The Sphere is Finite

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Hi Folks,

The title of this post states the obvious: the area of a sphere is finite.  We even have a nice formula for it, 4πr2.  The same is true for an ellipsoid, which is just a sat-upon sphere, although computing the area gets more complicated.

But the plane is infinite.  If we combine this with the fact that the OGC (implicitly) assumes that all geometry objects have a finite area, then any OGC-valid geometry has exactly one reasonable interpretation.  If I ask you to fill in this polygon:

image

You have only one reasonable choice:

image

Not:

image

You can’t reasonably give me the latter one, since it would have an infinite area.

But since the sphere already has a finite area, a ring like this on the sphere just cuts it into two finite areas.  So if I ask you to fill in this box:

image

You have a problem, since you don’t know for sure what I mean: do I want you to fill the portion containing the United States, or the part containing the rest of the world?  The request is underspecified.

We fix this by using orientation, which I’ll discuss next time.

Cheers,
-Isaac