A map problem for trig geeks

[Sholari Joe]

I am not a math geek. I am several other flavors of geek, but not math. And there is a mapping problem that involves three dimensional measurements.

I want to do a star map for RPGs, and do not know what format it would be best to present with end users.

Stars. Local stars. Say, 12 Light years diameter around Sol. I can do the 2d map, and even indicate position from the sun, above and below the plane of the ecliptic.

But I would like to deal with distances between stars ... as the crow flies. And we can assume the Crow doesn't always want to go back by Sol to see Aunt Gramma. Sometimes you just want the shortest route. It would be easy to present the resulting data from a 2-axis chart, but getting the distances is more of a problem than my tiny brain can wrap around.



This is the fourth of five posts before I am considered real. The CAPTCHAs weren't enough of a clue, I guess.

And here is my regular white for a higher contrast options for low vision map geeks, like me. I can get high contrast using the mobile phone format otpion, but I cannot post maps to a map forum to discuss maps in that readable format. So I'm guessing. I've got my screen blown up to 'damn big' and still can read the black on brown options.

If the idea was to evoke the old map persona, you know what would really evoke the old map persona - black on beige. Ink on parchment. Ink on foolscap. Ink on pulp paper. But very few maps were printed in yellow with brown backgrounds.

[Azélor]

Personnaly, I'm not that good in math either but I would mostly use the Pythagore theorem .

Take Wolf for example. You already draw the line arriving at the Sun's equator. I'll refer to this as the dot.

First you need to find the distance between the dot and the Sun. You can do that by tracing a circle, like the others, one that intersect the dot. To find the distance, look where that circle crosses the x axis, from right to left. Since your actual circle is 5 ly , you can find the distance by using the cross multiplication, after mesuring the distance berween sun and dot.

After that, you find the distance between the dot and wolf. This is easy. Mesure the distance cross multiply it with your scale.

Now you have 2 of the 3 sides of the triangle, use pythagore to find the actual distance between sun and wolf.

That's the sinpliest method I can think of.

[Falconius]

Presumably he'd want to measure between planets though not the sun. Which would mean measuring the distance between the Dot's and then finding the difference of the elevation and then doing some good old Pythagoras Theorem on that (which in case one was wondering is a^2+b^2=c^2 where a and b are the measurements of the perpendicular axis of the triangle and c the connecting line).

[Redrobes]

I am not entirely sure I understand whats required here but if you have 2 x 3D points in space as planet positions called (x1,y1,z1) and (x2,y2,z2) then distance between them is:

sqrt( (x2-x1)*(x2-x1) + (y2-y1)*(y2-y1) + (z2-z1)*(z2-z1) )

No trig required.

I did a map like this years ago called "zenith of serendipity" cant seem to find it on the guild site any more to show you tho. I'll have a look on my backup drive to see if it still exists. Used the old Elite name generator for all of the stars and put them in randomly and then used perl magick to make it in 3D. But thats a bit off topic...

Edit: Gosh, that map was 2008 ! (oh and yellow on a brown background no less !)

[selden]

Celestia can calculate those distances for you, if you want to avoid doing the math yourself.

After you GoTo a star, Celestia's menu item Navigation -> Star Browser provides a list of nearby stars and the distances to them from where you are.



Celestia is a free 3D astronomical visualization program which is available for Windows, Macs and Linux. For more information, see https://celestiaproject.net/

[Hai-Etlik]

Well, you appear to be using a cylindrical coordinate system so to get distance you need to convert to Cartesian coordinates, subtract, and then use Pythagoras. http://mathb.in/151353