I read their previous post, and nowhere do they explicitly say "a transform is a...". One might assume that it is indeed a linear transformation, as you suggest, but it shouldn't be up to the reader to do detective work just to understand the objects the author is talking about.
What I meant was that based on what they said in their previous post ("[g]iven a transform T and a point x, we can find the transformed point with T∗x") and the interactive graphics, I felt certain they meant a linear map.
I agree it's sloppy, at least a reference or something should be given if one doesn't want to spend time on the full definition.
Maybe the author could have used a more general notion, then, if omission and brevity were going to be present? Like, instead of a linear map or transform, he could have said an operator or something.
I don't know what is the general form of a transform or linear map. I think it's something like operator, though.
True, however I don't know how well versed the author is. Back in my late teens when I was deep into 3D graphics and ray tracing, I knew a lot about that specific math but not much beyond it. To me, "transform" was crystal clear to mean some kind of linear transform, and I hadn't yet learned of the more general operator notion[1].
So I can see myself writing something similar thinking it was clear.
Author here. My background is game development. Now I work on 3D modeling software. I wouldn't say I know "higher level math", because that seems like a very deep well...
What would be the best way to define "transform" here? What I mean is something that can be applied to a point, like a linear map. So translation, and/or rotation, and/or scaling, and/or skewing, are all things that can be done by this "transform" in 3D.
In computer graphics these are often expressed as 3x3 or 4x3 (or sometimes 4x4) matrices. But a "translation+quaternion" can also be a transform, or just a quaternion (a unit quaternion can be used to rotate points for example). So I'd be happy to use a better definition for "transform" than 'given a transform T that can be applied to a point' but I'm not quite sure what the best definition would be.