Introduction to interpolation ↩
 What is interpolation?
 Terminology
 Interpolation requirements
 Interpolation workflow
 GlyphMath
 MutatorMath
 Superpolator
What is interpolation?
At its most basic level, interpolation is finding a number between two other numbers.
The basic interpolation formula is: start with one value (a), than add a fraction (factor) of the difference with another value (b).
a + factor * (b  a)
Translating the formula into code:
def interpolateNumbers(factor, a, b):
return a + factor * (b  a)
print(interpolateNumbers(0.3, 0, 100))
print(interpolateNumbers(0.3, 200, 500))
30.0
290.0
Interpolation can be applied to anything that can be represented as numbers: position, dimensions, colors… and glyph shapes too.
Terminology
 masters
 Data objects that are used in an interpolation system.
 instances
 Data objects generated by interpolating the masters.
 interpolation factor

A number between
0
and1
. For example: factor is
0.0
→ result is identical to the first master  factor is
1.0
→ result is identical to the second master  factor is
0.5
→ result is exactly between the two masters
 factor is
 extrapolation
 Interpolation with factors outside the
0
–1
range.  axis
 The particular change in an object when interpolating from one master to another.
Extrapolation
Extrapolation is using interpolation to find a number beyond the masters – using a factor that is less than 0
or greater than 1
.
print(interpolateNumbers(1.2, 200, 500))
print(interpolateNumbers(0.2, 200, 500))
560.0
140.0
Interpolating colors
To interpolate between two ndimensional objects, we simply interpolate each dimension separately.
Here’s an example using (r,g,b)
tuples representing colors:
def interpolateColors(factor, c1, c2):
# unpack color tuples
r1, g1, b1 = c1
r2, g2, b2 = c2
# interpolate each channel separately
r = interpolateNumbers(factor, r1, r2)
g = interpolateNumbers(factor, g1, g2)
b = interpolateNumbers(factor, b1, b2)
# return resulting color
return r, g, b
print(interpolateColors(0.5, (1, 0.1, 0), (1, 0, 1)))
(1.0, 0.05, 0.5)
Interpolation requirements
Interpolation works only if the two data objects being interpolated have the same “topology”:
 the same amount of dimensions
 matching types of dimensions
Interpolating glyphs
A glyph is described by numbers too: the position of all points, anchors and components, the glyph’s advance width, mark color, etc.
The RGlyph
object in FontParts has an .interpolate()
method which takes an interpolation factor and two glyphs as input:
glyph.interpolate(factor, glyph1, glyph2)
The interpolation factor can be a tuple of two values, one for each dimension:
glyph.interpolate((factorX, factorY), glyph1, glyph2)
The
RFont
andRKerning
objects also have.interpolate()
methods.
Interpolation workflow
Interpolation can be used in different stages of a project:
Interpolating glyphs
In the design stage, you might want to interpolate a few glyphs only, to see how the result looks like – making quick tests with key glyphs to find the right interpolation factors.
Interpolating fonts
In the production stage, you can interpolate a whole font, or a series of fonts at once – without using the UI to speed things up.
Proper interpolation between fonts involves interpolating not just the glyphs, but also the kerning and some numerical font info attributes, such as blue zones, OS/2 weight numbers, etc.
GlyphMath
If two glyphs are compatible, they can also be used in GlyphMath expressions.
GlyphMath uses operator overloading to add basic arithmetic operations to glyph objects: glyphs can be added or subtracted by each other, and can be multiplied or divided by a number.
GlyphMath can be used to create interpolation effects, transplant transformations from one glyph to another and superimpose several effects at once.
MutatorMath
MutatorMath is a Python library to calculate interpolations between multiple masters in multiple dimensions. It was developed for interpolating data related to fonts, but it can handle any arithmetic object.
Superpolator
Superpolator is a macOS application for creating font families using multidimensional interpolation. It uses MutatorMath as its interpolation engine, and offers a rich interface for creating and visualizing the interpolation space and the instances.