Bells and Whistles
May. 24th, 2019 09:57 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
stoutfellowWhile trying to get Taxonomy III off the ground, I'm continuing to come up with ideas, and it's slightly frustrating - I don't *need* more ideas for that paper!
The fundamental machinery I will introduce in that paper involves what I call "central weighted transforms", functions that turn polygons into other polygons in certain nice ways. The stuff about the Varignon transform requires me also to consider "quasi-central" transforms, the Varignon transform being the type case. I understand quasi-central transforms better this week than I did last - the Varignon transform is not just typical, but prototypical - but thinking about them led me to toy with the idea of "anti-central" transforms. This morning, I realized that two of the transforms I introduced in Taxonomy I are anti-central, and that one of them is the prototype.
I'll have to add this stuff to Taxonomy III. Fortunately, it seems to be merely an aside; there may be more to be investigated there, but it doesn't seem immediately relevant.
So far.
The fundamental machinery I will introduce in that paper involves what I call "central weighted transforms", functions that turn polygons into other polygons in certain nice ways. The stuff about the Varignon transform requires me also to consider "quasi-central" transforms, the Varignon transform being the type case. I understand quasi-central transforms better this week than I did last - the Varignon transform is not just typical, but prototypical - but thinking about them led me to toy with the idea of "anti-central" transforms. This morning, I realized that two of the transforms I introduced in Taxonomy I are anti-central, and that one of them is the prototype.
I'll have to add this stuff to Taxonomy III. Fortunately, it seems to be merely an aside; there may be more to be investigated there, but it doesn't seem immediately relevant.
So far.
