Re: Best Fit Plane - Parallel to xyplane!

p4pradeep@xxxxxxxxxxx wrote:
Ok, I agree we have in that case only four points.

What about integration? For example, if we were in 2D, then we can do
an area integration. How will we do the integration here in this case
in 3D so that S of all the z coordinates = 0 (tends to zero). Some
kind of volumetric integration (I dont know how this term is called)?!?!

I'm not sure what you mean by "so that S of all the z coordinates = 0
(tends to zero)".

Perhaps you want to make the volume enclosed between the plane and the
surface, and presumably within some x-y region, equal to zero -
counting volume above the plane as positive and below the plane as
negative?

The question is: can you calculate the points on this surface on
demand? Given an x-coordinate and a y-coordinate can you calculate the
corresponding z? If so then you can space the points on a regular
square x-y grid, and then just average the z-coordinates, as has been
suggested before. Provided the grid is reasonably fine, this will
automatically zero the volume (as defined above) to a reasonable degree
of accuracy I think (hope that's right!)

Or do you just have the points you're given, and you need to construct
the "best" smooth surface passing through them? That would be more
difficult... you would need to interpolate the surface. Is that really
the essence of what you're trying to do: interpolate the whole surface
from a scattering of known points?

.

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