Plot distances between points matlab - matlab

Question

I've made a plot of 10 points
10 10
248,628959661970 66,9462583977501
451,638770451973 939,398361884535
227,712826026548 18,1775336366957
804,449583613070 683,838613746355
986,104241895970 783,736480083219
29,9919502693899 534,137567882728
535,664190667238 885,359450931142
87,0772199008924 899,004898906140
990 990
With the first column as x-coordinates and the other column as y-coordinates
Leading to the following Plot:
Using the following code: scatter(Problem.Points(:,1),Problem.Points(:,2),'.b')
I then also calculated the euclidean distances using Problem.DistanceMatrix = pdist(Problem.Points);
Problem.DistanceMatrix = squareform(Problem.DistanceMatrix);
I replaced the distances by 1*10^6 when they are larger than a certain value.
This lead to the following table:
Then, I would like to plot the lines between the corresponding points, preferably with their distances, but only in case the distance < 1*10^6.
Specifically i want to plot the line [1,2] [1,4] [1,7] [2,4] etc.
My question is, can this be done and how?

Answer 1

Assuming one set of your data is in something called xdata and the other in ydata and then the distances in distances, the following code should accomplish what you want.
hold on
for k = 1:length(xdata)
for j = 1:length(ydata)
if(distances(k,j) < 1e6)
plot([xdata(k) xdata(j)], [ydata(k) ydata(j)]);
end
end
end
You just need to iterate through your matrix and then if the value is less than 1e6, then plot the line between the kth and jth index points. This will however double plot lines, so it will plot from k to j, and also from j to k, but it is quick to code and easy to understand. I got the following plot with this.

Answer 2

This should do the trick:
P = [
10.0000000000000 10.0000000000000;
248.6289596619700 66.9462583977501;
451.6387704519730 939.3983618845350;
227.7128260265480 18.1775336366957;
804.4495836130700 683.8386137463550;
986.1042418959700 783.7364800832190;
29.9919502693899 534.1375678827280;
535.6641906672380 885.3594509311420;
87.0772199008924 899.0048989061400;
990.0000000000000 990.0000000000000
];
P_len = size(P,1);
D = squareform(pdist(P));
D(D > 600) = 1e6;
scatter(P(:,1),P(:,2),'*b');
hold on;
for i = 1:P_len
pi = P(i,:);
for j = 1:P_len
pj = P(j,:);
d = D(i,j);
if ((d > 0) && (d < 1e6))
plot([pi(1) pj(1)],[pi(2) pj(2)],'-r');
end
end
end
hold off;
Final output:
On a side note, the part in which you replaces the distance values trespassing a certain treshold (it looks like it's 600 by looking at your distances matrix) with 1e6 can be avoided by just inserting that threshold into the loop for plotting the lines. I mean... it's not wrong, but I just think it's an unnecessary step.
D = squareform(pdist(P));
% ...
if ((d > 0) && (d < 600))
plot([pi(1) pj(1)],[pi(2) pj(2)],'-r');
end

Answer 3

A friend of mine suggested using gplot
gplot(Problem.AdjM, Problem.Points(:,:), '-o')
With problem.points as the coordinates and Problem.AdjM as the adjacency matrix. The Adjacency matrix was generated like this:
Problem.AdjM=Problem.DistanceMatrix;
Problem.AdjM(Problem.AdjM==1000000)=0;
Problem.AdjM(Problem.AdjM>0)=1;
Since the distances of 1*10^6 was the replacement of a distance that is too large, I put the adjacency there to 0 and all the other to 1.
This lead to the following plot, which was more or less what I wanted:
Since you people have been helping me in such a wonderful way, I just wanted to add this:
I added J. Mel's solution to my code, leading to two exactly the same figures:
Since the figures get the same outcome, both methods should be all right. Furthermore, since Tommasso's and J Mel's outcomes were equal earlier, Tommasso's code must also be correct.
Many thanks to both of you and all other people contributing!