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Map-making requires two distinct processes, first to produce the data -- latitude, longitude and elevation -- of the points to be mapped; and second to represent this data on a flat surface as a map.

Cartography nicely covers the science of creating the map from the data -- plotting points to give an accurate representation of desired properties, realising that at least one of shape, area, direction or distance, has to be sacrificed.

Is there an overall name for the initial gathering of data? Terms like "surveying" seem to me to be too specialised or limited to cover all the processes involved, and "topography" seems too broad.

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Surveying is the process of taking topographical measurements of latitude, longitude and elevation. It is also the process of marking out lines for engineering/construction designs of such things as roads, tunnels, fence lines, boundaries & foundations of buildings.

Surveying provides the topographical data that cartographers, engineers and other professionals use for their purposes.

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Thank you @Fred. Surveying and Topography do cover it but they both have wider meanings than the restricted use I am after.

Topometry is the closest official word I have found. Here is the definition from the Wiktionary:

Noun

topometry ‎(uncountable) (chiefly medicine) Any of various imaging or surveying techniques in which the three-dimensional positions of an array of points is recorded.

The combinatiom of "topo" for shape and "metry" for measurement seems to cover it nicely.

So, adding "geo" for the earth, I would like to coin the word Geotopometry to express the exact meaning I am after, although my spell checker doesn't like it, and probably not many people will know what I mean when I use it.

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