Tim Ahrens

@TiroTypeworks @justvanrossum @letterror Normalising the setup based on the bounding box would be an elegant solution to the issue at hand. However, I believe we have another requirement: Adding a master to the setup must not change the visible result for those instances that do no use it. I am thinking of scenarios like adding an extreme master late in the design process or even after the initial release. Unfortunately, this rules out simple bounding box normalisation.

@TiroTypeworks Oh, with the help of that evil new technology I just found out how all this would elegantly be expressed by a maths pro: “Delaunay triangulation is not affine-invariant”. There you go!

@TiroTypeworks @justvanrossum @letterror Far less impressive than Just’s visualisation, but as I have made it already, here is mine. I didn’t include any triangulation but it’s easy to imagine that there is a risk that an interpolation mechanism, generally speaking, treats the two options very differently even though they are practically the same, only with different axis scales.

@TiroTypeworks @letterror It seems surprisingly difficult to explain what I mean. This is not about intervals. What I am talking about is simply scaling the entire setup by a certain factor in one dimension. In other words, multiplying a certain coordinate of each point with the same factor. I believe the requirement for a new interpolation mechanism should be that this must not affect the interpolations. [Edit] As far as I can tell, all the existing mechanisms (VF, MM, Glyphs) fulfil this requirement.

@letterror There are some axes which can’t be re-scaled easily, though. For example, the weight axis nowadays is expected to range from 100 to 1000, while the width axis is typically scaled at 50 (compressed) to 100 (regular). This means the width axis has a built-in dominance of roughly 1:10 over the weight axis. Only because someone, a long time ago, decided that 400 is regular and 700 is bold. Had they decided that 40 is regular and 70 is bold then our interpolated fonts would look differently. I am not prepared to accept that. 2/2

@letterror Looks very interesting! Are the triangles set manually, or are they determined automatically?

@letterror There is a challenge I have been struggling with for many years, though: Let’s say the user (i.e. font maker) has a given setup with multiple axes, and then decides to scale everything linearly in one dimension. For example, scaling one axis by factor 10 by adding a zero to the coordinate for all points. They would (rightly) expect that this does not affect the final result. As far as I can tell, Delauney violates this requirement. (Don’t shoot the messenger, I am hating this requirement myself but I consider it as inevitable.)

@letterror Each master has coordinates, a tuple of values, of course. Same for the interpolated instance(s). Let’s say in my font project, I have a foo axis that goes from 0 to 100. Then I decide that I want it to go from 0 to 1000 instead. I will simply add a zero to the foo value of each master and each instance. I’d expect that the interpolations remain perfectly identical.

@justvanrossum @TiroTypeworks @letterror Thanks, I see. This practically means “manually set with computer assistance”. The designer can decide to re-fresh (or not) the automatic edges after they have changed the setup. That’s certainly more robust. Even though, I’d feel uncomfortable that the automatically determined edges (which one would usually rely on) depend on the axis scaling, and there may be a different, more appropriate edge configuration out there, which I missed.

@letterror How would the triangles look in a perfectly rectangular set-up?

@gdc This sounds like HH, OO and VV would end up having the same _minimum_ distance?

@gabrowitsch@typo.social @FontsInUse@typo.social Oddly, under that URL, when I force-reload the page a few times, I am randomly getting one of two different articles. One is about finding and picking fonts, one is about Variable Fonts. They are both interesting, though!