From: horst.kraemer@snafu.de (Horst Kraemer)
Subject: Re: Calculating position from angles
Date: Sat, 20 Mar 1999 09:12:32 GMT
Newsgroups: sci.math
On Thu, 18 Mar 1999 13:46:52 +0100, Maurice van der Pot
wrote:
> Horst Kraemer wrote:
> > On Wed, 10 Mar 1999 16:59:18 +0100, Maurice van der Pot
> > wrote:
> > > I have three points at known coordinates and another point X of which
> > > don't know the position. I do know the angles of the three known points
> > > as seen from the position of X, but these angles are relative to
> > > eachother.
> > > How can I calculate the position of X?
> > In the plane the problem would be overdetermined.
> It would?? Would you care to explain to me why it is overdetermined?
Assume a triangle ABC and the angles c=angle(AXB) and a=angle(BXC)
given.
The locus of all points X such that angle(AXB)=c is a circular segment
limited by A and B (THALES) or a double circular segment in case
c=pi/2. The same is true for BXC. The intersection of these segments
adjacent at B is either no point or one point or a circular segment (B
is excluded).
The third angle would be either redundant or contradictory except for
one single degenerate case.
Regards
Horst