rough draft of my spline PhD thesis

raph's picture

I've been working on it for years, and recently pretty much gone into a cave to try to finish it, and, at long last, it's nearly ready. I finally have a reasonably complete draft of my PhD thesis on interpolating splines.

It's quite technical, and I'm not expecting too many people to follow along. Even so, I hope it gets across some of my motivation. Even though I hope the splines are useful in many applications, my primary reason for doing the work is to have a better tool for creating fonts. Also, I hope it gets across how deeply I have gone into the literature and theory.

The draft (in a compact format, not the actual thesis template) is here: http://levien.com/phd/frame.pdf

If anyone is inclined do detailed critique, chapters 1, 5, 6, 7, 8, and 10 are in near-final form. There's some reorganizing to be done of the elastica material, and integrating the results on the generator curve from the CAD paper. But overall I think it's pretty coherent. I'm excited!

Thanks to people here for expressing interest in the work, and responding to various queries and surveys I've thrown out over the years.

miha's picture

I’m excited too, I hardly wait to read it carefully. Congratulations!

abattis's picture

"The cipher reads “Qrzumu bapt dxqopddbbp...” and the key was published in the 1694 Curvatura Laminae with the detailed solution to the problem. Such techniques for establishing priority may seem alien to academics today, but are refreshingly straightforward by comparison to the workings of the modern patent system."

lol :)

guifa's picture

I've also downloaded it and am going to take a look either tonight or tomorrow. I figure you're not looking much for comments now in terms of general content and organization, so anything in particular —grammar, presentation, intelligibility by laypeople— you want us to keep an eye out for? It's the least we can do for bringing us spiro :)

jacobolus's picture

I enjoyed chapters 5 and 6, but didn't read them closely enough yet to offer critique. I'll try to get back to you in a week or two when I have more free time.

John Hudson's picture

Impressive work, Raph. I enjoyed the little chapter on real splines. There is a wooden boat building school on my island, and I'm now inspired to go down and look at their splines.

The chapter on the history of the elastica was fascinating.

raph's picture

Thanks so much for the kind words - it helps to hear as I'm on the final stretch.

@guifa: I think what would be most helpful right now is identifying parts that are unclear or don't make much sense. Obviously if it says "todo" or has ***'s, I already know about it, but I fear there passages that might have gotten munged in cut-and-paste, or older text that no longer makes much sense in context of newer work.

Thanks again!

Bendy's picture

Interesting stuff, will have a read through properly. You might already know section 2.1.1 (p5) ends mid-sentence?

jacobolus's picture

One thing that was a bit confusing was that chapter 3 referred repeatedly to equation 5.10, making the reader do a little non-linear run-around. Maybe the order of the chapters was reversed from an earlier version?

jacobolus's picture

Figure 2.7 also needs more explanation (a style of diagram used repeatedly later on). It's possible to figure out what it represents, but at first glance it's not clear what the points are or what the relation of top to bottom graphs is, especially since all the curvature definitions come in chapter 3.

enne_son's picture

Raph, I did a browse-through. This looks fascinating. I hope to look more closely when some of the balls I'm trying to keep in the air clear up.

William Berkson's picture

Lovely work, congratulations. I just read the beginning so far...

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