# Intersection and area calculations in geographic vs. projected coordinates

I think one should do intersection calculations when layers are in the same coordinate system, and one should do area calculations in the appropriate projected coordinate system.

The order matters, but is one preferred? In my system, I get slightly different areas if I

1) Perform intersection of two layers that are in the same geographic coordinate systems, project the resulting intersection to a projected coordinate system, and then calculate areas, or

2) Project two layers to the same projected coordinate system, intersect them, and then calculate areas of the resulting intersection.

Without getting into details of my specific situation, I wonder if one of these approaches is theoretically preferable? I assume the 2nd would be, but I can't articulate why that would be.

(I assume terms are standard, but this is the intersection I'm looking for: http://wiki.gis.com/wiki/index.php/Intersect)

• There are sufficient imponderables to make this an opinion-based question. Among the variables: The projections involved, the coordinate envelopes of the data the vertex accuracy and precision, whether densification is used in the reprojection process,... Commented Jan 4, 2019 at 21:01
• If performance is a consideration, and the intersection results in a smaller dataset, I would think option 1 would be preferable. Commented Jan 4, 2019 at 21:37
• It comes down to what your vector representation of polygonal features really means. Typically, successive vertices are connected by line segments in the coordinates, treating them as elements of a Euclidean space. That might be fine for representing a feature when it is originally digitized, but when you reproject it, those line segments ought to be curved arcs--yet the calculations in the reprojected system will treat them as being straight in the new coordinate system. That's where the differences arise. One rule, then, is do the intersection calculations in the original coordinates. Commented Jan 4, 2019 at 23:21
• Maybe you do need to go into more details. Why would you not choose option (0) Perform both the intersection and area calculation in the same geographic coord system? Commented Jan 8, 2019 at 19:47
• I want to make it clear that it's almost always best to perform the area calculations using an equal-area projection (or using calculations suitable for geographic coordinates). See gis.stackexchange.com/questions/20054. Commented Jan 10, 2019 at 23:42