B TeX dimensions

When producing this program, I became terribly confused about the variety of dimensions which appear in DVI and PK files. Table 1 is a summary of the sizes which appear, for the benefit of anyone else attempting a project like this. The reference [Dn] refers to section `' of the webbed DVItype document and [Pn] to section `' of the PktoPX document (see Section 7).

If you feel I have misunderstood something here, or got one of the conversion factors wrong (I hate these!), please correct me.

Context	Description	See
DVI preamble	num, den: multiply a `DVI unit' by to obtain a length in units of	[D17]
	mag: DVI units are actually multiplied by	[D17]
DVI font definition	d: a design size, in DVI units. The nominal size of the font.	[D18]
	s: a `fixed point' scale factor, range , scaling d (see note).	[D18]
PK preamble	ds: the font design size in units of points.	[P12]
	hppp, vppp: number of pixels per point, times (see note).	[P12]
Character	tfmwidth: the width of the character (see note).	[D37], [P9]
	w, h: the width and height, in pixels, of the character pixel map.	[P21]
	hoff and voff: offset of the pixel map from the reference point.	[P21]
	dm, dx, dy: the pixel escapements. dm in pixels, dx and dy in pixels times (see note).	[P21]

Table 1

Sizes in TeX

1. s scales the design size, so that a font is actually used at times its normal size.
2. hppp and vppp aren't used as sizes, but can be used to check you have the right fonts by comparing resolution, etc..
3. tfmwidth is the `physical' size of a character, and is the only size that TeX uses in its calculations, and which the DVI reader uses when working out how far to move the reference point when it sets a character. This is defined in [P9] to be in units of FIXes, where one FIX is times the design size in points. [D37] describes how to multiply these widths by scaling factors without overflowing.
4. The difference between the pixel escapements and tfmwidth is that the latter is a resolution-independent shift of the DVI reference point, and the former is the PK file's recommendation of the number of pixels the DVI processor should actually move. The DVI processor keeps track of the two reference points, and readjusts the pixel-based one when rounding errors move it too far from the resolution-independent one. See [D89] and [D91]; also [D40].

A few useful conversions are:

• The design size of a font is a physical length, of points. [P12]
• A FIX is a physical size, of length
• A TFM width is a physical size. The tfmwidth parameter is in units of FIXes, so that the TFM width is a length of tfmwidth fixes, which is equal to points.
• Writing `dviu' for the unit `DVI units', `sp' for the scaled point of points, `px' for pixels, and for Knuth's deci-micron, or ,