Add definitions for varLib-specific terms

Doc/source/varLib/index.rst

@@ -1,6 +1,93 @@
-######
-varLib
-######
+##########################
+OpenType Variation Support
+##########################
+
+The `fontTools.varLib` package contains a number of classes and routines
+for handling, building and interpolating variable font data. These routines
+rely on a common set of concepts, many of which are equivalent to concepts
+in the OpenType Specification, but some of which are unique to `varLib`.
+
+Terminology
+-----------
+
+axis
+   "A designer-determined variable in a font face design that can be used to derive multiple, variant designs within a family." (OpenType Specification)
+   An axis has a minimum value, a maximum value and a default value.
+
+designspace
+   The n-dimensional space formed by the font's axes. (OpenType Specification
+   calls this the "design-variation space")
+
+scalar
+   A value which is able to be varied at different points in the designspace:
+   for example, the horizontal advance width of the glyph "a" is a scalar.
+   However, see also *support scalar* below.
+
+default location
+   A point in the designspace whose coordinates are the default value of
+   all axes.
+
+location
+   A point in the designspace, specified as a set of coordinates on one or
+   more axes. In the context of ``varLib``, a location is a dictionary with
+   the keys being the axis tags and the values being the coordinates on the
+   respective axis. A ``varLib`` location dictionary may be "sparse", in the
+   sense that axes defined in the font may be omitted from the location's
+   coordinates, in which case the default value of the axis is assumed.
+   For example, given a font having a ``wght`` axis ranging from 200-1000
+   with default 400, and a ``wdth`` axis ranging 100-300 with default 150,
+   the location ``{"wdth": 200}`` represents the point ``wght=400,wdth=200``.
+
+master
+   The value of a scalar at a given location. **Note that this is a
+   considerably more general concept than the usual type design sense of
+   the term "master".**
+
+normalized location
+   While the range of an axis is determined by its minimum and maximum values
+   as set by the designer, locations are specified internally to the font binary
+   in the range -1 to 1, with 0 being the default, -1 being the minimum and
+   1 being the maximum. A normalized location is one which is scaled to the
+   range (-1,1) on all of its axes. Note that as the range from minimum to
+   default and from default to maximum on a given axis may differ (for
+   example, given ``wght min=200 default=500 max=1000``, the difference
+   between a normalized location -1 of a normalized location of 0 represents a
+   difference of 300 units while the difference between a normalized location
+   of 0 and a normalized location of 1 represents a difference of 700 units),
+   a location is scaled by a different factor depending on whether it is above
+   or below the axis' default value.
+
+support
+   While designers tend to think in terms of masters - that is, a precise
+   location having a particular value - OpenType Variations specifies the
+   variation of scalars in terms of deltas which are themselves composed of
+   the combined contributions of a set of triangular regions, each having
+   a contribution value of 0 at its minimum value, rising linearly to its
+   full contribution at the *peak* and falling linearly to zero from the
+   peak to the maximum value. The OpenType Specification calls these "regions",
+   while ``varLib`` calls them "supports" (a mathematical term used in real
+   analysis) and expresses them as a dictionary mapping each axis tag to a
+   tuple ``(min, peak, max)``.
+
+box
+   `varLib` uses the term "box" to denote the minimum and maximum "corners" of
+   a support, ignoring its peak value.
+
+delta
+   The term "delta" is used in OpenType Variations in two senses. In the
+   more general sense, a delta is the difference between a scalar at a
+   given location and its value at the default location. Additionally, inside
+   the font, variation data is stored as a mapping between supports and deltas.
+   The delta (in the first sense) is computed by summing the product of the
+   delta of each support by a factor representing the support's contribution
+   at this location (see "support scalar" below).
+
+support scalar
+   When interpolating a set of variation data, the support scalar represents
+   the scalar multiplier of the support's contribution at this location. For
+   example, the support scalar will be 1 at the support's peak location, and
+   0 below its minimum or above its maximum.
+
 
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