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From: Els on 21 May 2010 05:57
I plotted an ellipsoid [x,y,z]=ellipsoid (standard in Matlab)

Now I have a point C(x,y,z) which lays within this surface.
I am looking for the projection of C on the surface of the ellipsoid,called C', where the normal vector perpendicular to the surface is in line with the vector between C and C'.

Thanks in advance.
From: Torsten Hennig on 21 May 2010 02:49
> I plotted an ellipsoid [x,y,z]=ellipsoid (standard
> in Matlab)
>
> Now I have a point C(x,y,z) which lays within this
> surface.

But if C lies within the surface, its projection on
the surface is C itself. Or do you mean the point
opposite to C on the surface of the ellipsoid ?

Or do you mean something else, namely that C lies
within the _ellipsoid_, not within the _surface_ of
the ellipsoid ?


> I am looking for the projection of C on the surface
> of the ellipsoid,called C', where the normal vector
> perpendicular to the surface is in line with the
> vector between C and C'.
>
> Thanks in advance.

Best wishes
Torsten.
From: Els on 21 May 2010 07:22
I had to be more clear indeed, the point C lies within the ellipsoid, so not on the surface.

Point C is a point on the line between P1 and P2, a line which runs through the ellipsoid.

Point C' is the projection of C on the surface of the ellipsoid, along the normal vector.

Best wishes,
Els
From: Els on 21 May 2010 08:27
Where the normal vector is perpendicular to the Line from P1 to P2 and runs through C and C'.
From: Torsten Hennig on 21 May 2010 04:21
> I had to be more clear indeed, the point C lies
> within the ellipsoid, so not on the surface.
>
> Point C is a point on the line between P1 and P2, a
> line which runs through the ellipsoid.
>
> Point C' is the projection of C on the surface of the
> ellipsoid, along the normal vector.
>

I think there will be two projection points.
Which one does not matter ?

> Best wishes,
> Els
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