[css-values] Make 'hypot()' n-dimensional

[Loirooriol]

From https://drafts.csswg.org/css-values-4/#funcdef-hypot,

The hypot(A,B) function contains two comma-separated calculations A and B, and returns the length of the hypotenuse of a right-angled triangle with legs equal to A and B.

I would like to generalize this to the euclidean norm like in JS Math.hypot. Then

• hypot(A) would be the absolute value of A
• hypot(A, B) would be the hypotenuse of a right-angled triangle with legs equal to A and B.
• hypot(A, B, C) would be the length of the space diagonal of a rectangular cuboid with edge lengths A, B and C.
• and possibly more (though maybe not as useful as the previous cases).

[AmeliaBR]

I definitely like the idea of supporting a 3-value hypot for 3D geometry.

I can't think of any use cases for more dimensions on the web, but don't think it would complicate the implementation. The ECMAScript Math.hypot() implementation supports arbitrary numbers of arguments.

I think it confuses matters a bit to talk about hypot(A) to generate the absolute value. I mean, it doesn't hurt to support it. But, I'd rather go straight to adding an abs(A) function.

[tabatkins]

Allowing 2+ arguments sounds great, I'm sorry I forgot about it initially. ^_^ Allowing a single argument to effectively be abs() is fine; the general definition handles that case with no problem. (And JS allows it as well.)

[Loirooriol]

@tabatkins "the length of an N-dimensional vector" is not clear enough, you should specify that it's the euclidean norm, since vector spaces can have other kinds of norms.

[tabatkins]

Technically, yes. But euclidean norm is always assumed if not specified and there's nothing else in the context hinting that you might be talking about other norms.

If someone comes at me with some Manhattan distance, I'm gonna assume they're being a smart-ass. ^_^

[AmeliaBR]

It wouldn't hurt to specify the actual calculation (“the square root of the sum of squares of its arguments”, to use the ECMAScript text) for clarity. People who haven't taken advanced math may be confused by "the length of an N-dimensional vector", with or without specifying Euclidean space.

[Crissov]

Shouldnʼt the function better be called norm() then? Equivalence to hypot() in JS would be worth an informative note.

(I obviously donʼt value compatibility with JS nomenclature as highly as others; also dislike redundant atan2().)

[tabatkins]

People who haven't taken advanced math may be confused by "the length of an N-dimensional vector", with or without specifying Euclidean space.

Good point, I've done so.

Shouldnʼt the function better be called norm() then?

The JS-naming concordance besides, it's still also a hypotenuse of the right triangle defined by the origin, the point given by the first N-1 arguments, and the point given by all the arguments.

[Crissov]

… except in the degenerate case with a single argument.

[tabatkins]

Nope, it's still the hypotenuse there. The point given by the first N-1 arguments is the origin, because there are no arguments at all. The triangle is thus degenerate, but it still has a meaningful "hypotenuse", which is equal to the absolute value of the provided argument.

[Loirooriol]

BTW, should hypot() without arguments be allowed? It would represent the norm of a vector in a 0-dimensional space, i.e. +0. Seems pretty useless, but would be consistent with JS...

[tabatkins]

At that point I really think it's a step too far. Unlike 1-arg hypot() (which gives us abs()), another way of writing 0 doesn't seem useful.