Re: marching cubes help

"keith" <johndoe64738@xxxxxxxxx> wrote in message
news:gpqmoi$3s6$1@xxxxxxxxxxxxxxxxxxxxxx
Yes, it is. I did my homework before asking my question. The other
poster apparently did not believe I did. I've seen him in a nice santa
outfit on his website; he could have given me a nice gift in advance.

Ken is a long-time contributor and always has a lot to offer, a lot of
it seemingly forgotten by current generation folks. His style can be
somewhat different from what you prefer, but then again he and I
take turns presenting in ways people don't prefer. And always
consider the possibility that you assume you have provided clear
and concise question to which you expect a clear and concise
answer, but the reality is that your question is neither clear nor
concise and the responder attempts to infer what you meant. If
you don't like his answer, try to clarify or ask what was not clear.

So there are as many distribution functions as are points... This sounds
nice, but makes is slow to evaluate F(x, y, z). Circular Gaussian? You
mean a probability density function that falls with distance, but stays
constant at constant distance around a point?

By "circular", I mean that the distribution is radially symmetric about its
center: G(x,y,z,r) = A*exp(-r^2/(2*s^2)), where s is the standard
deviation, A is amplitude, and r^2 = x^2 + y^2 + z^2. I failed to mention
a choice for A. Given on other information for the points, you may choose
A to be a constant. If some points are "different" from others (you get to
choose what different means), this approach allows you to vary the A
with center.

Yes, the evaluation is slow. Is it slow enough that you cannot use it? Or
are you just making a general observation? Consider the classic case
of Gaussian blurring of a 3D voxel image. In this case all samples are
fit with a Gaussian distribution. As you increase s, the image becomes
blurred. Folks have used Fast Fourier Transforms to speed up the
calculations. Whether or not such tricks work for randomly distributed
point clouds is a possibility (I have not studied this). My guess is that
on
current-generation computers, "slow" is not going to be a show stopper.
You can always use multicore methods if need be.

And I need to choose L as well probably? That makes for 3 parameters to
choose. Are there any other possibilities? BTW, where did you get this
idea? Is there some paper about this and similar techniques?

I would start out choosing A = 1 and (in voxel coordinates) s >= 1. For a
smaller s, choosing L = 1, you just "clip" the tops of the distributions,
probably
leading to a large number of small connected components of triangles.
Increase
s to force the connected components to become larger, eventually your hope
is
that you get the largest acceptable surface. As with most techniques, it is
about impossible to algorithmically select the parameters. What you select
depends on your data.

As mentioned, the basic idea is from blurring a 3D image. The ideas also
show up in smoothed particle hydrodynamics for liquid/gas simultations.

--
Dave Eberly
http://www.geometrictools.com


.

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