GEOG 862
GPS and GNSS for Geospatial Professionals

Distortion

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Distortion, difficulty matching edges
Edge Matching Difficulty
Source: GPS for Land Surveyors

Here is a bit more on that idea. The design of local tangent plane projections must accommodate some awkward facts. For example, while it would be possible to imagine mapping a considerable portion of the earth using a large number of small individual planes, like facets of a gem, it is seldom done because when these planes are brought together they cannot be edge-matched accurately. They cannot be joined properly along their borders. And the problem is unavoidable because the planes, tangent at their centers, inevitably depart more and more from the reference ellipsoid at their edges, and the greater the distance between the ellipsoidal surface and the surface of the map on which it is represented, the greater the distortion on the resulting flat map. This is true of all methods of map projection. Therefore, one is faced with the daunting task of joining together a mosaic of individual maps along their edges where the accuracy of the representation is at its worst, and even if one could overcome the problem by making the distortion, however large, the same on two adjoining maps, another difficulty would remain. Typically, each of these planes has a unique coordinate system. The orientation of the axes, the scale, and the rotation of each one of these individual local systems will not be the same as those elements of its neighbor’s coordinate system. Subsequently, there are gaps and overlaps between adjacent maps, and their attendant coordinate systems, because there is no common reference system. Even if it was possible to accommodate, let's say, a GIS coordinate system with a local coordinate system, it wouldn't be terribly desirable because of the problems of scale and distortion as mentioned but also all problems of direction. Obviously, north changes as one goes from meridian to meridian around the earth. This must be accommodated by any plane coordinate system. So, the idea of a self-consistent, local map projection based on small, flat planes tangent to the earth, or tangent to the reference ellipsoid, is convenient, but only for small projects that have no need to be related to adjoining work. In that case there is no need to venture outside the bounds of a particular local system, it can be entirely adequate. But if a significant area needs coverage, another strategy is needed.