Finding Minimum Distance between two points

Hi, I am trying to make a function to find minimum distance between my random points and a point (0,0) and plot the distance as a line crossing from the (0,0) to the one of the closest rand pt.

    A=rand(2,10);
    x1=A(1,:);
    y1=A(2,:);
    scatter(x1,y1);
    [D I] = pdist2(x1,y1,'euclidean')

I have been trying to use 'pdist2' with 'euclidean' function however, it is not working well. :O

[KSSV]

Dear friend..there will be only fixed distance between two points. Think of your question once.

Answer 1

[Image Analyst]

You don't need pdist2() because you aren't asking for the distance of every point to every other point. You're only asking for the distance from every point to the single point at (0, 0). So you can simply use sqrt()! Try this:

% Create 10 random points.
xy = rand(10, 2);
x = xy(:, 1);
y = xy(:, 2);
plot(x, y, 'bo', 'MarkerSize', 10);
grid on;
% Compute the distance of each of those points from (0, 0)
distances = sqrt(xy(: , 1) .^ 2 + xy(:, 2) .^ 2)
% Find the closest one.
[minDistance, indexOfMin] = min(distances);
closestX = x(indexOfMin);
closestY = y(indexOfMin);
% Mark it with red *
hold on; % Don't blow away existing points.
plot(closestX, closestY, 'r*', 'MarkerSize', 8, 'LineWidth', 2);
% Draw a line from the closest point to (0, 0)
line([0, closestX], [0, closestY], 'LineWidth', 2, 'Color', 'r');

[Mojtaba Houballah]

Hello, this is a great code. However I am trying to do the same thing at each point. for example i want to start at (0,0) and reach all the points by using the minimum distance at each point, can this code be modeified to do that?, can you display it?

Many thanks in advance

Matlab beginner

[Image Analyst]

Yes you can. Just put into a loop where you find the distance from each point to the remaining points in the set. After you find the closest point, remove that point from the set and do the next iteration of the loop. Very simple.

[Paul Simon]

Can you show the code for it?

[Image Analyst]

Paul, did you try it yourself using my directions above? I'm sure you did, and you probably got something like the code below:

% Program to make a set of random points and travel from (0,0) to
% the closest other remaining point.
clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
imtool close all;  % Close all imtool figures if you have the Image Processing Toolbox.
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 14;

% Create 10 random points.
numPoints = 10;
xy = rand(numPoints, 2);
x = xy(:, 1);
y = xy(:, 2);
plot(x, y, 'bo', 'MarkerSize', 10);
grid on;

% First do it once to get the first point.
% Compute the distance of each of those points from (0, 0)
distances = sqrt(xy(: , 1) .^ 2 + xy(:, 2) .^ 2)
% Find the closest one.
[minDistance, indexOfMin] = min(distances);
closestX = x(indexOfMin);
closestY = y(indexOfMin);
% Mark it with red *
hold on; % Don't blow away existing points.
plot(closestX, closestY, 'r*', 'MarkerSize', 8, 'LineWidth', 2);
% Draw a line from the closest point to (0, 0)
line([0, closestX], [0, closestY], 'LineWidth', 2, 'Color', 'r');

% Now do it for the remaining points.
% Go from that point to the closest of the remaining other points.
alreadyUsed = false(1, numPoints);
counter = 2;
maxIterations = numPoints; % Failsafe
alreadyUsed(indexOfMin) = true; % Mark that point as having been used already.
while sum(alreadyUsed) <= (numPoints - 1) && (counter <= maxIterations)
	% Compute the distance of each of those points from the last point.
	lastx = x(indexOfMin(counter - 1));
	lasty = y(indexOfMin(counter - 1));
	% Set the already used distances to infinity so we won't consider them.
	x(alreadyUsed) = inf;
	% Compute distances from last point to all other points.
	distances = sqrt((x - lastx) .^ 2 + (y - lasty) .^ 2);
	[minDistance, indexOfMin(counter)] = min(distances);
	% Find out the x and y of the closest point.
	closestX = x(indexOfMin(counter));
	closestY = y(indexOfMin(counter));
	% Draw a line from the closest point to (0, 0)
	line([lastx, closestX], [lasty, closestY], 'LineWidth', 2, 'Color', 'r');
	% Mark this point as having already been used.
	alreadyUsed(indexOfMin(counter)) = true;
	counter = counter + 1;
end

Note that this will not always or necessarily give you the shortest path length, like solving the traveling salesman problem will.