Correcting a stupid mistake. It bothered me to leave it, sorry for the noise.
Ga?l
On Sun, Feb 25, 2007 at 01:03:03AM +0100, Gael Varoquaux wrote:
Interesting remarks. You forced me to think a bit more about what I was trying to achieve.
What I am trying to do is to find out the right size to use for symbols when used on a 3D cloud of points. I am not sure what the right "typical distance" should be used. If those symbols are arrows then it seems that should be smaller than the typical inter-point distance. I have in mind something like this:
if you have n points, find out the distribution of distances, divide it by n**3, then take the value at 0.2 from the smallest.
I am having diffculties expressing my point, but the idea would be to consider that the typical distribution will increase as n**3 (which is
n**(1/3.)
not obvious, for instance if the points are along a plane) and take the lower tail of the distribution, as we are interested in having symbols smaller than the inter-point distance. Taking not the smallest value, but the value at "20%" from the bottom helps getting rid of singular situations where a few points are very close but the major part is spread out.
Hi Gael,
Scaling relative to the cloud of points might be an easier way to go than scaling relative to the actual interpoint spacing. It would make sure your arrowheads are readable on the plot, even though some may appear oversized relative to their shafts. Also, points that are far apart in 3d space might appear close when viewed from particular angles, like 'optical doubles' in astronomy. If you want to make your symbols roughly the right size relative to the whole cloud, you might like a widely used quick-and-dirty method from statistics.: from scipy import * from numpy.linalg import eigh points = 2.*randn(100,3) C = cov(points.transpose()) D,V=eigh(points) Then the `error ellipse', the ellipsoid that kind of sort of tries to fit the point cloud, has major axes given by the columns of V with length equal to the sqrt of the corresponding elements of D. You could then calculate approximately how big or small the point cloud looks by projecting the major axes into your viewing plane. Hope that helps... that would be a milestone for me, my first time actually helping someone else on a Python mailing list. Cheers, Anand