# How to find the distance between two points along a curve?

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Sathiya on 26 Apr 2024
Commented: Mathieu NOE on 29 Apr 2024
I have a set of generated X and Y axis data, which have given a curved line. Now, I need to find the distance between two specified points along the curve, not the straight shortest distance between two points but along the curve path. Can someone help me finding this numerically?
Mathieu NOE on 26 Apr 2024
dr represents only the increment of arc length (quite constant in this example)
now you need to do a sum of them - see my answer
Sathiya on 29 Apr 2024
@Sam Chak, dr here gives the shortest distance (displacement) between two points. For eg. lets say, I need the distance along the curve from 1st point and 50th point, this formula finds the straight distance between data points, not along the curve.

Mathieu NOE on 26 Apr 2024
Edited: Mathieu NOE on 26 Apr 2024
hello
try this
th = linspace(-pi/2, pi/2, 100);
R = 200;
X = R * sin(th) ; % X-coordinates
Y = R * cos(th) ; % Y-coordinates
dx = diff(X);
dy = diff(Y);
ds = sqrt(dx.^2+dy.^2); % increment of arc length
s = cumsum(ds); % integration => total arc length
s = [0 s]; % add first point : arc length = 0
% compute arc length between two points (defined by index position)
k1 = 25;
k2 = 59;
d = s(k2) - s(k1)
d = 215.7771
plot(X, Y, 'r.-',X(k1:k2), Y(k1:k2), 'db');
axis square
Torsten on 27 Apr 2024
If you have an explicit equation of your curve, you can use the usual formula for arclength:
R = 200;
fun = @(t)sqrt((R*cos(t)).^2+(R*(-sin(t))).^2)
fun = function_handle with value:
@(t)sqrt((R*cos(t)).^2+(R*(-sin(t))).^2)
length_of_curve = integral(fun,-pi/2,pi/2)
length_of_curve = 628.3185
2*pi*R/2
ans = 628.3185
Sathiya on 29 Apr 2024
Yes, but I donot have a curve fitted equation for my curve.

Walter Roberson on 27 Apr 2024
Sathiya on 29 Apr 2024
@Mathieu NOE, understood. Now it is perfect to use then. Thanks Mathieu and all others who spent their time for my problem.
Mathieu NOE on 29 Apr 2024
my pleasure !!

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