length, SI, font size, EM, pixels

[takev]

I am trying to use mp-units in a GUI library, I need a few more units that I am trying to design, but I am bit stuck.

I added a new type pixel which is a length. Then I added a ppi (pixels per inch) type as: pixel / international::inch. This was easy, works perfectly, if my CSS file has a size in SI or international units, I can multiply it with ppi to get the size in pixels.

Now the next one is the one I get confused by: The CSS file may also list a length in em-quad this a length in multiples of the font-size (also read from the CSS file).

The font-size is normally described in SI/international units, like 12pt. So if I want to convert a quantity in em-quad to international units I need to multiply em-quad with the font-size, but that can only work if em-quad is a unitless quantity, but it is still a length at the same time.

We could also describe font-size as: international::point / em-quad. This would be weird, because font-sizes are normally described only in points.

Is there something in mp-units to solve this?

[mpusz]

Hi @takev, thanks for trying the library! 😃

Generally, it is easier for us to discuss such use cases if you could share a Compiler Explorer link with us. With that we can better understand your use case and propose some solutions as well.

Said that, I am not sure if pixels should be an isq::length? Maybe it should be some special quantity type? It could be either:

• a dimensionless quantity/count set as a kind,
• new separate quantity type like screen_coordinate,
• a special quantity type of kind isq::length.

Thanks to that, if you divide pixels/inch, you will end up with just a dimensionless quantity but something stronger (you could also name it somehow, e.g., pixel_density).

em-quad could be a unit of another quantity type as well (e.g. dimensionless) or a unit of length where instead of multiplying by the SI unit you could convert to it. Such conversion can be defined:

• at compile time and performed automatically by the library
• at runtime and performed by the user-provided function

We also have an old and simple prototype of the typographic system that could be extended with your use cases.

@JohelEGP has more experience in GUIs library, so maybe he can provide more guidance here as well.

[takev]

https://godbolt.org/z/PzaTWodxf

The typographic system you linked to only adds a few lengths that are based on physical sizes. The units I need to add are in another coordinate system, but are still lengths.

[mpusz]

I must admit I am not an expert in typography. I just read a few articles today to get a general understanding of the subject. From what I've read at https://fonts.google.com/knowledge/glossary/em it seems that the em is a relative unit and it specified per specific font-size (e.g., ideally we should not be able to mix ems of two different font sizes).

It is really hard to correctly define it that way. The only way to prevent accidental mixing of different font-sizes would be to define such a unit as a template, but this would require to know the font-size at compile-time: https://godbolt.org/z/EhEj78z9s.

Other options are less safe or correct. As you pointed out, we can define em as a dimensionless unit and use it as a scaling factor of a font size. Alternatively, we can provide a runtime conversion function that will convert em to the font-size (https://godbolt.org/z/n7qs3hd4a).

The above examples, are not final for sure. For example, the hierarchy of quantities still needs some polishing there. However, it should provide you some ideas to model this in a way that works best for you.