Calculate ellipse part arc lengths using ellipse parameter (theta1,theta2,a,b,​tolerance)

Calculates elliptic arc/ parts of ellipse lengths using infinite sum method given the ellipse

Calculates the arclength of elliptic curve starts from theta1 and ends at theta2, using infinite series approach given in the reference at end of description
NOTE:
* if theta1 > theta2 arc length will be negative
* maximum number of iterations is set as 100, change from code if necessary
Inputs:
* theta1 and theta2 are defined such that;
defined in ellipse parameter such that for a point (x,y) on ellipse:
x = a*cos(theta1)
y = b*sin(theta2)
* a,b are semimajor and semiminor axes of ellipse, however function
supports entering them as vice versa
* tolerance sets the accuracy of calculation
Outputs:
* arcLen: arclength in units of the input a and b
* precision: difference of ellipse length with one higher iteration calculation
* n: number of iterations
referenced from:
http://pages.pacificcoast.net/~cazelais/250a/ellipse-length.pdf
example:
[arcLen, precision, n] = ellipseArcLength(0, 2*pi, 5,4,1e-5)
Author: Mehmet Burak Ekinci
Mail: [e-mail]