NavList:

   

Reply

Doug Royer explains how to use angle bisectors to find
the MPP for a round of three or four (or more?) sights,
and wonders whether it's more or less precise than the
method that finds a circle that just touches each LOP.

For three sights, the three bisectors all meet at a point,
which is also the center of the circle that will just
touch each LOP.  Therefore, for three sights the methods
are equivalent.

To see this, imagine we have LOP's labeled A, B, and C,
with bisectors AB, BC, and CA.  Consider the point
where AB intersects BC.  Its distance from A is equal to
its distance from B, because it is on bisector AB.  And
its distance from B is equal to its distance from C,
because it is on bisector BC.  Therefore its distance
from A is equal to its distance from C, so it must also
be on bisector CA.  The only point where all three
distances are the same is the center of the circle that
is tangent to all three bisectors (as long as we are on
the proper side of each LOP, and both methods ensure that).

        -- Bill

   

Reply