Among other things, I started to look into the data that goes into making an italic. In trying to find out what the aforementioned values in hhea meant I came across Apple’s manual noting:
Note that since the slope is a ratio, values may be used which simplify or speed up calculations. A
caretSlopeRise of 8 and
caretSlopeRun of 6 means the same thing as
caretSlopeRise of 4 and
caretSlopeRun of 3.
I also found Adam Twardoch’s comment
about “rational angles,” which used simplified values.
However, as I looked into some italics from fonts I have (Harriet Text, Quadraat, Akko, and others) each had a caretSlopeRise of 1000 units and varied in the caretSlopeRun. Some could not be simplified, but others certainly could be. I figured it had something to do with the bounding box, but that doesn’t make sense considering a vertical font’s values would be the simplified Rise 1, Run 0.