Function kummer_elliptic_perimeter

fn kummer_elliptic_perimeter(radii: Vec2) -> f64

Calculates circumference C of an ellipse with radii (x, y) as the infinite series

C = pi (x+y) * ∑ binom(1/2, n)^2 * h^n from n = 0 to inf with h = (x - y)^2 / (x + y)^2 and binom(.,.) the binomial coefficient

as described by Kummer (“Über die Hypergeometrische Reihe”, 1837) and rediscovered by Linderholm and Segal (“An Overlooked Series for the Elliptic Perimeter”, 1995).

The series converges very quickly for ellipses with only moderate eccentricity (h not close to 1).

The series is truncated to the sixth power, meaning a lower bound on the true value is returned. Adding the value of kummer_elliptic_perimeter_range to the value returned by this function calculates an upper bound on the true value.