Angles Of View

We have been discoursing over the past several issues about the selection and sizing of fonts. Once we have chosen what appears to be a good face, we then perform some calculations which provide some absolute numbers describing the smallest size one of our projected symbols is allowed to be. Since the variables attending this process are numerous and even a little complex, this article will return one last time to review

The Casting of Characters

If we imagine ourselves positioned in front of a display screen and if that screen becomes filled with projected text, it is easy enough to see that our viewing angles from one portion of the image will differ greatly from another. The word or symbol appearing directly before our eyes may appear quite differently to the woman seated at the other end of our row. And, actually, if we stop to think about it, the area that all of us will have the most difficulty making out is either or both of the display's upper corners. In virtually all audience configurations, no viewer will be positioned on-axis and normal to each end of a screen's top edge. Any information which is projected onto those areas, therefore, will perforce be off-axis to its entire audience.



Figure 1

While this seems obvious enough, the thing to notice is that data appearing at those corners is off-axis to viewers in the horizontal and vertical planes. To read it, every one of us has not only to look to the side but has also to look up. And while we have learned to figure out how to accommodate for off-axis viewing in one dimension, what are we going to do about two?

Whatever we do, it's certain that we must ensure that each corner's data is projected large enough so that it can reliably be read from every seat in the house. And, of course, our answer for the upper corners will resultantly become the default for the entire display.

Our earlier efforts have taught us the value of requiring a subtended angle of at least 10 minutes of arc for the height of any lowercase character. That has translated, roughly, to mean ¼ inch of symbol height for every seven feet of viewing distance. When the viewing angle is larger than 0º, that ¼ inch or those 10 minutes of arc must consequentially be increased.

To see how these multiple parameters can be blended, let's create the following example: The job we'll concoct requires that we position an audience of thirty people before a 100-inch diagonal screen. We will further assume that the bottom of that screen is 48 inches off the floor and that the eye height of the average seated viewer is also 48 inches. Lastly, we will insist that the height of all lowercase characters subtends at least 10 minutes of arc on the retina of every viewer.

The two questions we want to answer are 1) How big should the characters on the screen be? And 2) If we assume an area of 6 ft² for every chair, how can we best configure the audience? The solution to this problem pops neatly out of some algorithms used by Dr. Joy Ebben (phdjoy@aol.com) and is graphically displayed in Figure 1.

To see what's happening here, notice first that the center of each of the two circles is exactly perpendicular to an outer edge of the screen. Each circle demarcates the floor area from which one upper corner of the screen can reliably be read. The area comprising the intersection of the two circles (outlined in bold), of course, works for both circles and is where we want to fit our seats.

Eye and Head Rotation
• Eye Rotation Only
— Optimum: 15° left - to - right
— Maximum: 35° left - to - right
— Optimum: Parallel and down 30°
— Maximum: 25° above parallel; 35° below parallel

• Head Rotation Only
— Optimum: Straight ahead
— Maximum: 60° left - to - right
— Maximum: 50° above and below parallel

• Eye and Head Rotation
— Optimum: 15° left - to - right
— Maximum: 95° left - to - right
— Optimum: Parallel and down 30°
— Maximum: 75° above parallel

Source: MIL-STD-1472D
909-941-4539
Joy M. Ebben, Ph.D.,CPE

It is interesting and perhaps a little counterintuitive to note that the front row is very much wider than the last but the discrepancy becomes immediately explicable when we consider both the viewing angle and the viewing distance to the edge of each row. The distance to the front row is calculated to keep the largest vertical viewing angle to not more than 25º. Dr. Ebben tries always to keep eye and head rotation within the limits presented in Figure 2.

Next we come to the character height of 0.9". If you play around with the math, you'll discover that this height is actually larger than necessary (by which we mean larger than 10 minutes of arc) for most areas of the display and for most seats. But it is not too large for the upper corners of the screen and, as we said earlier, it is those "worst case" areas which must govern.

Finally, it may be useful to indicate just how we can ensure that our projected characters will in fact stand at least 0.9" tall. As we sit before our computers, fine tuning the presentation we are about to make, is there a way to adjust our settings such that when our materials get put through a projector and up onto the screen they will meet our own standards? Fortunately, there is.

If we know that the height of the lowercase letter "x" must (in our example) be 0.9" high when displayed on a screen which is 60 total inches high, then we know that each "x" must be 60 / 0.9 or 1/67th of that screen height. Now we look at our computer monitor and recall that our projector will put up exactly a screenful of its contents at any one time.

Therefore, all we have to do is adjust our computer's point size setting until the "x" we see on its monitor is also 1/67th of that screen's height. The monitor on which this article is being written, for instance, has a viewing area height of exactly 9 inches. Dividing that number by 67, we get an "x" height of .134 inches which means that a lowercase "x" ought to be set at 14 points (in Times New Roman) and hence this high: x.

Please note that these proportions may not look right on your monitor and they certainly won't be right on a printed page because the latter contains more text than a monitor's screenful. Still, if you get a plastic word processing ruler, with scales on it that go down to at least 1/10th of an inch, you should have no difficulty measuring either your own computer screen or your client's.

The case for font and character control now rests. Its summation stresses the importance of its details. We have looked (in some depth) at many of the criteria which distinguish one font from another and we have examined (at some length) the sizing of projected symbols and the positioning of viewers expected to read them.

We do this work because we care about the quality of the display systems our industry delivers. Since the product of those systems is information, surely we, their creators, are obliged to be similarly informed.