"True" distance vs. horizontal distance

[LDWhite68]

For tracks that have significant elevation gain/loss, it would be very nice in Profile to have the option of either determining distances purely horizontally (as is normally done) or the hypotenuse (spline, if you want to get fancier) of the grades. Of course, there is always the issue of filtering spurious ups/downs, but you are already providing some options for users to control those in your calculations of climb, descent, effort, etc. Even for moderately steep tracks this option could help to alleviate discrepancies with wheeled distance and  to better represent true effort.

[Heath288]

For tracks that have significant elevation gain/loss, it would be very nice in Profile to have the option of either determining distances purely horizontally (as is normally done) or the hypotenuse (spline, if you want to get fancier) of the grades.... Even for moderately steep tracks this option could help to alleviate discrepancies with wheeled distance and  to better represent true effort.

Referring to the above post, I am wondering how determining distances using a spline, that is, a polynomial (parametric) curve, would be better than current configurations already accounting for climb, descent, etc.  Is it a matter of precision?

With purely horizontal distance determinations, how is elevation dealt with?