Variable Components

A proposal for an add-on to OpenType 1.8 by Black[Foundry]

Superceded by github.com/harfbuzz/boring-expansion-spec in 2023

Authors:

• Just van Rossum (@justvanrossum)
• Jérémie Hornus (@JeremieHornus)

Table of Contents

• Terminology
• What are Variable Components?
  • Use cases
• Proposal overview
  • Extend the OpenType format
• Format overview
  • The Component data structure
    • Transformation
    • Designspace location
• How to process VarC data?
• Format details
  • Notes on precision
  • Field formats
• New axis flag for the vartable
• Notes on non-linear interpolation
• Comparison to the COLRv1 proposal
• Prototype Implementation
• Prior Art

Terminology

• designspace: equivalent to the term “variation space”
• designspace location: a specific location in a designspace
• composite: a glyph that is composed of references to other glyphs
• component: a reference to another glyph
• base glyph: the glyph referenced by a component

What are Variable Components?

TrueType has had the capability to form composite glyphs since its inception. A composite glyph references other glyphs as “components”. This is a simple way to save data storage, for glyphs that can be composed of other glyphs, such as diacritics. Components can be arbitrarily positioned in the composite glyph, and can be scaled and rotated and skewed if needed.

“Variable Components”, as described in this document, add further parameters to customize the appearance of components in the composite glyph.

With OpenType 1.8, “variations” were added to the format, allowing for live interpolation between (say) regular and bold. These variations are global to the font: they are controlled by the user for the font as a whole. Such a font is no longer static, and the end user can navigate a designspace along dimensions (axes) defined by the font. The chosen variation is defined by the designspace location, as a set of coordinates in the designspace.

“Variable Components” add the possibility to place a variable glyph in a composite glyph, specifying the interpolation settings (the designspace location) for that single occurrence. A single glyph may define its own design space, for composites to use as they see fit.

Use cases

Some design tools already implement a methodology like Variable Components (for example “Smart Components” in Glyphs.app). Users find it often a more efficient way to design certain glyphs. Upon export as TTF, such components have to be converted to traditional outlines.

However, a lot of space could be saved if the Variable Component information would be stored in the font, instead of traditional outlines: a component reference will typically take up less space than a discrete outline.

This is especially true for CJK fonts, which tend to contain very large numbers of glyphs, many of which can be composed of variations of more basic glyphs.

More generally, fonts often contain glyphs that can be seen as variations of regular glyphs, for example superior and inferior numerals and small caps. It can be beneficial to represent these variations as local instances using Variable Components.

Proposal overview

The proposal presented here was informed by the following priorities:

• Only add to the OpenType 1.8 format, if possible
• Avoid changing existing OpenType 1.8 tables as much as possible
• Use existing data structures whenever possible
• Build on TrueType-flavored data
• Use the existing mechanisms available in OpenType 1.8 as much as possible:
  • Use glyf table composites/components
  • Use gvar for variations
• Make it easy for existing implementations to adapt
• Store the Variable Component data in a compact form, to maximize space saving

The first thing we need to pin down is how to do “local designspaces”. How does a glyph define its own designspace, to be used by composites?

Here are some of the insights that led to the current design, in order:

1. A component has full control over the designspace location of the component’s base glyph. It can even override a global axis value.
2. The global designspace location can affect the composite glyph, but to achieve the design goal of this propasal, it does not need to affect the designspace location of the base glyph directly. (This is still open for discussion, see #1)
3. A “base glyph” is just a regular glyf-based glyph, using gvar for variations, but it needs to be able to use axes that are not user-controllable.
4. We can use fvar axes, but we need to be able to flag an axis as “This axis is for variable component use only, do not expose it to the user, ever, at all”. This is perhaps more strict than the definition of the existing “hidden” axis flag, and we need to establish whether a new axis flag may be needed.
5. The total number of axes that can be used by a font (as specified in the fvar table) does not have an unreasonable limit per se (65536), but it is not without cost: in some places – for example in gvar variation tuples or VarStore regions – there is a value specified for every single axis in the font, even if that axis does not participate in a certain variation. This is especially relevant for gvar, as there can be many tuple variations (many glyphs × many variations per glyph), so adding even a single axis to a font can have a significant impact on the file size. So: let’s not use more axes than strictly necessary.
6. A Variable Component axis is not exposed to the user, and there is no need for “user coordinates”: the composite will only ever use “normalized coordinates” to specify a designspace location. Also: we don’t consider avar-like functionality to be necessary here.
7. A Variable Component axis is internally always referenced by its axis index. The “axis tag” is completely irrelevant. (Axis tags are only used for user interaction, and are not referenced anywhere in the font outside of the fvar table.)
8. The previous points lead to the conclusion that a single axis can be (re)used for different purposes by different base glyphs. The axis identity is no longer attached to a function that is meaningful for the end user, or any specific meaning at all. For example, base glyph X may use axis #2 to implement “stretching”, but base glyph Y may use the same axis #2 to implement “bending”. The meaning of an axis is completely local to the base glyph. Each component specifies the local designspace location for its base glyph.
9. Concluding, the local designspace for a base glyph does not need any more information than what we already have: it is completely defined by its variations’ locations in the gvar table.

Extending the OpenType format

To make Variable Components work, the only thing that is missing from OpenType 1.8 is the capability to store some additional information for each component of composite glyphs. The core of this proposal is to add a single new table, called VarC, that will provide a space for all new information.

A Variable Component reference needs the following information:

• The base glyph ID. This specifies which glyph we are referencing.
• A transformation (offset, scale, rotation, etc.)
• A designspace location
• Variations for the transformation and the designspace location, so the composite itself can become a variable glyph (whether as a “normal” glyph, or referenced as a Variable Component by another glyph)

We use the composites/components mechanism from the glyf table, so some of these values are already taken care of: the base glyph ID and the offset.

Components in the glyf table can optionally specify a scale value, or x/y scale values, or a 2×2 transformation matrix, but we chose not to use these for several reasons:

• Scale factors (and matrix values) are Fixed2Dot14, meaning they are limited to the range -2.0..+2.0, which is a problem for some use cases.
• gvar only supports interpolation of the component offset values, not of the scale values or the matrix.
• To interpolate 2×2 transformation matrices in a useful way is non-obvious and non-trivial, even when decomposing into scale, rotations and skew values.

Summarizing:

• For the base glyph ID, the component offset and its variations, we rely on glyf + gvar. Additional transformation values (scale, rotation, etc.) and its variations will be stored in VarC
• The component designspace location and its variations will also be stored in VarC

Base glyphs are totally ordinary glyf + gvar glyphs, but can also be composites themselves, using Variable Components, so we fully embrace the recursive nature of TrueType components.

Format overview

High level structure of the VarC table:

GlyphData is an array of offsets to Glyph subtables, indexed by GlyphID.

numGlyphs must be less than or equal to the numGlyphs field in the maxp table.

A Glyph subtable is an array of variable length Component data.

The VarC table depends on the glyf table: to parse a VarC Glyph, one needs to know the number of components from the glyf table. That number is not duplicated in VarC.

The Component data structure

The Component data structure stores the additional transformation fields, the designspace location for the components, and indices into the VarStore for each value that needs variations.

Transformation

The transformation data consists of individual optional fields, which can be used to construct a transformation matrix.

Transformation fields:

The TCenterX and TCenterY values represent the “center of transformation”. This is separate from the component offset as stored in the glyf table.

Details of how to build a transformation matrix, as pseudo-Python/fontTools code, where (X, Y) is the component offset from the glyf table:

# Using fontTools.misc.transform.Transform
t = Transform()  # Identity
t = t.translate(X + TCenterX, Y + TCenterY)
t = t.rotate(Rotation)
t = t.scale(ScaleX, ScaleY)
t = t.skew(SkewX, SkewY)
t = t.translate(-TCenterX, -TCenterX)

The transformation fields are stored as individual fields, and are interpolated as individual fields. If the client needs a transformation matrix, then this matrix needs to be constructed after interpolation.

Rationale for using a transformation center, using Rotation as an example:

• Rotation by default happens around the origin of the component
• For some cases this may be good enough, as the base glyph can be designed this way
• However, in other cases components may need to determine the rotation center locally, depending on how the component is used. Imagine a base glyph that represents a horizontal bar. In one glyph, this bar should be rotated using the left side as the center, and in another, it should be rotated using the right side as the center.
• This all wouldn’t make a difference if it wasn’t for interpolation: it’s really about how the component moves when transitioning from one composite master to another. (This should be illustrated visually)

Designspace location

The designspace location for components is stored as an array of axis indices and a matching array of axis values.

The VarStore subtable is used to store variation deltas. It uses 16 bit integer values, but we use these for various flavors of 16 bit fixed values, too.

How to process VarC data?

When preparing a glyph outline for the rasterizer, the following logic needs to be applied:

Inputs:

• glyph ID
• designspace location

Output:

• outline ready to be sent to the rasterizer

Steps:

• If the glyph is a composite and has an entry in the VarC table:
  • for each component:
    • Using the input designspace location, interpolate the transformation fields and the component’s designspace location
    • Retrieve the outline using this algorithm recursively, but using the component’s designspace location and glyph ID as inputs instead.
    • Transform the outline according to the transformation
• Else:
  • Proceed as usual, but apply the entire algorithm recursively, allowing for nested Variable Components

Or in pseudo code:

def getGlyphOutline(gid, location):
    if gid is a composite:
        for each component:
            if gid in VarC:
                compoTransform = instantiateTransform(location)
                compoLocation = instantiateLocalLocation(location)
            else:
                offset = instantiateOffset(location)
                compoTransform = getComponentTransform(component, offset)
                compoLocation = location  # global
            outline = getGlyphOutline(compoGID, compoLocation)
            outline = transformOutline(outline, compoTransform)
    else:
        outline = instantiateGlyfGvarGlyph(gid, location)
    return outline

To clarify: Variable Components completely determine the designspace location for the base glyph. Any axis not specified by a Variable Component has to be interpreted as set to its default, regardless of the global designspace location. In other words, Variable Components do not implicitly pass the global designspace location down to the base glyphs. (It can’t pass down local designspace coordinates, as local designspace may reuse axis IDs for different purposes. Axis X may do something completely different for glyph A than for glyph B.

This may be opened for discussion: it can be useful to pass down the global designspace coordinates down to base glyphs (unless overridden), but then we need to distinguish between global fvar axes and local (anonymous) fvar axes, due to the reusable nature of local axes in this design. To allow this, we need a new fvar axis flag in addition to the “hidden” flag. Please discuss here: #1

Local designspace coordinates need to be clamped, but it’s not clear yet how: #3

Format details

GlyphData: this is an array of offsets to glyph data subtables. It is indexed by glyph ID. If an offset is zero, then there is no Glyph data for this glyph. The numGlyphs field less than or equal to the total number of glyphs in the font.

VarStore: existing data structure to store all variation data, as used by GDEF, HVAR, VVAR, MVAR, etc.

Glyph: the data for a single glyph contains the component data for all components. The number of components is derived from the glyf table.

Component:

• Each VarIdx value represents an index into the VarStore, which contains all variation data.
• varIdxCount is determined by the sum of:
  • The number of axes that have a VarIdx
  • The number of transformation fields, if bit 4 of flags is set
• VarIdx entries are 1, 2, 3 or 4 bytes long. This is determined by the entryFormat field, see below.

Component flags:

Notes on precision

We chose to store all relevant fields as 16-bit values for maximum compactness, and compatibility with the VarStore format. The downside of this is that we need to choose the range of the fields carefully, as the range of delta values may exceed the range of master values by a factor related to the number of axes involved.

In one case (component scale factors) we chose to use a three-bit field to specify the number of integer bits to be used for scale factors. This gives us a flexible range that can be made to fit the required range.

In other cases (Angle16 and Coord16) we simply chose a larger range than required for the master values, so there is some wiggle room for delta values that are outside of the master value range.

Delta values are stored in the VarStore subtable, and they use the same formats as their corresponding master values.

We observe that https://github.com/googlefonts/colr-gradients-spec/ adds 32-bit value support to the VarStore format. VarC table could benefit from that as well, at the expense of compactness.

Field formats

Angle16: this is an int16 value used to represent an angle. To scale an angle in degrees to this format, multiply the angle by 0x8000 / (4 * 360). This gives us an effective range of -1440 degrees to +1440 degrees. Master values are expected to be between -360 and +360 degrees. The extra headroom is to allow for delta values that are outside of the master range.

Scale16: this is an int16 used as a 16 bit Fixed number, where the number of integer bits is specified by bits 0..2 of the flags field. This allows us to use 16 bits precision for a flexible range of scale values, depending on what the component needs. It avoids having a small maximum (as with Fixed2Dot14, which goes from -2 to +2) while sticking to 16 bits precision. The number of precision bits is 16 - number-of-integer-bits.

Coord16: this is in int16 value used to represent a coordinate in a designspace location. This is defined as a Fixed4Dot12. Master values are expected to be between -1.0 and +1.0, but delta values may be outside that range.

VarIdx array: this is a compactly stored array with VarIdx values, which reference items in the VarStore. A VarIdx value is normally 32 bit, using 16 bits for the outer index and 16 bits for the inner index. The array items are 1, 2, 3 or 4 bytes long, and are formatted as specified by the entryFormat field. This is identical to the entryFormat field of the DeltaSetIndexMap subtable from the HVAR table.

New axis flag for the fvar table

The axes used to implement local designspaces for components should never be exposed to users, and should be marked as such with a new fvar axis flag:

This is a backwards-compatible change, and therefore the fvar table version does not need to be updated.

Notes on non-linear interpolation

Because the (local) axes for VariableComponents are controlled by global (user) axes, this proposal contains the possibility to do non-linear interpolation, without the need for duplicate fvar axis tags (*). However, it is currently limited to variable components. It is possible to change the proposal in a small way that could apply the same control over designspace location and transformation on the outlines of the glyph, if it is not a composite.

*) By giving multiple fvar axes the same axis tags, many implementations allow multiple axes to be controlled from a single value.

Comparison to the COLRv1 proposal

There is a proposal which adds a much enhanced version of the COLR table: https://github.com/googlefonts/colr-gradients-spec/

There happens to be some overlap between the Variable Components proposal and the COLRv1 proposal.

A COLR glyph can be seen as a composite glyph, but with paint properties associated with each component. COLRv1 enhances this idea by adding transformations to the “components”, in a way that is conceptually very similar to the Variable Components proposal, but is different in every detail.

From a bird’s eye perspective, both proposals implement “doing components better”, but for different use cases.

We currently see two ways of addressing this:

1. Attempt to bring the data structures for component transformations together, so they can be shared in the spec.
2. Merge the two proposals completely, by adding “local designspaces” to COLRv1, and promote the idea that COLRv1 is about “better components” first, and about color second.

COLRv1 effectively adds a new glyph type, one that overrides glyf and CFF/CFF2 (but uses those as outline sources), whereas the Variable Components proposal builds on the composite/component structure of the glyf table (and is not compatible with CFF/CFF2).

More research and discussion is needed:

• #4
• googlefonts/colr-gradients-spec#88

Prototype Implementation

There is some prototype-level code that implements readers and writers for the VarC table as part of this repository: https://github.com/BlackFoundryCom/rcjk-tools

It relates to Black[Foundry]’s Robo-CJK RoboFont extension, which heavily uses variable components: https://github.com/BlackFoundryCom/robo-cjk

Prior Art

In March 2020 we published the RoboCJK Deep Components Proposal.

In September 2018, Microsoft published an XVAR Proposal.