Calculating the distance between points using vectorization.

Hi I have the matrix;

points = [2 5; 6 9; 7 8; 9 10; 6 10]

These points relate to a set of x and y coordinates. I want to calculate the distance between each of the points e.g. distance between 2 5 and 6 9 and 6 9 and 7 8 and so on until 6 10 is last point and the distance between it and 2 5. These points create an area such that I want to calculate the perimeter.

I know the distance formula is;

distance_between_two_points = sqrt((x2-x1)^2 + (y2-y1)^2)

So that the distance between 2 5 and 6 9 would be;

distance_between_two_points = sqrt((6-2)^2 + (9-5)^2)

How would I use vectorization to calculate the distance between all of the points. I also then need to calculate perimeter but I have figured I will use the sum function. Also how could I make it such that if the values for the points changed I would get the answer and so that if extra points were added this would be accounted for.

Thanks.

NOTE: No built in functions for perimeter or distance are to be used.

Answer 1

[Jan]

points = [2 5; 6 9; 7 8; 9 10; 6 10];
Diff   = [diff(points, 1); points(end, :)-points(1, :)];
Dist   = sqrt(sum(Diff .* Diff, 2));

[Giuseppe]

I like the simplicity of this. Thanks.

Answer 2

[Azzi Abdelmalek]

points = [2 5; 6 9; 7 8; 9 10; 6 10]
for k=1:size(points,1)-1
    p1=points(k,:);
    p2=points(k+1:end,:);
    a=bsxfun(@minus,p2,p1)
    d{k,1}=sqrt(sum(a.^2,2))
end
out=cell2mat(d)

Answer 3

[Mischa Kim]

Giuseppe, would this do?

 points = [2 5; 6 9; 7 8; 9 10; 6 10];
 b   = points - circshift(points,-1,1);
 len = sqrt(sum(b.*b,2))