如何正确缩放字体字形轮廓？

Question

How do I scale a font-glyph outline to match a certain point size?

For example, I have the outline of the T-glyph (Arial) which looks like this:

The top two points of that glyph are at the Y-Coordinate 1466. According to this TrueType document from Microsoft: https://docs.microsoft.com/en-us/typography/opentype/spec/ttch01#scaling-a-glyph

I have to calculate it like this:

pointSize * resolution / ( 72 points per inch * units_per_em )

units_per_em for Arial is 2048, my target DPI is 72 and the font size I want is 12, so if I do this I get:

1466 * 12 * 72 / (72 * 2048) = 8.589

This results in the rasterized image to look like the one on the right in this picture:

The left glyph here is a screenshot of the 12pt T in WordPad, the right one is my rasterized one.

As you can see mine is not only way smaller, but also blurry. This is due to it only being 8.589px tall and the top pixel being between two pixels. And when I use 96 DPI as a target device DPI the result is 11.4531, which I guess is what WordPad does (pt vs px) but it's still blurry since 11.45 is still between two pixels.

I am wondering, how do I scale the glyph outline to get an as crisp result as WordPad does? Any ideas?

Simply rounding the values to full pixels can't be the solution since that would not work for any glyph with diagonal lines (eg A). The colors that look like chromatic-abberations on the WordPad one are from Windows' ClearType feature which uses "subpixels" of the LCD for an even sharper result on diagonal glyph outlines. I don't worry about these for now.

Answer 1

After reading more about it, I realized that TrueType has an interpreter language to grid fit the glyphs. So I'll have to implement that :)