# finding closer points to a given co-ordinates

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Hi, everyone: I have two centers P(x1,y1) and Q(x2,y2). In each coordinate there are cluster of 10 points normally distributed with standard deviation 2,and mean 0. How to write code in matlab to find closer points around the P and Q and compare? If anybody have idea please share. Thank you.

Regards; SGiri

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### Answers (3)

Image Analyst
on 18 May 2018

Edited: Image Analyst
on 18 May 2018

Try this:

% Find point in x1 and y1 vectors that is closest to point P with coordinates (Px, Py).

distancesP = sqrt((x1 - Px).^2 + (y1 - Py) .^ 2);

[minDistanceP, indexOfMinP] = min(distancesP);

% Find point in x2 and y2 vectors that is closest to point Q with coordinates (Qx, Qy).

distancesQ = sqrt((x2 - Qx).^2 + (y2 - Qy) .^ 2);

[minDistanceQ, indexOfMinQ] = min(distancesQ);

##### 8 Comments

Image Analyst
on 19 May 2018

Edited: Image Analyst
on 19 May 2018

Ameer Hamza
on 18 May 2018

Edited: Ameer Hamza
on 18 May 2018

If cluster 1 elemets are arranged like this

X1 = [x1 y1;

x2 y2;

....

....

x10 y10];

and P is a row vector than to find the minimum distance point use

[minValue, minIndex] = min(vecnorm(X1 - P, 2, 2));

similarly, you can find points closest to Q.

##### 0 Comments

John BG
on 19 May 2018

Edited: John BG
on 19 May 2018

Hi Subarna Giri

On April 30th I answered the really similar question

nearest point from two matrices

My answer to that question not only finds the distance between the nearest points of 2 sets, like P and Q in your question, but also returns

1.-

a matrix Da that has all distances among all points ordered by proximity.

2.-

a matrix Na ranking the elements of both sets by proximity, it may also come handy, may it not?

Subarna, replace the following A and B with the sets P and Q of your question.

If you supply P and Q I will update my answer with the coordinates you make available.

clear all;clc;close all

N=10

Ln=[1:N]

A=randi([0 50],N,2);

B=randi([0 50],N,2);

plot(A(:,1),A(:,2),'r*');grid on

axis([0 50 0 50])

axis equal

hold on

for k=1:1:N

text(A(k,1),A(k,2),[' ' num2str(Ln(k))],'FontSize',12,'Color','red')

end

plot(B(:,1),B(:,2),'*','Color',[.2 .7 .2]);grid on

for k=1:1:N

text(B(k,1),B(k,2),[' ' num2str(Ln(k))],'FontSize',12,'Color',[.2 .7 .2])

end

.

.

Now let's define 2 matrices for the results

2.-

Da2=zeros(Na,Nb)

.

Da2 is for the distances of each element of A to all elements of B.

.

Na2=zeros(Na,Nb)

.

Na2 is for the ordered numerals according to distance, the 1st is the nearest.

for k=1:1:Na

% L1=[1:k];L1(end)=[];L1=[L1 k+1:N] % numerals of all B neighbour except kth neighbour

pa=repmat(A(k,:),Nb,1)

Da=(sum((pa-pb).^2,2)).^.5 % distance of a point to all B neighbours

D0=sortrows([Da Lnb'])

Da2(k,:)=D0(:,1) % update sorted distances

Na2(k,:)=D0(:,2) % update sorted numerals

end

3.-

The results

Na2 =

3 4 5 1 6 2

6 2 5 4 1 3

4 1 2 3 6 5

2 6 1 4 5 3

4 3 1 5 2 6

1 4 2 6 3 5

2 1 6 4 5 3

5 6 2 3 4 1

2 6 1 4 5 3

6 2 4 1 5 3

If you focus on the 1st column

Na2(:,1)

=

3

6

4

2

4

1

2

5

2

6

reading it as follows

1st element of A - GREEN, is closest to 3rd element of B - RED.

2nd element of A - GREEN, is closest to 6th element of B - RED.

3rd element of A - GREEN, is closest to 4th element of B - RED.

4th element of A - GREEN, is closest to 2nd element of B - RED.

.

Subarna

if you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?

To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link

thanks in advance for time and attention

John BG

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