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Radius of a Non-Uniform Sphereoid/Ellipsoid at a Given Surface Point?

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Hello! I have spent a few days mulling over this problem, but have made little progress. Unfortunately, spherical trigonometry is not my strong point. I hope you can help! What I require is a function that given an input vector, will return the radius of a sphereoid at the point where the vector would intercept the spheroid's surface, assuming assuming that the given vector extends from the sphereoid's center. ![alt text][1] [1]: /storage/temp/83825-example.png I've explored numerous equations, but most only handle elliptical radii (and I struggle to combine the third direction), or give me results that fluctuate as the input vector is modified. Any assistance is greatly appreciated! :) **Thank you and be well!** -S.

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