Is it safe to use cubic and quadratic curves in one path?

TimAhrens · November 8, 2023, 2:14pm

Just noticed that in Glyphs, it’s possible to use cubic and quadratic Bézier curves in one path. Nice! Feels like FontLab in the late 90s. It takes a bit of trickery like cutting and re-joining paths but it seems to work.

Is it okay to do so? Or are there any risks? Is it too hacky?

I feel that for simple, shallow curves, this is the perfect solution, as two cubic handles give unnecessary (and unwanted) control. Retracted cubic BCPs – another long-time favourite of mine even though advised against by some – generally give shallower and more asymmetrical curves than a single-BCP quadratic curve.

GeorgSeifert · November 9, 2023, 4:01pm

That should be relatively easy to test. But I suspect there is some code that might trip over those paths.

jkutilek · November 10, 2023, 9:16am

As I understand it, there is some work going on in the harfbuzz project to allow mixing cubic and quadratic segments in the glyf table.

github.com

harfbuzz/boring-expansion-spec/blob/main/glyf1-cubicOutlines.md

# `glyf`—Glyf Data Table Format 1: Cubic-Bezier Outlines

The glyf data table ([`glyf`](https://docs.microsoft.com/en-us/typography/opentype/spec/glyf)) stores the glyph outline data.  The format number for this table is stored in the [`head`](https://docs.microsoft.com/en-us/typography/opentype/spec/head) table's `glyphDataFormat` field.  The only currently defined format of the `glyf` table is format 0. We propose format 1 of the `glyf` table to add multiple features. See full [proposal](glyf1.md) for all features. In this proposal we cover: _Cubic-Bezier Outlines_.

In `glyf` table format 0, glyph outlines use quadratic Bezier curve segments.

In `glyf` table format 1, glyph outlines can mix quadratic and cubic Bezier curve segments.

## Specification

Add the following flag to the [Simple Glyph Description](https://learn.microsoft.com/en-us/typography/opentype/spec/glyf#simple-glyph-description) section's _Simple Glyph Flags_:
| Mask | Name  | Description |
|------|-------|-------------|
| 0x80 | `CUBIC` | Bit 7: Off-curve point belongs to a cubic-Bezier segment |

### Restrictions

Currently, there are several restrictions on how the `CUBIC` flag can be used. If any of the conditions below are not met, the behavior is undefined.

In the text below, wrap-around in a contour means whether the point after the last point of the contour is considered to be the first point of the contour, and symmetrically, the point before the first point of the contour is considered to be the last point of the contour. When we say "without wrap-around", no such consideration is made.

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So it would be nice if Glyphs allowed to work with that smoothly sooner or later

TimAhrens · November 10, 2023, 9:49am

I was not even thinking of mixing them in the final font file – of course, that is an interesting long-term goal. Currently, Glyphs simply converts them to one or the other on export anyway.

The question is, just as Georg mentioned, that there might be some code in Glyphs that malfunctions when it encounters mixed paths. This is what I had in mind when I wrote, “is it safe?”

Why is it easy to test, @GeorgSeifert? I tried exporting OTFs, which works perfectly fine, but there is some uncertainty left, some potential for errors that go unnoticed.

Mark · November 12, 2023, 10:39am

Is that a compliment or an insult‽

Anyway, I also wonder if that might affect quite a lot of plugins, which operates with paths. You could see with your own ones (Symmetrify, Harmonizer, RMX, …). I’d be curious about that too.

GeorgSeifert · November 13, 2023, 12:57am

Having it in the UI should be fine.
And I just had a quick look, exporting seems to work, too.

TimAhrens · December 1, 2023, 8:54am

Just wrote a small script that helps play around with quadratic curves:

github.com

justanotherfoundry/freemix-glyphsapp/blob/master/Delete BCP.py

#MenuTitle: Delete BCP
# encoding: utf-8

# by Tim Ahrens
# http://justanotherfoundry.com
# https://github.com/justanotherfoundry/glyphsapp-scripts

__doc__='''
Deletes the selected BCP(s).
If only one BCP in the curve remains then this makes it a quadratic Bézier.
'''

doc = Glyphs.currentDocument
layers = doc.selectedLayers()

for layer in layers:
	glyph = layer.parent
	glyph.beginUndo()
	for path in layer.paths:
		for i in range(len(path.nodes) - 1, -1, -1):

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Two things I noticed:

On export, Glyphs’ overlap removal fails if cubic and quadratic curves are mixed. I tried all possible combinations for the path directions; none of them worked. Maybe this could be fixed by changing the order in which the paths are processed (curve conversion vs overlap removal), or skipping an incorrect change of path direction?
When using “Convert to Cubic” from the menu, Glyphs likes to duplicate the starting node. Seems to be a little bug.

GeorgSeifert · December 1, 2023, 10:14am

The overlap removal code doesn’t handle quadratic curves at all. because intersecting quadratic curves is quite tricky. In the last few month I wrote some code that might help with this, but I didn’t integrate it with the remove overlap code, yet.

TimAhrens · December 1, 2023, 10:34am

If the font is exported as OTF then all curves are converted to cubic in any case. If you do this before you apply the overlap removal this should fix the problem. No need to support overlap removal with quadratic curves.

TimAhrens · December 1, 2023, 10:42am

I just managed to fix the overlap removal on OTF export by setting up a very simple PreFilter that calls path.convertToCubic() for all paths in the font.

This means this problem should be fairly easy to fix in Glyphs internally. Just convert the paths to cubic before you apply overlap removal.