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

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Sathiya 2024-4-26

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评论： Mathieu NOE 2024-4-29

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?

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Mathieu NOE 2024-4-26

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 2024-4-29

@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.

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Mathieu NOE 2024-4-26

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编辑：Mathieu NOE 2024-4-26

在 MATLAB Online 中打开

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

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Torsten 2024-4-27

在 MATLAB Online 中打开

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