On Tue, Jul 27, 2010 at 1:37 PM, Friedrich Romstedt
friedrichromst...@gmail.com wrote:
2010/7/26 Mathew Yeates mat.yea...@gmail.com:
Is there a simple function call for this? And finding the distance of
a point to the plane?
Hmm, when you are interested in the z distance alone, it should be a
matrix equation:
Z = X * m_x + Y * m_y + 1 * n
Meaning you can invert it with Moore-Penrose pseudoinversion, i.e.,
numpy.lstsq()?
When you have weights on Z, normalise first.
Friedrich
Just one quick note on this:
If you fit Z = aX + bY + c, you won't be able to resolve vertical planes.
Likewise, if you fit x = aY + Bz + c or y = aX + bZ + c you won't be able
to resolve horizontal planes.
If you need to robustly fit a plane to a point cloud, you'll need to try all
three formulations. See here for a quick example of what Friedrich mentioned
using all three formulations and choosing the most robust result:
http://code.google.com/p/python-geoprobe/source/browse/geoprobe/common.py#198
As far as finding the distance of a given point (x0, y0, z0) to the plane
defined by 0 = ax + by + cz + d, the equation is just abs(a * x0 + b * y0
+ c * z0 + d) / sqrt(a**2 + b**2 + c**2). See
herehttp://mathworld.wolfram.com/Point-PlaneDistance.html for
a more detailed explanation.
-Joe
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