[vanderZwan]

True, but it can be decomposed into different steps at least (trying to find less-wrong projections, effective 2D triangulation).

The complexity of working with 3D spaces typically feels worse and harder to untangle to me.

It's like.. I dunno, having two jugglers juggling ten balls each and passing them between each other, or one being asked to juggle twenty[0]. But that is a personal thing - it may also just be sign I'm bad at maths in 3D space.

[0] http://www.juggling.org/papers/limits/

[contravariant]

In the end it's a trade-off between having an extra dimension to deal with, or having to deal with a non-euclidean space. Between the two it's nearly always easier to go for the higher dimensional euclidean one, but exceptions might exist.

Of course if you want an approximate solution then projecting the sphere to 2D might be an option, but glueing together the different projections required could be a bit of a hassle.