Can i get arc length out of polyval?

Hello, i would like to know if i can get the arc lenght out of a polyval.

I work on the following steps:

1) Have data (vector) x and y(x)

2) fit a function between both data -> here polyval

3) now i want to calcuculate the arc lenght

I got a bigger project, but a simple function with the three steps would be like:

% 1) based on
x = 1:10;
y = 2+x.^2.; 

% 2) fit
p = polyfit(x,y,3);

% create a function handle for the integral
f = @(arg) polyval(p,arg);

%now the function for the arc length
r = sqrt(1+(diff(f)).^2.);
b = integral(r,0,10);

%plot it
xpl = 1:0.01:10;
plot(x,y,'r+',xpl,f(xpl)); 

Error report i get:

/* Undefined function 'diff' for input arguments of type 'function_handle'.

Error in asdfasdf (line 12)

r = sqrt(1+(diff(f)).^2.); */

-> What can i do to solve the error report?

Answer 1

[Star Strider]

Try this (lightly edited version of your code):

dfdx = @(f,x) (f(x + 1E-8) - f(x)) ./ 1E-8;         % Simple Numeric Derivative
% 1) based on
x = 1:10;
y = 2+x.^2.; 
% 2) fit
p = polyfit(x,y,3);
% create a function handle for the integral
f = @(arg) polyval(p,arg);
%now the function for the arc length
r = @(x) sqrt(1+(dfdx(f,x)).^2.);
b = integral(r,0,10);

[Daniel Wurster]

Thanks a lot for the quick response! The code works!

Just for my own comprehension:

What happens in this line of code or why do i need it? dfdx = @(f,x) (f(x + 1E-8) - f(x)) ./ 1E-8;

[Star Strider]

As always, my pleasure!

That is a simple numerical differentiation function. It takes function handle ‘f’ and independent variable ‘x’ as arguments, and returns the numerical derivative of ‘f’ at ‘x’.

Numerical differentiation functions can get much more elaborate. See for example the Wikipedia article on Numerical differentiation (link).

[John D'Errico]

I might note that the line in question is just a numerical derivative. However, you can compute the analytical derivative simply enough, since it ia a polynomial.

polyder does that for you, already a part of MATLAB.