Looped vector calculation and storage of answer

Hello, I have two horizontal vectors which contain points for plotting a circle; vector "x" for x-coordinates and vector "y" for y-coordinates. I am trying to write a piece of code which will determine the largest chord within that circle. The approach I am taking is to use the distance formula (sqrt((x2-x1)^2)+((y2-y1)^2)) and calculate the distance between the first point and the rest - store all the distances. Then the distance between the second point and the rest - store all distance to same place. And continue this till the last point. In the end I shall have a vector (or matrix) which contains all these distances, I can then run a "max" command to find the maximum distance. I am just not sure how to implement this into MatLab, in a neat looped script. All and any help will be greatly appreciated.

Answer 1

[Matt J]

You can use my interdists() function below. Since you say it is a circle, I don't see why you would want to compare all pairs of points. The only way this can give you a good approximation of the diameter is if the circle is well-sampled, and in that case, the distance to one particular point ,e.g.,

 data=[x;y];

 distances = interdists(data(:,1),data);

ought to be enough.

function Graph=interdists(A,B)
%Finds the matrix of distances between point coordinates
%
% (1) Graph=interdists(A,B)
%
% in:
% 
% A:  matrix whose columns are coordinates of points, for example 
%          [[x1;y1;z1], [x2;y2;z2] ,..., [xM;yM;zM]]
%     but the columns may be points in a space of any dimension, not just 3D.
% 
% B:  A second matrix whose columns are coordinates of points in the same
%     Euclidean space. Default B=A.
% 
% 
% out:
% 
% Graph: The MxN  matrix of separation distances in l2 norm between the coordinates. 
%        Namely, Graph(i,j) will be the distance between A(:,i) and B(:,j).
%
%
% (2) interdists(A,'noself') is the same as interdists(A), except the output 
%     diagonals will be NaN instead of zero. Hence, for example, operations
%     like min(interdists(A,'noself')) will ignore self-distances.
%
% See also getgraph

noself=false;
if nargin<2  
    B=A; 
elseif ischar(B)&&strcmpi(B,'noself')
    noself=true;
    B=A;
end

N=size(A,1);
B=reshape(B,N,1,[]);

Graph=l2norm(bsxfun(@minus, A, B),1);

Graph=squeeze(Graph);

if noself
    n=length(Graph);
   Graph(linspace(1,n^2,n))=nan;

[Mazhar]

Thank you Matt for your quick response. The reason I am needing to do this for all points is because I cannot be sure that the "circle" is completely circular, it could be deformed in to an oval or parts of it deformed like a 'dent' in the circle. That is why I will need to check every chord for the largest.

[Matt J]

OK, but it's clear to you that you can still do that with the utility I've presented, right? To get the full matrix, just do

 distances = interdists(data);

[Mazhar]

I am trying to make the code work, but so far no luck. My only inputs at the moment are; vector x and vector y. I'm not quite understanding the variables 'A' and 'B' here.

[Matt J]

The columns of A and B are your coordinates and you can omit B if A=B. For example, this gives the matrix of distances between the columns of eye(2)

>> interdists(eye(2))

ans =

           0    1.4142
      1.4142         0

[Mazhar]

Ok, I see. I've replaced A and B with my vectors. If A and B represent my data, then why use x,y for the line 'data=[x;y];'? Also when I try to run the script I am getting an error for line 36: "Graph=l2norm(bsxfun(@minus, x_raw, y_raw),1);" "Undefined function 'l2norm' for input arguments of type 'double'"

[Mazhar]

Say I have these values; x=[6 5.5 4 3 2 0 -2 -3 -4 -5 -5.5 -6 -5.5 -5 -4 -3 -2 0 2 3 4 5 5.5 6]; y=[0 2 3.5 4.5 5 5.5 6 5.5 5 4.5 3.5 2 0 -2 -3.5 -4.5 -5 -5.5 -6 -5.5 -5 -4.5 -3.5 -2 0]; How would I use your code to get the out put I want? Or how can I use a Loop for this!

[Mazhar]

Got it to work :D Thanks Pal!