# How do you get the furthest point from more than one point? As in, a point with maximum distance from two or more other points?

How do you get the furthest point from more than one point? As in, a point with maximum distance from two or more other points?

1. 4 weeks ago
Anonymous

I think what that means is you have a collection of nodes v1, ..., vn, that you haven't visited yet, and then a collection of nodes u1, ..., uk, that you have already visited. Then for each fixed i<n+1 and each fixed j<k+1, we can take d(i, j)=d(vi, uj) to be the distance between vertex vi and vertex vj. We can then use this collection of distances to define a norm on the set v1,...,vn, which will be analogous to the standard euclidean norm. In particular, for i fixed, we define the norm N(i) to be sqrt(d(i, 1)^2 + ... + d(i, k)^2). The next node to visit would then be given by whichever node minimizes the value of N(i).

• 4 weeks ago
Anonymous

Brute force the calculations. Calculate all distances between all points and pick the biggest one

2. 4 weeks ago
Anonymous

>d(i, j)=d(vi, uj) to be the distance between vertex vi and vertex vj

*d(i, j)=d(vi, uj) to be the distance between vertex vi and vertex uj

3. 4 weeks ago
Anonymous

>How do you get the furthest point from more than one point? As in, a point with maximum distance from two or more other points?
You don't. The point that is furthest from one point could be the point closest to the other and vice versa. You can try to maximize some weighted function of the distances, I guess, but the way to do that is application-specific.

• 4 weeks ago
Anonymous

I realise it's an optimization problem but I can't figure out what function to optimize.

I think what that means is you have a collection of nodes v1, ..., vn, that you haven't visited yet, and then a collection of nodes u1, ..., uk, that you have already visited. Then for each fixed i<n+1 and each fixed j<k+1, we can take d(i, j)=d(vi, uj) to be the distance between vertex vi and vertex vj. We can then use this collection of distances to define a norm on the set v1,...,vn, which will be analogous to the standard euclidean norm. In particular, for i fixed, we define the norm N(i) to be sqrt(d(i, 1)^2 + ... + d(i, k)^2). The next node to visit would then be given by whichever node minimizes the value of N(i).

>d(i, j)=d(vi, uj) to be the distance between vertex vi and vertex vj

*d(i, j)=d(vi, uj) to be the distance between vertex vi and vertex uj

Brute force the calculations. Calculate all distances between all points and pick the biggest one

What I mean is you have two points, A and B, and a set of other points {D,E,F}, how to find which point in the set maximizes the distance from both A and B.

• 4 weeks ago
Anonymous

>I can't figure out what function to optimize.
What are you trying to accomplish? Like I said, chances are you won't find one point that is simultaneously furthest from the others, so you have to make some compromises depending on what you're trying to do.

• 4 weeks ago
Anonymous

>What are you trying to accomplish?
Find the point as close to equally furthest from the others as possible.

• 4 weeks ago
Anonymous

>Find the point as close to equally furthest
What does this even mean?

• 4 weeks ago
Anonymous

Dude you have 4 points, select 2 points, find a point from the remaining two that's furthest from the selected points.

• 4 weeks ago
Anonymous

Okay, I select A and B. Which of the remaining points is "the furthest" from the selected points?

• 4 weeks ago
OP

Either C or D, it doesn't matter in that case.
Anyway I think I figured it out.
You get the total distance minus the difference between the max distance and the min distance.
Then the maximum of that would be the best point, because the best point would have the least difference between the distances, therefore the least impact on the total distance.

Whereas in the worst case the difference would be equal to one of the distances, taking it completely away, which should I'm thinking always be less than the best total.

• 4 weeks ago
Anonymous

So you just pulled some arbitrary metric out of your ass. Good for you.

• 4 weeks ago
OP

It might be an interesting geometry proof to show if it's always the case.

• 4 weeks ago
Anonymous

shitstain, you keep changing your question.
fucking pick one and stick to it, fucker.

• 4 weeks ago
OP

I'm not changing anything.

So you just pulled some arbitrary metric out of your ass. Good for you.

Actually maybe I'm overcomplicating it. I wish someone here was good at maths.

• 4 weeks ago
Anonymous

>Actually maybe I'm overcomplicating it. I wish someone here was good at maths.
Retard, no one can help you since you can't specify what you're trying to accomplish. You have some vague idea of a "furthest point" stuck in your head that makes no sense at face value, but you won't rub your two braincells together and attempt to specify what properties your "furthest point" should have specifically.

• 4 weeks ago
Anonymous

Yeah, you are.
Too much of a shit brain to see it.

• 4 weeks ago
Anonymous

>A and B, and a set of other points {D,E,F}, how to find which point in the set maximizes the distance from both A and B

find the vectors AD AE AF BD BE BF and find which pair is the biggest AD + BD, AE + BE, AF + BF

• 4 weeks ago
OP

>find the vectors AD AE AF BD BE BF and find which pair is the biggest AD + BD, AE + BE, AF + BF
That's not correct, that just gives you the point with the biggest total distances. Look at the picture, your idea won't work.

• 3 weeks ago
Anonymous

>What I mean is you have two points, A and B, and a set of other points {D,E,F}, how to find which point in the set maximizes the distance from both A and B.

>find the vectors AD AE AF BD BE BF and find which pair is the biggest AD + BD, AE + BE, AF + BF
That's not correct, that just gives you the point with the biggest total distances. Look at the picture, your idea won't work.

>Look at the picture

tarded

• 3 weeks ago
Anonymous

Yeah it was a fucking example with just the first 2 points to make it easier for your banana brain to handle. But you couldn't even handle that.

• 3 weeks ago
Anonymous

Usually, the distance between a point x and a set S of points {a, b, c,...} is the minimum of the distances between x and each of the points in S. That may seem more obvious when S is a continuous body, but it looks like what the original picture was doing with its discrete set of points.

so go be retarded somewhere else.

• 3 weeks ago
Anonymous

>a wrong version of a shortest distance function is exactly what I need for my longest path algorithm

You suck at this

• 3 weeks ago
Anonymous

How many times were you dropped as a kid exactly?

4. 4 weeks ago
OP

[deleted post]

>You're question isn't even well defined
It literally says the fucking question in the picture, and I wrote it out a bunch of times.
Find the fucking farthest point from multiple other points.
It's not just finding the norm between all points and getting the max.

5. 4 weeks ago
OP

OP here, I think I figured it out, it's actually quite simple.
It's just max(min({norm1,norm2,...}), min(norm1,norm2,...)) and you pick the vertex with the biggest minimum distance.
At least it solves the example in the picture.

6. 4 weeks ago
Anonymous

Usually, the distance between a point x and a set S of points {a, b, c,...} is the minimum of the distances between x and each of the points in S. That may seem more obvious when S is a continuous body, but it looks like what the original picture was doing with its discrete set of points.

• 4 weeks ago
Anonymous

>Usually, the distance between a point x and a set S of points {a, b, c,...} is the minimum of the distances between x and each of the points in S.
Looks like you confirmed my idea

OP here, I think I figured it out, it's actually quite simple.
It's just max(min({norm1,norm2,...}), min(norm1,norm2,...)) and you pick the vertex with the biggest minimum distance.
At least it solves the example in the picture.

I can't believe it took me hours to figure this out.

7. 4 weeks ago
Anonymous

Center = (Vec3_A + Vec3_B)/2

check: distance(Vec3_X,Center) for all points to be tested and the one with the furthest distance is your point.

• 4 weeks ago
Anonymous

And for N number of points it's

Center = (Vec3_A + Vec3_B+ Vec3_C)/3

and so on.

• 3 weeks ago
Anonymous

And for N number of points it's

Center = (Vec3_A + Vec3_B+ Vec3_C)/3

and so on.

That's not correct, it's distance from multiple points, not distance from centroid.

8. 4 weeks ago
Anonymous

Shitstain OP:
>How do you get the furthest point from more than one point? As in, a point with maximum distance from two or more other points?
>What I mean is you have two points, A and B, and a set of other points {D,E,F}, how to find which point in the set maximizes the distance from both A and B.
>Find the point as close to equally furthest from the others as possible.
>Dude you have 4 points, select 2 points, find a point from the remaining two that's furthest from the selected points.
These statements and questions are not all equivalent.

• 3 weeks ago
Anonymous

>These statements and questions are not all equivalent
Yes they are.

• 3 weeks ago
Anonymous

No they aren't.

Shitstain OP:
>How do you get the furthest point from more than one point? As in, a point with maximum distance from two or more other points?
>What I mean is you have two points, A and B, and a set of other points {D,E,F}, how to find which point in the set maximizes the distance from both A and B.
>Find the point as close to equally furthest from the others as possible.
>Dude you have 4 points, select 2 points, find a point from the remaining two that's furthest from the selected points.
These statements and questions are not all equivalent.

OP is doing math in bad faith

>find the vectors AD AE AF BD BE BF and find which pair is the biggest AD + BD, AE + BE, AF + BF
That's not correct, that just gives you the point with the biggest total distances. Look at the picture, your idea won't work.

>Look at the picture, your idea won't work.
Picture is unrelated.

If the picture was related you would be saying something like, "What is the maximum path length?"

• 3 weeks ago
Anonymous

>Picture is unrelated.
Ok I'm done you're fucking retarded.

9. 4 weeks ago
Anonymous

with loops the problem has no bounds
without loops just set the distances between points to 1/distance and take the shortest path

• 3 weeks ago
Anonymous

lol ignore this what is this problem even referring to
i think you want a bipartite graph and to select from one side based on

Center = (Vec3_A + Vec3_B)/2

check: distance(Vec3_X,Center) for all points to be tested and the one with the furthest distance is your point.

but the problem is a word salad

• 3 weeks ago
Anonymous

no