Resampling of xy-coordinates based on cumulative length (NOT time)

The cumulative lengths for a set of x1 and y1 coordinates ("waypointsOriginal" in the mat file attached) can be obtained using the function (function file attached as well):

[cumLengthWP,~,~] = CalcCurvature(waypointsOriginal(:,1:2));

However, I was wondering, for a vector cumLength (also can be found in the mat file) which has a different dimension, is there a way to find the corresponding x2 and y2 coordinates such that when I do

plot(x1,y1,'r',x2,y2,'b')

the two plots will be identical?

Thank you in advance for your effort and time. I will be glad to clarify any confusion regarding the question.

FYI: I am not looking for time resampling foor which I know we can use the resample command.

Answer 1

[J AI]

I have found a workaround for this which works for my particular application. I have basically used the polyfit function:

load('waypointsData.mat')

px = polyfit(cumLengthWP,waypointsOriginal(:,1),3); % using 3rd order polynomial
py = polyfit(cumLengthWP,waypointsOriginal(:,2),3); % using 3rd order polynomial

for i = 1:length(cumLength)
    waypoints_resampled(i,1) = px(1)*cumLength(i)^3 + px(2)*cumLength(i)^2 + px(3)*cumLength(i) + px(4); % x2
    waypoints_resampled(i,2) = py(1)*cumLength(i)^3 + py(2)*cumLength(i)^2 + py(3)*cumLength(i) + py(4); % y2
end

plot(waypoints_resampled(:,1),waypoints_resampled(:,2),'r',waypointsOriginal(:,1),waypointsOriginal(:,2),'b--')
legend('Resampled','Original')

I definitely look forward to hearing more efficient way(s). Thanks again!