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Thread Subject:
Geometric reconstruction of axes

Subject: Geometric reconstruction of axes

From: Johannes Korsawe

Date: 1 Oct, 2007 13:21:57

Message: 1 of 2

Hi out there,

i have a twofold question. Let us consider three points in
space, e.g. px, py and pz.

Now i am looking for a fourth point po (point_origin), s.t.
the vectors (px-po, py-po, pz-po) form a orthogonal right-
hand-system.

First aspect: Is there a unique or finite number of
solutions? How can they be classified?

Second aspect: How do i calculate a solution to this task
in MATLAB?

Best regards,
Johannes Korsawe

Subject: Geometric reconstruction of axes

From: Michael Garrity

Date: 2 Oct, 2007 14:30:28

Message: 2 of 2

"Johannes Korsawe" <johannes.korsawe.nospam@volkswagen.de> wrote in message news:fdqs9l$nj9$1@fred.mathworks.com...
> Hi out there,
>
> i have a twofold question. Let us consider three points in
> space, e.g. px, py and pz.
>
> Now i am looking for a fourth point po (point_origin), s.t.
> the vectors (px-po, py-po, pz-po) form a orthogonal right-
> hand-system.
>
> First aspect: Is there a unique or finite number of
> solutions? How can they be classified?
>
> Second aspect: How do i calculate a solution to this task
> in MATLAB?
>
> Best regards,
> Johannes Korsawe
>

I believe that there are an infinite number of such
points and that they all lie on the surface of the sphere
that passes through the three points and whose
center is in the plane of the three points. I think that
it follows from Thale's theorem. Can't give you a
proof off the top of my head though.

    -MPG-

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