Equally spaced points along a nonlinear path

I have a path linear by parts that I need to equally divide with points. How do I do that?

Answer 1

[Manikanta Aditya]

Hi @Kacper

To equally divide a path that is linear by parts, you can follow these steps:

Calculate the total length of the path and determine the spacing between the points and place the points along the path.

Check the following code as a example for your understanding:

% Define the path as a list of points
path = [0, 0; 1, 1; 2, 0; 3, 1];

% Calculate the total length of the path
lengths = sqrt(sum(diff(path).^2, 2));
total_length = sum(lengths);

% Display the total length of the path
disp(['Total length of the path: ', num2str(total_length)])

Total length of the path: 4.2426

% Number of divisions
num_divisions = 10;

% Calculate the spacing
spacing = total_length / num_divisions;

% Display the spacing
disp(['Spacing between points: ', num2str(spacing)])

Spacing between points: 0.42426

% Place the points
points = [];
current_length = 0;
for i = 1:size(path, 1)-1
    while current_length < lengths(i)
        points = [points; path(i, :) + (path(i+1, :) - path(i, :)) * current_length / lengths(i)];
        current_length = current_length + spacing;
    end
end
points = [points; path(end, :)];

% Display the points
disp('Equally spaced points along the path:')

Equally spaced points along the path:

disp(points)

         0         0
    0.3000    0.3000
    0.6000    0.6000
    0.9000    0.9000
    3.0000    1.0000

I hope this answers your question.

[Kacper]

Thanks. I thought there was a neat function to do it for me and I just coudn't find it, but as long as it works.

[Manikanta Aditya]

Thanks!

Answer 2

[John D'Errico]

Simpler yet, just download my interparc from the file exchange. It allows you to do the operation in a variety of ways, using several variations of spline interpolant, or assuming piecewise linear segments.

https://www.mathworks.com/matlabcentral/fileexchange/34874-interparc?s_tid=srchtitle

It does all the work for you, and it is free.

x = randn(6,1);
y = randn(6,1);
% 500 points, equally spaced along the curve in arclength
Pspline = interparc(500,x,y,'spline');
plot(x,y,'ro',Pspline(:,1),Pspline(:,2),'-')