[R-sig-Geo] Location polygon from triangulation data

[Barry Rowlingson]

On Wed, Jul 18, 2012 at 7:24 PM, Robby Marrotte <robbymarrotte at gmail.com> wrote:
> Hello everyone,
>
> I have data where for every tracked individual we have 3 radio-telemetry xy
> locations with an orientation (0-360 deg). What I want to do is create
> triangles which represent the possible locations of each individual. It
> seems quite simple, but I haven`t found a script which does this yet. I
> tried Hawth`s tools but it doesn't have anything like this.

Hawth? Who that?

 I'm no expert in this, but I've had a good search for anything that
might do this in R, but can't find anything either. Found some
literature (Russell V. Lenth appears to be quite the man for this) and
some of the techniques in "On Finding The Source Of A Signal" in
Technometrics 1981 by him should be easy to implement in R if anyone
has a spare day...

 The naive method of intersecting the lines should be doable with
high-school geometry, but Lenth warns:

"""
A simple method for estimating (x, y) would be to use the
componentwise average of the n(n - 1)/2 bearing intersections
(assuming the observation points are distinct and that each bearing
intersects all other bearings). However, these points of intersection
are not stochastically independent. Moreover, their error structures
depend on the distances from the corresponding observation points as
well as the angle of intersection. Thus it would be difficult to
determine the statistical properties of such an estimator."""

Barry