ellipse.
Figure 5C is the same without all the grid lines. You will notice that the centre of the ellipse is not the centre of the circle and square in perspective — of course not, how could it be if perspective foreshortens, i.e. we see more of the near half than of the distant half. The ellipse is at its widest just forward of the centre in perspective. But notice also that it is a perfect ellipse.
Some people will tell you that the curvature of the near half of the circle in perspective is different from the distant half. They are wrong. That will only happen if you break the rules of perspective set out in my previous article — if you try to take in too wide an angle of view. In fact the ellipse is a useful guide and test for drawing accurate squares in perspective. But back to the subject of spinning.
In figure 6A I have added spokes to the circle. Using the grid I have drawn the spoked wheel in perspective in figure 6B. The ends of the spokes can be treated as the series of positions of a point on an object animated rotating. What the points represent is again up to your imagination. Figures 7 and 8 illustrate sequences from my film Chess Board. The same principles can be applied to any flat object rotating. In theory they can be developed to rotate solid objects but I confess that I have never had the patience to do this. I find flat surfaces much more dramatic, but what little I do know about rotating solids fills me with admiration for the number crunching involved in computer animation that tumbles and falls. I find that sixteen spokes to the circle gives smooth animation when filming on twos, i.e. 16 positions in a spin lasting about 1 and a half seconds. To vary the effect, you simply plot a different number of evenly spaced spokes. The beauty of rotating about a fixed point is that you can repeat the sequence of drawings to continue the spin for as long as you like.
If you want a good book on perspective, I can recommend Perspective for Artists by Rex Vicat Cole, a paperback published by Dover, ISBN 0 486 22487 2. I bought my copy recently in London at Paperchase, Tottenham Court Road (a stones throw from Chromacolour Animation Supplies) for £3.60. It is a reproduction of a book written in 1921. It is excellent value although it does not deal specifically with animation. It sets out the basic principles clearly and is particularly useful for solving tricky problems.
The main reason I wrote these articles was because I could find little in books on animation about perspective and some of what I did find was wrong or misleading. Now I am not so arrogant as to believe that my own explanations are above criticism. In fact I would welcome other reader’s comments. Having given away some of my own secrets, I would like to learn from other people in return.
I would like to emphasise that you do not have to use a technical pen and ruler to apply the principles of perspective. They also apply to freehand drawing. You simply use vanishing points, ellipses and any other handy principles to check the general accuracy as you go along. The animator has an advantage over other artists when it comes to plotting perspective. One of the main problems in preparing these articles was to make illustrations understandable. I do all the preparation of my perspective drawings on punched animation paper over a light box or even onto cel. However simple the construction of the drawings seems to be at first, I soon end up with a hopeless mess of lines. I simply take another sheet of paper, put it on the peg bar and trace the lines which really matter. And so the process goes on until I end up with the finished drawing which shows none of the complexity which went into the construction. If the construction involves vanishing points which are a metre or more outside the drawing area, it is simply a question of taping the peg bar onto a large flat surface.
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Printed in Animator Issue 23 (Summer 1988)