Stem widths & heights management

Introduction & Background:

One of the primary purpose of grid-fitting is to ensure that some important features are preserved. One of them, if not the most important, is keeping the widths and heights of stems consistent on each character pixel size.

A naive approach would grid-fit each stem width by simply rounding it, independently of other consideration. However, this can create visible inconsistencies at small pixel sizes, when two stem widths that are close in pixel space become visibly distant due to the thresholding in the rounding process. This artefact is indeed very similar to the one that requires specific treatments in blue zones.

This problem is illustrated by the following picture:

As you can see, incoherent stems are really difficult to bear when reading text.

Standard widths and heights

The classical ways of dealing with this problem, as described in the Type 1 font format specification is to choose one or more "standard" widths that will serve as references in pixel space when computing the pixel dimensions of stems.

It merely consists in two phases:

  • First, at design time, an histogram of the stem widths and heights of all font glyphs is built, and peaks are detected (through any given thresholding method). The median of each peak is stored within the font file in a list of "standard stem widths".

  • During alignment control, each standard width is scaled and rounded to integer pixel coordinates. Then, for each glyph, stem widths and heights are compared to the standard ones in pixel space. If they are sufficiently close, the stem's width is snapped to the pixel standard width. Otherwise, it is rounded normally.

This scheme works as long as the standard widths and heights stored in the font are coherent and meaningful. However, there is no way to extract this information from many other formats, including TrueType. We thus need a fast way to compute standard widths on-the-fly.

To do it, we simply re-compute the standard width, or an approximation of it, each time a new face is loaded in the auto-hinter. This is done very simply by loading a few well-known characters like the "O", "o", "I", "i", "Z", "z" and taking the size of their largest stems.

Width normalisation

Once the standard widths are computed in the master space, we can scale them to the current pixel grid, and round them to integer pixel widths.

When aligning edges, we compute the scaled width of stems and compare it to the (unaligned) standard widths. If a stem width is sufficiently close to a given standard width (using a typical threshold of a half pixel), its is snapped to the rounded standard width.

However, if the stem width is not close enough to one of the standard widths in pixel space, it needs to be aligned. A first implementation consists in simply rounding its pixel width to an integer. However, this sometimes creates unpleasant artefacts, that are much rarer than the discepency demonstrated in the introduction picture.

These artefacts are rare, usually appear for a single point size which varies with the font, but still exist. A general principle of coherency is that it is better to be wrong by 10% all the time than completely correct in 95% cases, and greatly wrong in 5% cases.

To avoid these problem while following the coherency principle, we essentially change the rounding threshold depending on the position of the stem width compared to its closest standard width.

For example, if the stem width is greater than its closest standard width, we use a rounding threshold of 3/4 instead of 1/2. Similarely, if is is lower than the closest standard width, we use a treshold of 1/4, like in:

    if (width > closest)
       width = (width+16) & -64;
    else if (width < closest)
       width = (width+40) & -64;

Of course, a similar choice is performed when the stem is under the standard width. We thus have a way of making stem widths slightly closer to the standard width, and avoid most artefacts this way.

XXX : An alternative implementation could consist in moving the stem width towards the standard width, using the delta that was used to grid-fit the latter when it is in the right direction.

XXX : Yet another alternative implementation could also try to move the stem width closer by a fixed distance (like a half pixel) then round it later.