# How to divide a distance into some equal parts?

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### Answers (2)

Mohammad Sami
on 25 Jan 2020

Assuming the coordinates are variable p1, p2

% p1 = [x1 y1];

% p2 = [x2 y2];

midpoint = p1 + 0.5.* (p2-p1); % halfway point

% just change 0.5 to something else for other point along the line between p1 and p2

John D'Errico
on 25 Jan 2020

Edited: John D'Errico
on 25 Jan 2020

You have two points. Call they xy1 and xy2, where the xy are row vectors of length 2. For example...

xy1 = [-1,3];

xy2 = [2,5];

Now, you wish to create new points, that are equally spaced in distance along the line that connects the points. Lets say you want to divide the line segment into n equal parts. That means, including the two original points, you will have n+1 points as a result, with n-1 additional points created. I'll pick, for example, n=5 here. So there will be 5 segments of equal length, so 4 new points to be created in addition.

n = 5;

t = linspace(0,1,n+1)';

xy = (1-t)*xy1 + t*xy2;

plot(xy(:,1),xy(:,2),'b-o')

xy

xy =

-1 3

-0.4 3.4

0.2 3.8

0.8 4.2

1.4 4.6

2 5

As you can see, xy is an array with n+1 rows and 2 columns. The first and last rows are the original points, with the desired 4 new rows in between.

If you want to appreciate why it works so simply, note that I have taken a weighted linear combination of xy1 and xy2. Some would call this a convex linear combination, I suppose. The important thing to understand is that the weights, thus (1-t) and t respectively, sum to 1, and they are created using a tool like linspace, so they uniformly vary from 0 to 1.

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