Why doesn't STDifference between a LINESTRING and a POINT on the line string yield a MULTILINESTRING of the two pieces?

DECLARE @Route geography
SET @Route = geography::STLineFromText('LINESTRING(-0.175 51.0, -0.175 59.0)',4326)

DECLARE @Route2 geography
SET @Route2 = @Route.STDifference(geography::STPointFromText('POINT(-0.175 52)', 4326))

SELECT @Route2

Why does @Route2 evaluate to LINESTRING (-0.175 59, -0.175 51) instead of a MULTILINESTRING consisting of the line segments on either side o开发者_C百科f the point?

The only way I have been able to do this is by creating a second LINESTRING with very small length (0.0001) and use this to subtract. It works, but it isn't very elegant.

It appears the issue arises from the fact that the engine doesn't have a way of representing the following: (I'm using 1D syntax to make it simpler to understand.)

[1, 3] - 2 = [1, 2) U (2, 3]

Instead, it does [1, 3] - 2 = [1, 2] U [2, 3] and then simplifies this back to [1, 3].

The solution in this case is to either do the calculation manually, or, if your application will allow for it, add a very small buffer around the subtracted point to make it occupy space. In the example from the question, I do:

DECLARE @Route geography

SET @Route = geography::STLineFromText('LINESTRING(-0.175 51.0, -0.175 59.0)',4326)

DECLARE @Route2 geography
SET @Route2 = @Route.STDifference(geography::STPointFromText('POINT(-0.175 52)', 4326).STBuffer(0.01))

SELECT @Route2

This 0.01 meter buffer is irrelevant in my application but it solves the problem -- I now get a MULTILINESTRING with two pieces. The only gotcha is that they don't intersect, but I suppose this is to be expected.