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SpatiaLite supports a remarkable number of different dimension models.

Interestingly, some of their values support a "measure" coordinate (XYM, XYZM). How would this measure-coordinate be used, and what is the correct term for searching to figure out how it is used?

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Found this in the FDO data concepts page:

A geometry is represented using geometric constructs either defined as lists of one or more XY or XYZ points or defined parametrically, for example, as a circular arc. While geometry typically is two- or three-dimensional, it may also contain the measurement dimension (M) to provide the basis for dynamic segments.

So M stands for measurement dimension.

Here's another useful definition from a mailing list:

m' is 'measure' an extra axis of information not associated with the cartesian x/y/z space. The most common use for 'measure' is actually for 'measurements', the adding of physically known measurements about a feature to the abstract 'feature' represented in x/y space in the GIS. For example, highway management systems often understand the location of facilities in terms of 'mile posts'. So, in addition to x/y coordinates, each vertex is also assigned a 'mile' measurement in 'm' which allows the system to accurately place facility information relative to the 'milepost' system. (Why not just use the x/y coordinates and calculate distances off of them? Because they are representational, the distances calculated from the x/y will not be the same as the actual milepost measurements.)

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It also can refer to a linear measure, as in a linear referencing system. – blah238 Nov 2 '12 at 4:40

Or... You can think of M being any kind of variable for a given location, like temperature, time,... which isn't directly interpreted as a location.

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