This is a follow-up question to my previous one, Can you suggest some well-written introductory texts about coordinate system projections?
Let's assume I'm working with the CH1903 map projection, which for all I know is conformal, but not equidistant. Meaning, angles (shape) have been preserved, but not areas, distances, or scale. (At least these have not been preserved exactly). So far so good.
I'm wondering what kind of calculation ArcGIS performs when I now want to calculate the distance between two points. In ArcObjects, I could use the
IProximityOperator interface as follows:
IPoint a = ..., b = ...; double distance = ((IProximityOperator)a).ReturnDistance(b);
Question: When I'm working with a reference system that does not accurately preserve distances, what would ArcGIS do when I query it for the distance between two points (as shown above)?
Does it simply do some Pythagorean maths (a2 + b2 = c2) to get the distance, meaning the returned distance will only be as accurate as the projection allows?
Or will it do something more complicated, like some form of re-projection, to get a more accurate distance?
(The same question, but more generally: Once that geometries have been projected, does ArcGIS perform all calculations simply in Euclidean space, or does the used map projection still influence calculations of distances, angles, areas, etc.?)