Geography Reference
In-Depth Information
Tissot Indicatrix
A visual way to examine projection distortions was developed by the mathe-
matician Nicholas Tissot in the 19th century. The concept is simply that any
small circle on a spheroid or ellipsoid, when projected to the same point on
the f lat map, will show the distortion created by the map projection through
the projected shape and size of the circle. When the circles are plotted at var-
ious points on a map, they allow for a visual comparison of distortion (Fig-
ure 4.11). You should note that the changed shapes and sizes of the
indicatrix refer to individual points and cannot be used in evaluating distor-
tion of continents or water bodies.
The indicatrix has two characteristics that can used to evaluate distor-
tion. The first is the two radii, semimajor (
a
) and semiminor (
b
), which are
perpendicular to each other. The semimajor axis is aligned in the direction
of the maximum SF and the semiminor axis is aligned in the direction of the
minimum SF. The second is the angle between two lines
l
and
m
that inter-
sect the center of the indicatrix circle, but are turned 45
in respect to the
center, if there is no angular distortion. The distances of the semimajor and
the semiminor axes, respectfully, indicate the scale factor distortion along
each axis. The angle between two lines
l
and
m
indicates the amount of angu-
lar distortion. For example, a circle where
l
and
m
intersect at right angles
indicates no distortion. If the shape of the circle is distorted into an ellipse,
but the area is the same as the circle and the two lines
l
and
m
intersect at
angles greater or less than 90
°
°
, there is no areal distortion, but there is angu-
lar distortion.
A map showing multiple Tissot indicatrix circles is a valuable aid to
determine projection distortion. The revealed patterns of distortion help in
choosing the appropriate projection for a particular area.
Combining Geographic Information from Different Projections
The large number of projections available for the same area means that
great care must be taken when working with geographic information from
Tissot's indicatrix circle indicating no
areal and no angular distortion.
Search WWH ::
Custom Search