Since the force of gravity is everywhere perpendicular to the
geoid (not to the ellipsoid), our measurements (land-based or satellite-based) are
influenced by the geoid. A slight vertical deviation of the measuring instrument may
create differences of hundreds of meters when reporting a position from the geoid
to the ellipsoid. The geomatics science dealing with the geoid and the ellipsoid is
called physical geodesy; it provides the basis for all measurements (see Hofmann-
Wellenhof & Moritz, 2005).
Once we know the difference between the geoid and the ellipsoid, we must project
the measured position to a flat surface such as a paper map or a computer display.
This cannot be done without distortion, either of angles, areas, or more typically,
of both at the same time. This has an immediate impact on the shapes of objects,
04 B?©dard, Rivest, & Proulx
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lengths, perimeters, areas, and positions, for example. To control these distortions,
we use different map projections having different mathematical properties. Thus,
from a unique position and shape on an ellipsoid, we may obtain different shapes
and positions on different maps. These differences may be up to hundreds of meters
in some cases.
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