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| 2024-10-09 20:23:07 +0200 | <darkling> | That works, too. |
| 2024-10-09 20:22:58 +0200 | <Lears> | Coming in late: "just multiply by i" |
| 2024-10-09 20:22:55 +0200 | <tomsmeding> | er, hm |
| 2024-10-09 20:22:36 +0200 | <tomsmeding> | dolio: visualise it in 3D with two points a and b that are a bit away from the origin, but fairly close together |
| 2024-10-09 20:21:42 +0200 | <darkling> | (Or just visualise an angled vector, then its 90° rotation, and it's pretty obvious you swap the ordinates and negate one) |
| 2024-10-09 20:21:33 +0200 | <tomsmeding> | that matrix is quite literally "swap the components and negate one of them" :p |
| 2024-10-09 20:21:24 +0200 | <dolio> | Why (a1, a2, 1) etc.? |
| 2024-10-09 20:20:57 +0200 | <tomsmeding> | right |
| 2024-10-09 20:20:52 +0200 | <tomsmeding> | {{0,1},{-1,0}} |
| 2024-10-09 20:20:28 +0200 | billchenchina- | (~billchenc@103.152.35.21) (Remote host closed the connection) |
| 2024-10-09 20:20:03 +0200 | <darkling> | That's one's simple enough, and I've done enough of them, I can remember it by now. :) |
| 2024-10-09 20:20:00 +0200 | <tomsmeding> | which is admittedly not terribly difficult, but solving the dot product is about the same amount of work :p |
| 2024-10-09 20:19:31 +0200 | tomsmeding | would have to re-derive that matrix first |
| 2024-10-09 20:19:19 +0200 | <tomsmeding> | darkling: but then you actually have to _remember_ stuff! |
| 2024-10-09 20:18:25 +0200 | <tomsmeding> | (and indeed this yields the other, lol) |
| 2024-10-09 20:18:08 +0200 | <Lears> | That said, there are /two/ orthogonal directions. I hope they guess the right one! |
| 2024-10-09 20:18:03 +0200 | <tomsmeding> | incidentally, (a1, a2, 1) x (b1, b2, 1) = (a2-b2, b1-a1, _) |
| 2024-10-09 20:17:44 +0200 | <Lears> | You can also embed R^2 in R^3 and project a cross product with a normal vector back into the plane. |
| 2024-10-09 20:17:32 +0200 | <darkling> | I just worked out the first vector and multiplied by the matrix to rotate through 90° :) |
| 2024-10-09 20:16:05 +0200 | <tomsmeding> | the vector a -> b is (b1-a1, b2-a2); what has inner product zero with that? Well, exchange the two components (so that both products are equal) then negate one of the components (so that they cancel) |
| 2024-10-09 20:15:15 +0200 | lxsameer | (~lxsameer@Serene/lxsameer) lxsameer |
| 2024-10-09 20:15:10 +0200 | <tomsmeding> | seydar: a way to remember darkling's formula is to recall that two vectors are orthogonal iff their inner product is zero |
| 2024-10-09 20:12:51 +0200 | ubert | (~Thunderbi@178.165.187.120.wireless.dyn.drei.com) (Ping timeout: 252 seconds) |
| 2024-10-09 20:12:13 +0200 | ChanServ | +v yahb2 |
| 2024-10-09 20:12:13 +0200 | yahb2 | (~yahb2@user/tomsmeding/bot/yahb2) yahb2 |
| 2024-10-09 20:09:22 +0200 | hseg | (~gesh@46.120.20.246) (Ping timeout: 272 seconds) |
| 2024-10-09 20:08:33 +0200 | nadja | (~dequbed@banana-new.kilobyte22.de) dequbed |
| 2024-10-09 20:08:17 +0200 | nadja | (~dequbed@banana-new.kilobyte22.de) (Read error: Connection reset by peer) |
| 2024-10-09 20:07:47 +0200 | TimWolla | (~timwolla@2a01:4f8:150:6153:beef::6667) TimWolla |
| 2024-10-09 20:07:06 +0200 | TimWolla | (~timwolla@2a01:4f8:150:6153:beef::6667) (Quit: Bye) |
| 2024-10-09 20:06:52 +0200 | sus0 | (zero@user/zeromomentum) zeromomentum |
| 2024-10-09 20:06:48 +0200 | op_4 | (~tslil@user/op-4/x-9116473) op_4 |
| 2024-10-09 20:06:34 +0200 | op_4 | (~tslil@user/op-4/x-9116473) (Read error: Connection reset by peer) |
| 2024-10-09 20:06:30 +0200 | yahb2 | (~yahb2@user/tomsmeding/bot/yahb2) (Ping timeout: 246 seconds) |
| 2024-10-09 20:06:28 +0200 | acidjnk | (~acidjnk@p200300d6e72cfb59bd2c072e962d353d.dip0.t-ipconnect.de) acidjnk |
| 2024-10-09 20:06:16 +0200 | sus0 | (zero@user/zeromomentum) (Quit: Ping timeout (120 seconds)) |
| 2024-10-09 20:01:03 +0200 | alp_ | (~alp@2001:861:e3d6:8f80:e3a4:78d2:48d1:1e0) |
| 2024-10-09 19:54:47 +0200 | briandaed | (~root@185.234.210.211.r.toneticgroup.pl) |
| 2024-10-09 19:52:41 +0200 | ljdarj | (~Thunderbi@user/ljdarj) (Ping timeout: 252 seconds) |
| 2024-10-09 19:49:57 +0200 | CiaoSen | (~Jura@2a05:5800:2e5:2400:ca4b:d6ff:fec1:99da) CiaoSen |
| 2024-10-09 19:48:20 +0200 | mantraofpie | (~mantraofp@user/mantraofpie) mantraofpie |
| 2024-10-09 19:43:43 +0200 | alioguzhan | (~Thunderbi@78.173.89.238) |
| 2024-10-09 19:42:45 +0200 | acidjnk | (~acidjnk@p200300d6e72cfb597c01f41ab12f33b9.dip0.t-ipconnect.de) (Ping timeout: 248 seconds) |
| 2024-10-09 19:38:53 +0200 | Tuplanolla | (~Tuplanoll@91-159-69-59.elisa-laajakaista.fi) Tuplanolla |
| 2024-10-09 19:35:31 +0200 | <seydar> | thank you |
| 2024-10-09 19:35:30 +0200 | <seydar> | why am i making this so hard |
| 2024-10-09 19:34:56 +0200 | <darkling> | Direction orthogonal to AB is (b2-a2, a1-b1), IIRC. Normalise that, and multiply by m. Add to c. |
| 2024-10-09 19:33:55 +0200 | tromp | (~textual@92-110-219-57.cable.dynamic.v4.ziggo.nl) |
| 2024-10-09 19:32:32 +0200 | gmg | (~user@user/gehmehgeh) (Quit: Leaving) |
| 2024-10-09 19:29:08 +0200 | ljdarj | (~Thunderbi@user/ljdarj) ljdarj |