Distance difference from center

Hi,

I created a cross section by using kmeans function from two different data (indicated by X and * in image),

My aim is to determine the distance difference of two data from center (o) of cross section,

Briefly i try to find the;

Distance between O and X (d1)

Than i need to find the nearest * to X,

Than calculate the distance between O and * (which is nearest X) (d2)

And lastly i need to calculate the difference between (d1) and (d2)

And i want to do this calculations for all X to * in cross-section.

Thank you...

My current code is given below: my points are represented by m,n and o in code...

clc;clear;

x=xlsread('king1.xlsx', 'A:A');

y=xlsread('king1.xlsx', 'B:B');

z=xlsread('king1.xlsx', 'C:C');

a=xlsread('king2.xlsx', 'A:A');

b=xlsread('king2.xlsx', 'B:B');

c=xlsread('king2.xlsx', 'C:C');

xyz=[x y z];

abc=[a b c];

rng(1);

[idx1,C1] = kmeans(xyz,100,'distance','sqEuclidean','MaxIter',500, 'Replicates', 10);

[idx2,C2] = kmeans(abc,100,'distance','sqEuclidean','MaxIter',500, 'Replicates', 10);

[dist,idx3] = pdist2(xyz, C1, 'euclidean', 'Smallest',1);

newVar = xyz(idx3 ,:);

plot3(newVar(:,1), newVar(:,2), newVar(:,3), 'bx');

hold on;

xlabel ('x - axis', 'fontsize', 12);

ylabel ('y - axis', 'fontsize', 12);

zlabel ('z - axis', 'fontsize', 12);

grid

[dist2,idx4] = pdist2(abc, C2, 'euclidean', 'Smallest',1);

newVar2 = abc(idx4 ,:);

plot3(newVar2(:,1), newVar2(:,2), newVar2(:,3), 'r*')

newVar3 = mean (newVar)

newVar4 = mean (newVar2)

newVar5 = (newVar3 + newVar4)/ 2

plot3(newVar5(:,1), newVar5(:,2), newVar5(:,3), 'go');

m=[newVar(:,1) newVar(:,2) newVar(:,3)];

n=[newVar2(:,1) newVar2(:,2) newVar2(:,3)];

o=[newVar5(:,1) newVar5(:,2) newVar5(:,3)];

[darova]

Do you have a question?

[Mehmet Volkan Ozdogan]

I could not make the calculation..

I need to find the distance between d2-d1

X in figure are represented by variable m in code,

* in figure are represented by variable n in code,

and the center of cross section is represented by variable o in code

thank you

Answer 1

[darova]

I did this

xyz0 = (mean(xyz)+mean(abc))/2;                % O point
XYZ0 = repmat(xyz0,size(xyz,1),1);             % duplicate rows
d1 = XYZ0 - xyz;                               % Distance(s) between O and X   (d1)

    % find the nearest * to X
D = pdist2(xyz,abc);                           % every possible combinations
D(D==0) = max(D(:));                           % fill zeros with max    ( (:) - convert matrix to column vector )
[~,ind] = min(D(:));                           % find index of min element
    % Found index of min element in vector. Find correspoding indices of points
[i,j] = ind2sub(size(D),ind);                  % extract row and column (i - index of xyz, j - index of abc)

    % calculate the distance between O and * (which is nearest X)  (d2)
d2 = xyz0 - abc(j,:);                          % difference between O point and * (nearest X)
D2 = repmat(d2,size(d2,1),1);                  % duplicate rows
d = D2 - d1;                                   % distance(s) between d2 and d1

[Mehmet Volkan Ozdogan]

Thank you for your answer and clear explanation

But I think i could not tell my self clearly,sorry about that,

In my current code i did not use xyz and abc, i used them to find the "newVar" and "newVar2"

"newVar" = X and "newVar2" = *, and also "newVar5"= o

Also i need the distance but "d1 = XYZ0 - xyz" gives coordinate.

I changed the variables and also changed the distance calculation but i have still a problem with the code . Because results are not sensible.

On the other hand i do not understand why you duplicated the rows

Do you have any other suggestion, thank you...

clc;clear;
x=xlsread('king1.xlsx', 'A:A');
y=xlsread('king1.xlsx', 'B:B');
z=xlsread('king1.xlsx', 'C:C');
a=xlsread('king2.xlsx', 'A:A');
b=xlsread('king2.xlsx', 'B:B');
c=xlsread('king2.xlsx', 'C:C');
xyz=[x y z];
abc=[a b c];
rng(1);
[idx1,C1] = kmeans(xyz,100,'distance','sqEuclidean','MaxIter',500, 'Replicates', 10);
[idx2,C2] = kmeans(abc,100,'distance','sqEuclidean','MaxIter',500, 'Replicates', 10);
[dist,idx3] = pdist2(xyz, C1, 'euclidean', 'Smallest',1);
newVar = xyz(idx3 ,:);
plot3(newVar(:,1), newVar(:,2), newVar(:,3), 'bx');
hold on;
xlabel ('x - axis', 'fontsize', 12);
ylabel ('y - axis', 'fontsize', 12);
zlabel ('z - axis', 'fontsize', 12);
grid
[dist2,idx4] = pdist2(abc, C2, 'euclidean', 'Smallest',1);
newVar2 = abc(idx4 ,:);
plot3(newVar2(:,1), newVar2(:,2), newVar2(:,3), 'r*')
newVar3 = mean (newVar)
newVar4 = mean (newVar2)
newVar5 = (newVar3 + newVar4)/ 2
plot3(newVar5(:,1), newVar5(:,2), newVar5(:,3), 'go');
%m=[newVar(:,1) newVar(:,2) newVar(:,3)];
%n=[newVar2(:,1) newVar2(:,2) newVar2(:,3)];
%o=[newVar5(:,1) newVar5(:,2) newVar5(:,3)];
newVar52 = repmat(newVar5,size(newVar,1),1);                         % duplicate rows
[d1,idx5] = pdist2(newVar52, newVar, 'euclidean', 'Smallest',1);     % Distance(s) between O and X   (d1)
             % find the nearest * to X
D = pdist2(newVar,newVar2);                                       % every possible combinations
D(D==0) = max(D(:));                                              % fill zeros with max    ( (:) - convert matrix to column vector )
[~,ind] = min(D(:));                                              % find index of min element
    % Found index of min element in vector. Find correspoding indices of points
[i,j] = ind2sub(size(D),ind);                                    % extract row and column (i - index of xyz, j - index of abc)
    % calculate the distance between O and * (which is nearest X)  (d2)
[d2,idx6] = pdist2(newVar5, newVar2(j,:), 'euclidean', 'Smallest',1);       % difference between O point and * (nearest X)
D2 = repmat(d2,size(d2,1),1);                                                % duplicate rows
d = D2 - d1;   

[darova]

Sorry. forgot about that. Those are not coordinates, when you subract coordinates you get coordinates difference

p1(x1,y1) - p2(x2,y2) = v(dx,dy)

xyz0 = (mean(xyz)+mean(abc))/2;                % O point (ONE point)
XYZ0 = repmat(xyz0,size(xyz,1),1);             % duplicate rows
d1 = XYZ0 - xyz;                               % difference(s) between O and X (dy,dy,dz)
d1 = sqrt(sum(d1.^2,2));                       % absolute distance(s) (euclidean)
    % the same because xyz0 - one point
d1 = pdist(xyz0,xyz);
    % or
d1 = pdist2(xyz0,xyz,'euclidean','smallest',1)

I duplicated rows, because forgot how pdist2() works

• Distance between O and X (d1)
• Than i need to find the nearest * to X, - i misunderstood you here
• Than calculate the distance between O and * (which is nearest X) (d2)
• And lastly i need to calculate the difference between (d1) and (d2)

Try this:

d1 = pdist2(varO,varX);                            % distance(s) (many) between O and X
% varS == var*
[~,idx] = pdist2(varS,varX,'euclidean','smallest',1);    % indices of nearest * for EACH X
d2 = pdist2(varO,varS(idx));                       % distance(s) between O and * (nearest to X)
d2 - d1

[darova]

Sorry, didn't test it (missed ':' for column). Try:

d2 = pdist2(newVar5,newVar2(idx,:)); 

[Mehmet Volkan Ozdogan]

Thank you for your helps,

I made a little uptade on your code

d2 = pdist2(varO,varS(idx)); have to be ;

d2 = pdist2(varO,varS(idx, :))

thank you again

[Mehmet Volkan Ozdogan]

works great thank you again...

Answer 2

[e_oksum]

hi mehmet, here is an example code performing what you explained,

example uses random positions, you can adopt by yours..and also simplify it for more compact without plotting etc..

X=rand(1,10)*10       ;% your x position of X
Y=rand(1,10)*10      ;% your y position of X
xs=rand(1,10)*10      ;% your x position of *
ys=rand(1,10)*10      ;% your y position of *

xo=5      ;% center x
yo=5      ;% center y
plot(X,Y,'ro','markerfacecolor','r');
hold on
plot(xs,ys,'k+');
plot(xo,yo,'go','markerfacecolor','g');

for i=1:numel(X)
d1(i)=sqrt((X(i)-xo).^2+(Y(i)-yo).^2);% distance d1 of X(i) Y(i) to center
%find position of nearest xs,ys to X,Y
L=sqrt((xs-X(i)).^2 + (ys-Y(i)).^2);
idx=find(L==min(L));
xp(i)=xs(idx); %(xp yp are the nearest nearest X)
yp(i)=ys(idx);
d2(i)=sqrt((xp(i)-xo).^2 + (yp(i)-yo).^2); % distance d2 of nearest xp yp to X(i),Y(i)
diffd1d2(i)=(d1(i)-d2(i)); % diffrence between d1 d2

% check by plot
l1=plot([X(i) xo],[Y(i) yo],'-r'); % line d1
l2=plot([xp(i) xo],[yp(i) yo],'-k'); % line d2
pause(1)
delete(l1)
delete(l2)
end
list=[X' Y' xp' yp' d1' d2' diffd1d2']

[Mehmet Volkan Ozdogan]

Thank you for your helps and advice, i solve my problem with previous answer.