Fresh
Had a very good weekend.
Made some progress modelling a twist spun knot in Blender, still not fully working but getting there I think…
Spent today preparing slides for a talk on Wednesday.
Want to try and get to grips with https://doi.org/10.1016/0040-9383(88)90041-9 this week.
Beep beep beep, in other cases, boop
Let’s see…
金：Tried yet again to produce a render of an n-twist spun knot in Blender. Initially was using Geometry Nodes but wasn’t satisfied with the results (incorrect), so started trying to do it via the Python interface. Yet to get it working but will keep trying. Have decided to step away from Regensburg paper for a bit. Nobody seems to be in a rush to finish the draft and I’m sick of looking at it for the moment.
土：Lazed around. Good day.
Today: Lazin’ and Blender today I think.
ugh
Another day pissed away fiddling with diagrams instead of tidying up the last bits of writing I want to do. Some writing got done but nowhere near as much as I wanted to. I will finish this damn thing this week so help me…
Confident that the reason I’m struggling to just write this last few bits is the seeming half a dozen different notions of “normal form” — all pretty much the same but with subtle enough differences in some places I’m questioning what the correct “universal” formulation should be. Also feel like having actually correct examples of marked vertex diagrams and banded unlink diagrams is a bottleneck… not confident in what I’ve drawn at the moment.
Told students today to just put something down and then refine later — I should practice what I preach…
My big fear is that I will have spent all this time making diagrams and they’ll turn around and go “mmm nah don’t actually want/need this”.
Feel a blister on the sole of my left foot -__-
駱駝［らくだ］：camel
ugh
Another terrible night’s sleep.
Spent a good chunk of the day trying to figure out best way to draw/render the first Roseman move — two branch points joined by an arc of double points… Yet to produce anything satisfactory.
Was quite happy with this “fill in double point” I did yesterday. No luck pulling off the same for the equivalent with a triple point though…
pdflatex rendering fix
Saving the graphic as an eps did the trick, hurray. Haven’t tried any tests with gradients containing transparency yet but those seem to be rendering fine in the final pdf (so far anyway) — though overleaf does seem to have issues rendering them in the online preview, so keeping an eye out.
Hmmm transparency + gradients seem to be too much: one or the other it seems?
Second night this week of being jolted awake by dreams in the 3-4am region.
ああああああ
After finally fiddling around with mesh gradients in Inkscape I discover that the way pdflatex handles pdfs (at least when used as a graphic) means that the final output has issues when viewed in Preview (namely, the mesh gradient doesn’t get rendered, similarly with some gradients containing transparency). Bloody ridiculous that this has been an issue apparently for at least the last 15 years! Very frustrating. The thought of having to rasterise the gradients first is incredibly disheartening — sorta defeats the point of having vector graphics. Or what, just have some kind of disclaimer at the start of the document saying “don’t open in Preview”? Bollocks.
Playing around with some kind of flat shading for the ‘cone over fig-8’ branch point picture but yet to produce anything to my liking. Below is the closest I’ve gotten but I don’t know…
I exported the above at 300dpi and yet it looks like arse uploaded here, what on Earth..?
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Really want to render a Cappell—Shaneson knot. Crazy that the simplest Cappell—Shaneson knot has ‘triangulation complexity’ just two and yet somehow is still sufficiently complicated that nobody has tried to draw it… I think. Chasing through some papers, but seems like not even Scott Carter has done it.
Something different: tame immersions of exotic pairs…? Seems tricky.
Pub.
RSPFaA II
Tweaked the ‘movie frames’ diagram a bit.
Worked on the (written) section itself a bit as well, although not as much as what I wanted to. Not overly optimistic about the state the section will be in by the end of tomorrow. I think I only have one or two other ‘core’ diagrams to make but the actual writing itself needs quite a bit of tidying up.
Saw the new 28 Years Later (2) this afternoon. Enjoyed it. Ralph Fiennes was excellent as usual.
Figure fatigue
More fiddling around in Blender though not as successfully today. Was hoping to get some renders of n-twist spun knots going but couldn’t get it working. Will have another go tomorrow probably.
Redid the ‘movie frames’ diagram. Initially tried to actually use Blender to generate the frames to have some more procedural control over things but again, couldn’t get it working to my satisfaction.
A bit worried the section isn’t going to be as tidied up by Thursday as what the bosses want…
First Blender test
Sunday so took it easy. Tried messing around in Blender a bit for the first time. Attempted a ‘broken surface diagram’ for a spun Figure 8 (or something of that ilk…)
First attempted render of a knotted sphere in blender.
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Whoops didn’t upload yesterday… (the 9th).
2026-01-09: Finished the 2nd version of that diagram.
2026-01-09 (cont.): Opened up the structures paper for first time since August last year. Third time’s the charm… want to get that sorted and out within the next couple of months.
Went to the pub with FP in the arvo for a couple of beers.
2026-01-10: Did bugger all :)
Another day another diagram
Weather was miserable today so worked from home.
Starting from a sketch drawn by FK, I decided after a couple of attempts to create a 3D model in Mathematica to use as a reference graphic.
I drew the knot diagram in Inkscape first, and then used it as a texture for a surface in the Mathematica model — that way I wouldn’t have to fiddle about with perspective warps and could just trace directly over the transformed image in Inkscape.
After a first draft a few modifications had to be made. Will finish tomorrow.
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Worked on diagrams from the office in the afternoon.
Finished the “cut-and-fold sheet of paper” diagrams for the branch point model. Quite happy with how they’ve turned out (well, for now anyway…).
Made a couple of draft banded unlink diagrams.
Started a 2nd draft of the “slices” diagram.
It sounds like things got done, but still felt like a largely unproductive day.