christianp,
@christianp@mathstodon.xyz avatar

Inspired by @slowe sharing a chart showing a permutation, I nerdsniped myself into looking at how the curves between points are drawn, looking to make it easier to trace individual curves.
I've set up a @glitchdotcom experiment comparing curves with randomised control points against curves with fixed control points:
https://randomised-permutation-chart-curves.glitch.me/

I think the randomised one looks better more often than not, but it occasionally produces worse results.
If I was really getting stuck into this, I'd look into trying to make all the intersections happen as close to right-angles as possible.

SvenGeier,
@SvenGeier@mathstodon.xyz avatar

@christianp zI agree that the non-identical control points make for a better graph. Maybe instead of randomizing them, it would be even better if they were somehow linearly ascending or descending from top to bottom?

lisyarus,
@lisyarus@mastodon.gamedev.place avatar

@christianp @slowe @glitchdotcom Maybe you can compute the intersection points and iteratively try to optimise for the minimal distance between them?

christianp,
@christianp@mathstodon.xyz avatar

@lisyarus yeah, that was the general idea I had. Not sure if I've got it in me to do anything clever with gradient descent, but randomly moving the worst control point on each iteration might do something

narain,
@narain@mathstodon.xyz avatar

@christianp @lisyarus Iteratively moving the worst control point is coordinate descent!

christianp,
@christianp@mathstodon.xyz avatar

@narain @lisyarus !!!!

This is like the time someone told me I'd reinvented simulated annealing.

You computer scientists sure do give fancy names to simple stuff 😉

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