Math Help - Find co-ordinates of a point in a 1D, 2D or 3D space, given only distances

1. Find co-ordinates of a point in a 1D, 2D or 3D space, given only distances

I play EVE online. I like to mine, occasionally. My mining lasers have a range of 15km. The asteroid belts within which I mine are often much much larger than 15km. My Exhumer (the ship with which I mine) is impossibly slow, thus slowboating to new 'roids is silly, so, I bookmark 'roids, warp off, then warp to the bookmark, essentially giving me a new 15km sphere of ore to consume.

I know enough Python to write a program to give me the optimal 'roids to bookmark, but I've fallen down on the equations/procedure. I decided to start small, with 1 dimension, as opposed to 3.

I've tried several things, and nothing has worked so far. I figured I'd need 3 points from which to measure from, so I can first find the co-ordinate of the points, (assuming p0 is at co-ordinate (0)), then use an equation I already have working to use p0 and p1 to find x.

I've tried Googling, and usually, my Google-fu is strong, but today, it returned me nothing but distances from a point to a line, which is of course not what I want.

(Also, is this a pre-university problem, or not? I wouldn't know, as this is obviously a personal endeavour.)

2. No help whatsoever?

I've since worked out that as direction isn't given, orientation doesn't matter. I've ignored the 1D example, as it confuses me, so let us consider the points O1(1,3) O2(2,1) O3(4,2)

O1->2 = $\sqrt{5}$
O1->3 = $\sqrt{10}$
O2->3 = $\sqrt{3}$

That set of three distances is all we have.

Thus, if we assume that O1 = (0,0), we can also assume that O2 = $(0,\sqrt{5})$, meaning that if we draw a circle of radius $\sqrt{10}$ with the center (0,0), and a circle of radius $\sqrt{3}$ about point $(0,\sqrt{5})$, we should end up with 2 points, (or one, in certain cases) upon which O3 can be. We'll need another point if we want to know which of these is the appropriate point, I believe, but I haven't got that far yet.

Also bump.

3. Even if you knew the exact location of two of the points, with the location of the third being unknown, and you knew the distances between all three of them, there would be an infinite number of possibilities for the location of the third point.

4. I am inclined to disagree. There's a reason the word "triangulation" exists. As a triangle made of three lines of fixed length can only be made one way, if all distances between all points are known, a lattice can be constructed to find the co-ordinates of any chosen point.

5. Originally Posted by Asday
As a triangle made of three lines of fixed length can only be made one way, if all distances between all points are known, a lattice can be constructed to find the co-ordinates of any chosen point.
My previous statement is true in three dimensions. And your statement is false, because without knowing something about the location of at least one of the points, you cannot draw any conclusions about the locations of the other two. Also, from Wikipedia: In trigonometry and geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly. The point can then be fixed as the third point of a triangle with one known side and two known angles.

6. If you were to read my point in case in the first post, you'd see that I can know the distances between any point of my choice, and by abstraction, do indeed have a list of all idstances between all objects.

7. Originally Posted by Asday
If you were to read my point in case in the first post, you'd see that I can know the distances between any point of my choice, and by abstraction, do indeed have a list of all idstances between all objects.
You have not clearly defined what the problem is with your first post. You have said that you want to determine which asteroids to bookmark. But there are things that people who don't play the game don't know, such as how much of a speed advantage warping gives you. There must be a good reason for not bookmarking all of the relevant asteroids, but I don't know what this could be. All I am responding to is the ability to find the location of points in space given only distances.

8. "Slowboating" is pretty slow. About 86m/s. To move 30km+, this is a sucky speed.

Warping can be taken as nigh instant.

I reread my post, and I'm pretty sure that anyone who's heard the term "warp" ever can work it out, and even if they haven't, they can very easily assume that it's faster than "slowboating".

If this wasn't clear, I apologise.

9. Originally Posted by Asday
Warping can be taken as nigh instant.
And can you warp wherever you like or is there some sort of limitation, such as "you can't warp to a place you haven't explored" or something like that?

10. You need a bookmark to warp to, and you need to be on the same "grid" (about a 250km bubble, where objects load) as something to bookmark it.

11. So what are we looking for? The fastest way to bookmark a set of mining nodes?

12. Nearly. We're looking for the most comprehensive set of bookmarks, so that after visiting all of them, there will not be one asteroid that hasn't been within 15km of me.