coordinate system - Difference between latitude and longitude - Geographic Information Systems Stack Exchange
What is the difference between Latitude and Longitude?
What is the correct definition of latitude and longitude?
Eli5 Why is latitude from -90° to 90° but longitude from -180° to 180?
What is longitude?
What is the distance per degree of longitude?
What is latitude?
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Because the Earth is not a sphere, measuring the latitude from the equator plane is the only way to have circular parallels. Therefore I think that any geographic coordinate system that would not use the equator plane as a reference would have more disadvantages than advantages.
If you need a specific coordinate system, I would therefore rather suggest that you use a projected coordinate system.
Some people use rotated spheres as a basis for further mapping. I turned up a blog post about the capabilities of D3 here with has examples and here's another page about the some of the math behind it, although from a graphics perspective.
For earth solutions, usually a sphere is rotated rather than an ellipsoid because of the simpler mathematics.
Not what you're looking for but I've also seen papers discussing use of a triaxial ellipsoid.