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Are long lines in shapefiles to be considered geodesics or straight lines in the 2D latlong space?

In various representations, such as shapefiles and kml, polygons are defined by their vertices. My question is what is the nature of the "line" which links two vertices? Is it a great circle arc? Is it whatever is a straight line in the current projection? If the latter, then the actual interior of the polygon in a function of the current projection, which seems undesirable.

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