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It occurred to me that latitude and longitude are not homologous in that the lines of latitude lie on parallel planes or slices through Earth, while lines of longitude are not parallel and meet at the poles, forming segments through Earth. Obviously the Earth's rotation gives us two points that make sense to use as intersection points, but it struck me that there could be potential advantages for using arbitrary points for intersection points for longitude, or for disregarding the poles for latitude. Not knowing the names of these I was not able to find any information online.

Is there a name for this difference, or names for the two types? Are there any coordinate systems that use parallel longitudes (or non-parallel latitudes) and what would the implications of this be?

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    This seems like a non-question to me. Can you explain what exact issue you want to solve by this?
    – Devdatta Tengshe
    May 13, 2015 at 8:15
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    I believe the question is quite clear, but you feel it does not fit the community guidelines. I refer to gis.stackexchange.com/help/dont-ask. Although this is not a "practical" question in that it is not meant to solve an exact issue, it is not a subjective question and it does meet the following requirements: "inspire answers that explain “why” and “how”; tend to have long, not short, answers; have a constructive, fair, and impartial tone" Please advise if you disagree and I will remove it.
    – 08Dc91wk
    May 13, 2015 at 10:55
  • This question isn't about an actual problem that you are having; It is primarily opinion-based, and likely to generate discussion rather than answers. Unfortunately these kinds of questions are not a good fit for Stackexchange.
    – Devdatta Tengshe
    May 13, 2015 at 12:03
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    How can this possibly be opinion based? I'm asking for the name for a coordinate-type whose lines intersect and the name for a coordinate-type whose lines do not intersect; I'm asking whether there is a coordinate system which has non-intersecting lines, or where both coordinates are intersecting. These are facts, not opinions!
    – 08Dc91wk
    May 13, 2015 at 14:06
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    The answer to your last question seems to be yes: earth-centered Cartesian coordinates will create three sets of level curves on a spheroid that look like latitudes. Other coordinates systems are possible, too, such as hyperbolic coordinates. One place to start your online investigation would be to learn about orthogonal coordinate systems. It is unclear, though, whether your question focuses on coordinate systems used for earth reference or concerns mathematical coordinate systems in general.
    – whuber
    May 13, 2015 at 15:52

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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.

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  • As a possible counterexample, an ECI frame does not measure latitude relative to the equatorial plane, but has advantages for some applications, especially for high-accuracy orbital motion calculations.
    – whuber
    May 13, 2015 at 15:57
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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.

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