Converting a geocentric latitude to a geodetic latitude

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I'm working with a 3D model of the earth (WGS84).

The input to my problem is a geocentric lat-long. Is there an efficient way to convert this to a geodetic lat-long?

My initial attempt to solve this seems to work correctly: First, convert the geocentric lat-long back to it's corresponding point in 3D space. Then, feed that XYZ into a library function that returns the geodetic latitude.

It's straightforward, but the conversion from XYZ to geodetic lat-long is not cheap because it uses some fixed number of iterations to come up with a reasonably accurate result... I am looking for something that runs faster.

Given the geocentric latitude, is there a more efficient route I can take to get the corresponding geodetic latitude?



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