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PostPosted: Wed Apr 12, 2017 2:56 pm 
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Winchell Chung (aka the godfather of starmapping) has a formula available to convert from celestial XYZ (e.g. the original 2300 map, and I think maybe Omer's Near Star 2D map) to galactic XYZ.

EDG's premade data, and the results of his very useful bulk converter are both already in galactic XYZ.

What I'd like to do is convert back to celestial, so that I can present a fairly busy map from two perspectives. It's hard in a top-down map to really "click" that the +21z star isn't right next to that -14z star, so if you can see it from another angle...

Anyway, I'm not quite sure how I'd reverse that formula. I'm quick to pick up on things, but it's been a looooooooooong time since I took a math class. I'm pretty sure Reagan was prez, know what I'm sayin'?

Suggestions welcome.


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PostPosted: Wed Apr 12, 2017 3:15 pm 
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If this proves to be ridonkulously complicated, I'll just swap the Y/Z axes or something.


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PostPosted: Wed Apr 12, 2017 6:53 pm 
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I suggest keeping the galactic coordinates, but doing three orthogonal maps: x-y, x-z, and y-z.


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PostPosted: Wed Apr 12, 2017 7:03 pm 
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This map does a pretty good job of conveying three-dimensional positions. The approach would probably be unworkable if the map contains may more items, though.

https://upload.wikimedia.org/wikipedia/ ... 29.svg.png

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PostPosted: Wed Apr 12, 2017 8:47 pm 
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Matt Wilson wrote:
Anyway, I'm not quite sure how I'd reverse that formula.

It's a set of simultaneous linear equations. Three equations in six unknowns. The straightforward way to solve it is by eliminating variables (the way to solve a set of linear equations that you would have been taught in high school), The way a mathematician would do it is by inverting the matrix. Or you could do Gaussian Elimination on
Code:
⎡ -0.0550, -0.8732, -0.4839 | 1, 0, 0 ⎤
⎢  0.4940,  0.4449,  0.7470 | 0, 1, 0 ⎥
⎣ -0.8677, -0.1979,  0.4560 | 0, 0, 1 ⎦


Which is, of course, inverting the matrix

Code:
⎡ -0.0550, -0.8732, -0.4839 ⎤
⎢  0.4940,  0.4449,  0.7470 ⎥
⎣ -0.8677, -0.1979,  0.4560 ⎦


There's probably a 3×3 matrix inversion tool on line somewhere. Or your calculator might do matrix inversions.

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PostPosted: Wed Apr 12, 2017 9:32 pm 
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Put it this way, I couldn't figure it out when I did the bulk converter on my website. I had to get a lot of help from way more knowledgeable people (mostly Grant Hutchison on the now-probably-dead Celestia forums).

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PostPosted: Wed Apr 12, 2017 9:38 pm 
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Agemegos wrote:
There's probably a 3×3 matrix inversion tool on line somewhere.

Using the one I found at https://matrix.reshish.com/inverCalculation.php I got

xeq = 0.58074 xgal + 0.81792 ygal + -0.72362 zgal
yeq = -1.44633 xgal + -0.73681 ygal -0.32781 zgal
zeq = 0.47736 xgal + 1.23662 ygal + 0.67377 zgal

That's for the Epoch 2000 conversion given at http://www.projectrho.com/public_html/starmaps/coords.php#id--Epoch_2000.0

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PostPosted: Wed Apr 12, 2017 11:32 pm 
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There is a trap for young players.

The equatorial co-ordinate system is a right-handed system, with X, Y, and Z positive in the directions of the northern vernal equinox, a point on the celestial equator 90° east of that, and north.

There are two versions of the galactic co-ordinate system: both have V positive to spinward and W positive to galactic north, but one has U positive towards the Core and the other has U negative towards the core (the description in Wikipedia is was wrong, nonsensical, and does did not match the source cited so I changed it). One is a right-handed system and the other is a left-handed system, and it's not the way around that you would expect because the galactic north pole is a negative pole, not a positive pole (it is the galactic pole that is in the northern hemisphere of Earth's sky, not the positive pole of the galaxy's rotation). Depending which one your source was using, the conversion may effect a reflection as well as a rotation, and if you don't plot the maps carefully one might end up back to front.


This is all connected to my grumbles about "galactic" co-ordinates. A proper set of galactic co-orodinates would have its origin at the centre of mass of the Galaxy, not at Sol (which is moving, goddammit!, besides being not in the Galactic plane). The first co-ordinate would be a convenient direction in the galactic plane. The second would be another direction in the plane 90° to spinward of the first. And the third would be the positive spin axis of the Galaxy, i.e. Galactic south.

The centre of the Galaxy ought to be at (0, 0, 0), not at approximately (27 000, 0, -8 000). The Galaxy ought to rotate right-handed about the z axis, not left-handed about an axis parallel to the z axis but about 27,000 light-years distant.

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Last edited by Agemegos on Thu Apr 13, 2017 12:28 am, edited 1 time in total.

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PostPosted: Thu Apr 13, 2017 12:26 am 
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I have mended the Wikipedia article.

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PostPosted: Thu Apr 13, 2017 12:02 pm 
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Wow, thanks Brett. You are a mensch. Remind me to buy you a beverage when I next visit Australia.


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