Re: fitting data points to local spheres

"John D'Errico" <woodchips@xxxxxxxxxxxxxxxx> wrote in
message <fpf7md$roa$1@xxxxxxxxxxxxxxxxxx>...
"Thomas Uhrmann" <Thomas.Uhrmann@xxxxxxxxx> wrote in
message
<fpf6d7$c7l$1@xxxxxxxxxxxxxxxxxx>...
Hi guys,
I have a complicated free-form surface (f(x,y)) given
on
discrete data points. My goal is to fit spheres to each
data point, maybe based on derivatives at the point.

Does anybody has experience with fitting points to a
sphere
and can make suggestions on how to go about it?


I'm confused. How do you intend to fit a
sphere to single points? Even if you knew
the local surface gradient at that point,
this is insufficient information to determine
a sphere.

Do you claim to know the local curvature(s)?
Knowledge of the local radius of curvature
plus the gradient, this would be sufficient
to determine a sphere that lies tangent to
your surface, EXCEPT that you won't have a
single radius of curvature. A general complex
surface will probably have different curvatures
in each direction. In effect, this will determine
an ellipsoid that lies tangent to the surface.

John


Dear John,
Thanks for your response. I have the first and second
derivative at each data point at my disposal.
Initially I thought to sample very high and to choose
tiny patches, for which the surface approximation with
a sphere would be not too bad.

For the purpose what I have it would be even better to
use ellipsoids instead of spheres as you suggested. I
somehow have to fit locally ellipsoids with the known
curvatures (in x and y) at each of the data points.

Best Regards,
Tobias
.

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