Racetrack Update

 

You may not recall, but a while ago, I drew some paths using Voronoi Regions (look back to Genuary Day 26). 

I was pleased with the output, but a little perplexed that the hairpin turn on the NE corner of the westernmost track seemed to be too sharp a turn. More specifically, if the notional "cars" were going from the fairly vanilla hexagon at the far N of the track, into the "diamond" shaped pentagon, with the pointy bit to the south, on to the flat hexagon, back to the diamond pentagon. 

My code should not generate tracks based on previous regions - what's going on?

I've got all the code from the various works, and each of those used a seed string, so I could reproduce the calculations that I considered suspect. So, I dug back into the code, made a copy, and (re)enabled some debugging information, along with drawing a lot of dots.

One thing I discovered in my spline code was that I was asking for 10 points on my curve, but my generators were evaluating from 0 to 10, inclusive. This caused some of my curve data to overshoot the intended data.

Another thing I discovered was that my tracks (the blue curve, here) were based on the generating points for the voronoi regions. I'm not doing anything fancy like using the centerpoint of the edge between regions, to ensure that the curve would be centered on that edge. I'm basically just drawing a polyline from generating point to generating point, but then I round off the corners.

What's important(?) to recognize here is that that generated polyline may cross between regions along the voronoi edge between those regions, or it might not.

If you look super carefully at the "flat hexagon" and the "apparent pentagon" to its west, there's a tiny little edge connecting them, which is what my track layout algorithm used. But the line connecting the generating points crosses back into the diamond pentago on its way from the flat hexagon to the "apparent pentagon" (which is actually a hexagon, because the 6th side is tiny, and the flat hexagon is a heptagon).

I'm sure you were as curious as I was about why the tracks weren't working. Now they are. Although I suspect the drawings are just about indistinguishable. But now they're right, and we understand why.