Finding length of curve created using 'fit' function

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.

Answer 1

[Star Strider]

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.

Answer 2

[John D'Errico]

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.

[Prabs]

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