Floating Radius Calculator
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Given three latitude/longitude coordinate pairs, this calculator finds the radius and
center of the circle which passes through these points. Stated differently, one obtains
the radius and center of the circle that circumscribes the spherical triangle defined by the
three points.
Those interested in the actual algorithm may wish to
View the Source Code.
In the context of county highpointing this type of calculation corresponds to finding a
"floating glob radius" - the largest circle that fits entirely inside a glob of contiguous counties.
The three points must be carefully chosen such that the resulting circle does not
contain any unclimbed county, or portion thereof, that lies in the circle's interior.
Some trial and error may be needed. However it will almost certainly be the case
that at most several points need be tested.
Note: To find if a fourth glob-limiting point lies within the computed circle,
use the distance calculator to find
the distance from the point to the computed center.
If this distance is less than the computed radius then the chosen triple of points
do not serve to define the floating glob radius ... and another triple must be sought
to that end.
In general you should be careful to select at least one of the three points to lie
across the glob from at least one of the remaining two points. If this is not done
the resulting circle may not be confined to the glob's interior. This is a case
of GIGO: "Garbage in - Garbage out".
Allowed input formats include decimal degrees; (integer) degrees plus decimal minutes;
(integer) degrees plus (integer) minutes plus seconds. The degree symbol (°)
may serve to separate the degree from arcminute values. The arcminute symbol (')
may serve to separate the arcminute from arcsecond values. The arcsecond symbol (")
may be placed after the arcsecond value.
As an alternative to these standard symbols, the colon symbol (:) may serve as a separator
between degree, arcminute and arcsecond values as deg : min : sec . The colon symbol (:)
and degree symbol (°) cannot be simultaneously present in-between the degree and
arcminute fields. The colon symbol and arcminute symbol (') cannot be simultanesouly
present in-between the arcminute and arcsecond fields: (N 45 : 23 ' 50.2 ") is allowed
whereas (N 45 : 23 :' 50.2) is not.
Whitespace is ignored throughout such that you may space input fields at you please.
To specify hemispheres either use a "-" sign for South and West OR use "S" and "W"
(case insensitive) either in front of OR after the degree through arcsecond values.
North and East are signified by either specifying nothing; a "+" sign in front of the
degree through arcsecond values; or by "N" or "E" (case insensitive) either before OR
after the degree through arcsecond values.
You must specify "West" with either a "-" sign or a "W" or a "w".
If this is not done then strange, amusing (and incorrect) results will appear.