Logs: liberachat/#haskell
| 2026-01-19 21:11:36 | <probie> | Would every ball on this plane have an infinite numbers of rays going through it? |
| 2026-01-19 21:12:23 | <probie> | Or are there a finite number of points on each curve? |
| 2026-01-19 21:12:24 | <jreicher> | BTW by "two rays" do you mean one on one side of the curve and one on the other? So the idea is one ray is "inside" the shape and the other is "outside"? |
| 2026-01-19 21:14:44 | <EvanR> | noodling it out, points might have finite rays through it, or infinite if there was a caustic focus point |
| 2026-01-19 21:14:50 | <EvanR> | jreicher, yeah |
| 2026-01-19 21:16:40 | <jreicher> | If you don't "step" along the curve in discrete amounts I think probie is right and that every point will have an infinite number of rays passing through. You might be able to concoct some kind of "density" measure though. incidentally this is reminiscent of https://en.wikipedia.org/wiki/Jordan_curve_theorem |
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| 2026-01-19 21:16:53 | <EvanR> | not every point |
| 2026-01-19 21:18:12 | <EvanR> | e.g. taking a solid square tile as an example, the interior has 8 rays going through it at any given point |
| 2026-01-19 21:18:28 | <EvanR> | 4? |
| 2026-01-19 21:18:29 | <jreicher> | Ah, no I get you. |
| 2026-01-19 21:18:33 | <jreicher> | *now |
| 2026-01-19 21:18:45 | <jreicher> | There was a bit of ambiguity about what would happen at the corners |
| 2026-01-19 21:19:03 | <EvanR> | at corners if there are any, stop and start again in another direction |
| 2026-01-19 21:20:31 | <jreicher> | So if the curve is an analytic function (very smooth) then you agree every point on the plane will be coloured? |
| 2026-01-19 21:24:16 | <EvanR> | no, that was a botched prediction |
| 2026-01-19 21:24:32 | <EvanR> | taking the square again, it misses huge parts of the plane entirely |
| 2026-01-19 21:24:44 | <EvanR> | or you mean if it's one closed curve |
| 2026-01-19 21:25:30 | <EvanR> | then it sweeps over the entire plane |
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| 2026-01-19 21:34:32 | <jreicher> | Not just closed, but "no corners" |
| 2026-01-19 21:34:38 | <jreicher> | ("smooth") |
| 2026-01-19 21:35:37 | <EvanR> | yeah |
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