I got an interesting idea today.
As you may already know, I’ve been making models of Klein bottles an’ stuff; heretofore they’ve all been in the form of bent rods, but where possible I’d prefer a continuous surface. (A hollow body must have holes so that unused powder can be shaken out; but not all of my designs have enclosed spaces.) How to place a minimum number of vertices so that deviations from the abstract shape are within the resolution of the process? That’s less obvious with more degrees of freedom.
So, today’s idea. Start with an arbitrary set of sample nodes (in the abstract space of the parametric variables, rather than on the target surface itself), and their Delaunay triangulation. Along each edge of the triangulation, measure the deviation of the surface from a straight line; this gives the edge a weight. Move each node to the weighted average of its neighbors (with a bit of noise); thus, an edge whose image is strongly curved gets shorter.
After the movement phase, each edge ought to be checked, whether it’s still a Delaunay edge or needs to be replaced by the other diagonal of the quadrilateral formed by its two triangles. I don’t yet have criteria for adding nodes where existing nodes are too far apart, or merging them if they become redundant.
steam and circuitry
One of my favorite games is Ticket to Ride (despite its silly name), in which a strategic element is choosing tickets: pairs of cities to be joined. The value of a ticket is the length of the shortest path that could fulfill it.
It occurs to me that, if each segment of track is considered as a resistor, the resistance between two cities may be considered a measure of the difficulty of the ticket: you’re less likely to be blocked if redundant paths exist. One could then make a list of tickets ranked by payoff divided by resistance. But each move changes this: after a route is claimed, it has zero resistance for its owner and infinite resistance for others.
Your first act in the game is to choose two or more tickets from a draw of three or four or five; it’s not obvious how to apply this idea to find the most compatible set.
Gail Simone asks:
Question of the day: if you could have one piece of art drawn by any living comics artist, not to sell, what artist and what character?
I haven’t followed (paper) comics in a long time, but several possibilities come to mind; in rough order of seriousness:
- Churchy & Owl (from Pogo) by Bill Watterson
- Adam Warlock and Gamora by Walt Simonson
- … with Thanos by Kate Beaton
- Dr Strange by R Crumb
- Batman or Batgirl or Catwoman by Dorothy Gambrell
- Cheech Wizard by Dave Sim
In Atlas Shrugged, John Galt invented a radical new engine and (according to folklore) emigrated to Atlantis to keep his invention out of the hands of parasites.
Charles Stross’s novel Neptune’s Brood is about uncovering the true history of the Atlantis colony, which gathered an unusual concentration of talent before suddenly going silent. Some say that Atlantis was working on a FTL drive, which happens to be a motif in a perennial scam. Was Atlantis ever more than a Potemkin village, bait for investors? Was it destroyed because the FTL project succeeded?
Once or twice before, I’ve asked Charlie whether he intended an allusion and he said
“ha, no, I didn’t notice that, ” so I won’t assume that the name “Atlantis” (which is unrelated to the Neptune of the title) is a poke at Rand. It’s funny either way.
I’ve seen such changes
How old do you need to be to understand this gag from 1978?
Each month I look through my HTTP log for new incoming links. Most of them are phony. In December, Russian porno was up and other commercial spam was down.
A notice to renew my domain registration prompts thoughts of what I might have used instead: ansher, anwood, tonsher, tonwood ?
tonsher reminds me of an acquaintance whose bald spot looks uncannily like a monk’s tonsure — and that’s even funnier on a Jew. My own bald spot is not so sharply defined.