Finding length of curve created using 'fit' function

Question

Prabs 2014-5-23

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https://ww2.mathworks.cn/matlabcentral/answers/130871-finding-length-of-curve-created-using-fit-function

编辑： Star Strider 2014-5-24

So I've created a polynomial curve using the 'fit' function based on a range of coordinates. Is there any way of finding the length of the curve that has been created?

line1 = fit(middle_points(:,1),middle_points(:,2),'poly3');
plot(line1);

Thanks for the help in advance.

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Answer 1

Star Strider 2014-5-23

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https://ww2.mathworks.cn/matlabcentral/answers/130871-finding-length-of-curve-created-using-fit-function#answer_138049

编辑：Star Strider 2014-5-24

在 MATLAB Online 中打开

Using the techniques in Arc Length (and every calculus book I’ve seen), I would use the x and y line coordinates from the line you have already calculated, create in integrand using hypot and then trapz to do the integration:

p = [3 -5 -7 -11];                % Polynomial
x = linspace(0,5);                % Independent variable
y = polyval(p,x);                 % Calculate y-values
CLF = hypot(diff(x), diff(y));    % Calculate integrand from x,y derivatives
CL = trapz(CLF)                   % Integrate to calculate arc length

Using cumtrapz is also a possibility if you are interested in the intermediate values of the arc length.

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Answer 2

John D'Errico 2014-5-23

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I'll make some fake data.

x = linspace(-pi/2,pi/2,20);
y = sin(x);
% fit a quintic (degree 5) polynomial
P5 = polyfit(x,y,3);
% differentiate the polynomial
P5der = polyder(P5);
fun = @(x) sqrt(1 + polyval(P5der,x).^2);
integral(fun,-pi/2,pi/2)
ans =
     3.8224

Note that I've also got a function called arclength on the file exchange that will return the arc length, WITHOUT needing to go through the intermediate of a polynomial fit. That polynomial fit may introduce errors that are unacceptable.

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Prabs 2014-5-24

Hey John, I tried the arclength function that you've created. Doesnt seem to be working correctly for me. I've got x coordinates and y coordinates of the points that I've plotted, and I used 'fit' to plot the curve of best fit. Now in your arclength function, I'm using the x coordinates as px and the y coordinates as py. Are those the correct inputs I should be using? Correct me if I'm wrong please. Thanks

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