Perimeter of an ellipse

A method for computing the perimeter of an ellipse.

A method for computing the perimeter of an ellipse.

Essentially, the problem of calculating the distance from the equator to the pole is to calculate the quadrants and the perimeter of an ellipse.

There is no unique solution to this, so here are several formulas that can be used.

Two solutions with infinite series are the most accurate.

Vectorized.

Version: 1.00 13 Oct 22

Input: a - ellipse major semi-axis [meter]

b - ellipse minor semi-axis [meter]

Output: p - ellipse perimeter [meter]

Reference: Kawase, Kazushige. "A general formula for calculating meridian arc length and its application to coordinate conversion in the Gauss-Krüger projection." Bulletin of the Geospatial Information Authority of Japan 59 (2011): 1-13. https://yadda.icm.edu.pl/baztech/element/bwmeta1.element.baztech-3b526150-d9d6-4f81-a65a-b1bce37472ab/c/Weintrit.pdf

Keywords: geometric geodesy, perimeter ellipse, map projection, coordinate conversions

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