Raster and Height Issues

Contents

• Raster Units
• Width
• Reasons
• Music

1 - Raster Units

I suppose that the topic of this chapter is something that isn't even an issue, save in my own mind. When I was in elementary school, I always puzzled over counting and subtraction. How many days between Monday and Friday? Mathematically, four (5 - 1 = 4), but it feels much more like five on Monday morning. I find that I still have to doublecheck myself when making hotel reservations, as these are calculated in nights, but include at least part of both the beginning and ending days.

A similar problem arose in my mind when trying to understand the height of Dr. Hershey's characters. In "Calligraph for Computers" [Hershey 1967], the "basic" heights of the Indexical and Normal sizes are given as 13 and 21, respectively. In [Wolcott & Hilsenrath 1976], the Cartographic size is given as 9 raster units.

Now, a "raster" display is one in which there are a series of dots arranged in lines. If I have a raster display, and I take 9 lines of it, I would expect to be able to count these lines 1, 2, 3, ... 9. So if I were to plot an uppercase "A" on it, I would put the lowest part of the A at 1 and the upper at 9. That is to say, like a poor student on Monday morning, I would count both the beginning unit and the end.

However, if you count the height of an "A" in the Hershey vector repertory, the Cartographic size, for example, goes from -5 to +4 (the Y dimension increases going downward). That's -5, -4, ..., 0, 1, ..., 4, for a total of 10. Similarly, the Indexical "A" (glyph 1001) goes from -7 to +6 (total, inclusive: 14) and Normal "A" (glyph 501) goes from -12 to +9 (total, inclusive: 22).

So Dr. Hershey's "raster units" are the horizontal and vertical spaces between the coordinates of the end points of the lines.

2 - Width

Dr. Hershey gives the "basic" width of the Indexical size as 10, and the Normal size as 14 [Hershey 1967], [.. FINISH THIS (remember, this is a Notebook, not a work polished for publication!)]

3 - Reasons

Dr. Hershey explains some of the reasons for his choice of these "basic" heights and widths in "Calligraphy for Computers." Having determined the minimum possible sizes for polygonalized circles, he bases (as I understand it) his smaller type sizes on these. For example, he notes that the "smallest ['satisfactory polygonalization of a small circle' is] an octagon of 4 or 6 raster units diameter and a dodecagon of 8 raster units diameter" (11) and that "the various round characters should be coordinated with small circles." (13) By way of illustration, the circular portion of the Cartographic "9" (glyph 209) is indeed an octagon of 6 raster units diameter. To take another example, he notes that in the Roman alphabet "some lower case letters are two-thirds as high as the upper case letters." (13) His choice of 21 raster units for the height of the Normal glyphs allows such a division into thirds.

4 - Music

Understanding Dr. Hershey's "raster units" allowed me finally to understand a passage in "Calligraphy for Computers" which had heretofore baffled me:

The digitalization of musical symbols depends upon the spacing between the lines of the staff. A whole note can be centered over a line only if its height is an even number of raster units. The note can be centered between lines if the spacing between lines is even. ... (15)

So imagine a note that is 4 raster units high, drawn from Y=2 to Y=-2. Such a note could be centered on a staff line drawn at Y=0. Of course, the staff line itself must be thought of as being zero raster units wide.