Re: Best Fit Plane - Parallel to xyplane!

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?

This is what we need.

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!)

Below I will try to give an example. Suppose we have a 3cm x 2cm
surface to analyse and the distance between adjacent points are 1cm. Do
you think this xy grid will be reasonably fine?

Let these are the x, y, z coordinates
(x,y,z)
-------
(1,1,2)
(1,2,4)
(1,3,5)
(1,4,3)
(2,1,2)
(2,2,3)
(2,3,1)
(2,4,6)
(3,1,3)
(3,2,6)
(3,3,2)
(3,4,1)


y-axis (cm)
^
|
|
| 3 6 2 1 <----|
3 | .----.----.----. |
| | | | | |
| |2 |3 |1 |6 <----|------ z-axis (cm)
2 | .----.----.----. |
| | | | | |
| |2 |4 |5 |3 <----|
1 | .----.----.----.
|
-----------------------> x-axis (cm)

0 1 2 3 4

you need to construct
the "best" smooth surface passing through them? That would be more
difficult... you would need to interpolate the surface.

If we interpolate the surface to find the best smooth surface, will
that plane have a slope?

.

Relevant Pages

  • Re: Best Fit Plane - Parallel to xyplane!
    ... counting volume above the plane as positive and below the plane as ... square x-y grid, and then just average the z-coordinates, as has been ... Provided the grid is reasonably fine, ... automatically zero the volume to a reasonable degree ...
    (sci.math)
  • Re: Poles an Zeros
    ... First, you have to wrap your mind around a plane that represents all possible frequencies in two dimensions, called the S plane. ... A zero frequency, representing DC, is the origin. ... The S plane frequency representation is based completely on representing the signals and responses as complex exponentials (e raised to an exponent with real and imaginary parts, representing the two dimensions of the S plane. ...
    (sci.electronics.basics)
  • zero and infinity Revisited
    ... A recent debate under the subject heading "zero and infinity" ... length to the zero mark on the dual plane scale, ... the base of dimension is set locally. ... motion is through a 2D environment, but is always measured in 1D. ...
    (sci.physics.relativity)
  • Re: Floating point errors in collision routines
    ... zero is fundamentally futile. ... Newer collision engines, like Gino's SOLID, get ... > the sphere has sufficient energy to collide with, ... > the plane.) ...
    (comp.lang.cpp)
  • Re: What has fractal theory achieved?
    ... 1905 to 1907 papers, in which he discusses the likely ... integer power of the linear scale factor. ... It is clear that the mere fact that the plane content ... is zero is merely to assert that Fhas the limit ...
    (sci.math)
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