[OTVAR] Exact definition of “bounding box” in a variable font.

Belleve Invis

In a nutshell: the exact definition of the "bounding box" used to calculate metrics (LSB & TSB in HMTX-HVAR/VMTX-VVAR). Will the rasterizer use a fixed bounding box for all the instances (like the one stored in glyf table), of the dynamically calculated bounding box, one for one distance?

Peter Constable

The bounding box computed by the rasterizer -- the "phantom" points -- is derived (in a TT-flavoured font) solely using the 'glyf' and 'gvar' tables: the 'glyf' table provides phantom points for the default instance, and the 'gvar' table provides deltas that describe how the phantom points get translated for non-default instances, in the same way as it describes other points.

Note: In the 'gvar' table, the number of glyph points is equal to the number of points in the glyph description in the 'glyf' table, plus the four phantom points (the last 4 points in 'gvar' point numbering).

The hmtx/HVAR and vmtx/VVAR tables are expected to produce the same results as the rasterizer phantom points, modulo that the phantom points can potentially be adjusted by hints whereas hmtx/etc. values are not (just as in a non-variable font).

Belleve Invis

@Peter Constable The phamtom points already had side bearing.
Let's consider the situation for VVAR. We have a glyph with only two points, z1 and z2, with their (default) coordinates being y1 and y2 (y1 < y2), and the delta under the chosen instance being δy1 and δy2. In vmtx and VVAR the TSB is defined as t + δt, and the advance height is h + δh.

Following the definition of glyf’s bounding box, the ymax would become y2, and the vertical origin would be y2 + t in the default instance. This is the peaceful old world we know.

However in the variable world, the advance height would become h + δh, which is simple. However the top side bearing is now t + δt, and the definition of vertical origin become ambiguous now:

-        If we follow the glyf’s ymax then the vertical origin would become y2 + t + δt.

-        If we follow the true bounding box, the vertical origin would become max(y1 + δy1, y2 + δy2) + t + δt. This is a complex formula and it is even not representable in the OTVar’s “value + delta” manner, as the designers expected.

Belleve Invis

This problem gets more serious for CFF2: given that the "true bound" of a glyph is not representable in "value + delta" mechanism, and there is no phantom point in CFF2, how can we encode the top side bearing if we want the vertical origin being a fixed, or a simple varible quantity? If we eliminate TSB some rasterizer would make use a constant TSB and make the metrics incorrect.