You may have seen the computer generated workings of Big Ben in Disney’s Basil, the Great Mouse Detective. It was very impressive, but I would challenge the makers on the angle of view. As we flew around between the gears I got the distinct impression that the angle was far greater than 90 degrees. Perhaps I was in a minority in concentrating on the distortion at the edge of the screen rather than the action in the centre. There is bound to be a temptation in widescreen productions to exceed the normal rule, but it results in a reduction in the sense of involvement with the action. Since the view is no longer on a human scale, there is no sense of “being there”.
An alternative way of showing an angle of view greater than 90 degrees is to use cylindrical perspective, which I will describe later.
Measuring the angle of view of a picture is difficult but at the planning stage it is worth making a rough bird’s-eye view of the scene, the drawing surface and the viewpoint. Because of the formats in which we work, it is the width of view which matters more than the height.
Apart from taking this precaution you will normally realise that the view is too wide when the angles towards the edge of the picture become impossible. Figure 4 shows a surface with squares. Imagine you were standing in such a place. The corner of a square at your feet is of course 90 degrees. The near corner of any square in front of you and further away will appear to be progressively greater than 90 degrees, yet the nearest corner of the square at the bottom of the picture is less than 90 degrees. That simply is not a human view of such a scene, and yet the horizon and vanishing points seem correct. It is an example of perspective run riot. If the horizon was at the very top of the picture and the square at our feet was at the very bottom, then we would be taking in a view of 90 degrees from top to bottom and we would be looking down at an angle of 45 degrees. The glass would be tilted at 45 degrees. Figure 4 has tried to take in an area above the horizon and between our feet and thus exceeds the rules of perspective.
It may help to describe angles of view in terms of camera lenses. A 35mm stills camera requires a 30mm lens to give a view about 60 degrees wide. A 16mm cine camera requires a 9mm lens and a super 8 camera lens would have to be set at 5mm (to keep it simple, I am talking here about the width of the view rather than the diagonal from top left to bottom right). From this you will realise that 60 degrees is about as wide as most normal camera lenses go.
Incidentally, a camera is the perfect perspective machine. Because the lens and the film are locked together, the picture plane is always kept at a right angle to the line of sight.
Of course, whether the end result of all this artwork is a picture, a television image or a cinema screen, it is unlikely to fill our field of view. In the case of television it may only occupy 5 degrees. The whole system only works because our brain is able to think itself into the picture, even if we are sitting to one side. This is fortunate, as otherwise there would only be one point from which to view the picture.
To avoid confusion it is useful to mention non-perspective projection. In these systems parallel edges are always drawn parallel. See Figure 5. In reality this is only true for small distant objects but it can be used successfully for closer and larger objects, especially if there is no pretence at a relation. It is a normal approach in technical and engineering drawing, where its special rules have been formalised so that precise measurements can be plotted.
I apologise if I seem to have drifted away completely from the subject of animation, but I feel that it is important to establish the basis of perspective before applying it to the subject of movement. I hope that you will find the next article of more practical application.
Printed in Animator Issue 22 (Spring 1988)