Knitting the polar way

Hi folks.
I've been playing with some knitting-related maths lately, and after a certain amount of experimenting I've just about got a design ready to be playing with.
This kind of follows on from the ideas behind the 'science doilies', trying to knit standard shapes in non-standard ways. Particularly, I've been looking at knitting colourwork radially.
Planning colourwork when knitting flat is fairly straightforward, the lack of shaping means that the stitches obey nice easy-to-follow patterns. If you knit radially(starting at a central point and work outwards), it becomes a lot harder to judge. The reason for this is that flat knitting is based on cartesian coordinates, where radial knitting is using polars.
So to make this work, I came up with another little Maple program which will take a curve(given in normal cartesian coordinates), convert this into polar form, then use some numerical trickery to convert this into a workable knitting pattern. This seems to work pretty well, with one caveat that you need to be a little careful about spacing your increases - the calculation assumes that the increases are all entirely homogeneous about each round, which isn't possible in practice because the stitches are discrete. In particular, the standard trick of distributing increases evenly along the round(as you would for most lace doilies) isn't even enough, I think it distorts the colourwork pattern too much.
The reason I'm really excited about this though, is that the same program could also be used to work out short row patterns for knitting non-trivial shapes in the same radial way. Initially I'd hope to be making sensible rectangular pieces, but ultimately I think there's the potential for some truly mind-boggling designs from this.

I'm working on a design just now which will be a bit of a trial run for this - the plan is to make a little baby jacket for my little nieceling, the back panel of which will be knit radially with a pattern of colourwork hearts. I'll blog about that design specifically another time, because there's some nifty maths behind the heart pattern(if you're part of the 'geekcraft' group of Ravelry, you may have heard me being excited about this already). I'm not too sure how I'll do with the rest of the jacket, will have to play with it a bit more.

So yep, more about that when the actual knitting is underway, and assuming more goes well, I'll say some more about the mechanics of the radial coordinate program then too.

Happy knitting!
Hugh.