Give a reference of a text,pdf,anything , where geodesic passing by a certain point is calculated.

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I'm looking for a text , pdf , any reference , where it calculated in details geodesic passing by a certain point , for example on a surface of revolution.

Something in the type , a geodesic passing by (0,0,0) can be found doing ... I'd like the expression to be given explicitely and not "left to the reader".

I'm trying to verify that i understand how to do it but i need to enter in calcul depths to check it.