1################################## 2varLib: OpenType Variation Support 3################################## 4 5The ``fontTools.varLib`` package contains a number of classes and routines 6for handling, building and interpolating variable font data. These routines 7rely on a common set of concepts, many of which are equivalent to concepts 8in the OpenType Specification, but some of which are unique to ``varLib``. 9 10Terminology 11----------- 12 13axis 14 "A designer-determined variable in a font face design that can be used to 15 derive multiple, variant designs within a family." (OpenType Specification) 16 An axis has a minimum value, a maximum value and a default value. 17 18designspace 19 The n-dimensional space formed by the font's axes. (OpenType Specification 20 calls this the "design-variation space") 21 22scalar 23 A value which is able to be varied at different points in the designspace: 24 for example, the horizontal advance width of the glyph "a" is a scalar. 25 However, see also *support scalar* below. 26 27default location 28 A point in the designspace whose coordinates are the default value of 29 all axes. 30 31location 32 A point in the designspace, specified as a set of coordinates on one or 33 more axes. In the context of ``varLib``, a location is a dictionary with 34 the keys being the axis tags and the values being the coordinates on the 35 respective axis. A ``varLib`` location dictionary may be "sparse", in the 36 sense that axes defined in the font may be omitted from the location's 37 coordinates, in which case the default value of the axis is assumed. 38 For example, given a font having a ``wght`` axis ranging from 200-1000 39 with default 400, and a ``wdth`` axis ranging 100-300 with default 150, 40 the location ``{"wdth": 200}`` represents the point ``wght=400,wdth=200``. 41 42master 43 The value of a scalar at a given location. **Note that this is a 44 considerably more general concept than the usual type design sense of 45 the term "master".** 46 47normalized location 48 While the range of an axis is determined by its minimum and maximum values 49 as set by the designer, locations are specified internally to the font binary 50 in the range -1 to 1, with 0 being the default, -1 being the minimum and 51 1 being the maximum. A normalized location is one which is scaled to the 52 range (-1,1) on all of its axes. Note that as the range from minimum to 53 default and from default to maximum on a given axis may differ (for 54 example, given ``wght min=200 default=500 max=1000``, the difference 55 between a normalized location -1 of a normalized location of 0 represents a 56 difference of 300 units while the difference between a normalized location 57 of 0 and a normalized location of 1 represents a difference of 700 units), 58 a location is scaled by a different factor depending on whether it is above 59 or below the axis' default value. 60 61support 62 While designers tend to think in terms of masters - that is, a precise 63 location having a particular value - OpenType Variations specifies the 64 variation of scalars in terms of deltas which are themselves composed of 65 the combined contributions of a set of triangular regions, each having 66 a contribution value of 0 at its minimum value, rising linearly to its 67 full contribution at the *peak* and falling linearly to zero from the 68 peak to the maximum value. The OpenType Specification calls these "regions", 69 while ``varLib`` calls them "supports" (a mathematical term used in real 70 analysis) and expresses them as a dictionary mapping each axis tag to a 71 tuple ``(min, peak, max)``. 72 73box 74 ``varLib`` uses the term "box" to denote the minimum and maximum "corners" of 75 a support, ignoring its peak value. 76 77delta 78 The term "delta" is used in OpenType Variations in two senses. In the 79 more general sense, a delta is the difference between a scalar at a 80 given location and its value at the default location. Additionally, inside 81 the font, variation data is stored as a mapping between supports and deltas. 82 The delta (in the first sense) is computed by summing the product of the 83 delta of each support by a factor representing the support's contribution 84 at this location (see "support scalar" below). 85 86support scalar 87 When interpolating a set of variation data, the support scalar represents 88 the scalar multiplier of the support's contribution at this location. For 89 example, the support scalar will be 1 at the support's peak location, and 90 0 below its minimum or above its maximum. 91 92 93.. toctree:: 94 :maxdepth: 2 95 96 builder 97 cff 98 errors 99 featureVars 100 instancer 101 interpolatable 102 interpolate_layout 103 iup 104 merger 105 models 106 mutator 107 mvar 108 plot 109 varStore 110 111.. automodule:: fontTools.varLib 112 :inherited-members: 113 :members: 114 :undoc-members: 115