How to find the distance between two points along a curve?
16 views (last 30 days)
Show older comments
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?
7 Comments
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
Answers (2)
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)
plot(X, Y, 'r.-',X(k1:k2), Y(k1:k2), 'db');
axis square
4 Comments
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)
length_of_curve = integral(fun,-pi/2,pi/2)
2*pi*R/2
See Also
Categories
Find more on Surface and Mesh Plots in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!