From: Sahra winter on
I have some spheres/points plotted in 3D & would like to give each of them a random motion?
Any idea how to do that?

any help is appreciated
-Sahra
From: Walter Roberson on
Sahra winter wrote:
> I have some spheres/points plotted in 3D & would like to give each of
> them a random motion? Any idea how to do that?

Should the motion be constrained to a maximum Euclidean magnitude, or are x
and y and z independent and constrained?

Somewhere around 10 days ago, Roger Stafford showed how to create a random
simplex, which is needed in order to construct vectors whose total magnitude
is constrained; the naive methods tend to result in the corners (e.g., high x,
low y, low z) being avoided.
From: Walter Roberson on
Walter Roberson wrote:
> Sahra winter wrote:
>> I have some spheres/points plotted in 3D & would like to give each of
>> them a random motion? Any idea how to do that?
>
> Should the motion be constrained to a maximum Euclidean magnitude, or
> are x and y and z independent and constrained?

Another question: what distribution of random values are you looking for?
Should, for example, M*(1/10,3/22,1/50) and M*(1/sqrt(3),1/sqrt(3),1/sqrt(3))
be equally probable -- so any point with magnitude 0 to M should be
equi-probable? Or should low velocities be more likely and velocity M should
be the infinite limit of exponentially decreasing probabilities? Or should an
average velocity of M/2 be more probable with a bell curve for the others?

Should all ways of reaching a given velocity the same probability or should
(for example) equal-magnitudes on the 3 axes be more probable than straight
along one of the axes?

Should a random radius (velocity) be taken and then a random point on a sphere
be constructed to find the components of the individual magnitudes?
From: Sahra winter on
Dear Walter:
If possible the motion should be constrained to a max Euclidean magnitude (moving points/sphere should be constraint to a certain volume in space)
Probability of any point with magnitude 0 to M does not have to be
equi-probable. basically I just want to have some points/particle that are moving in a 3D volume... the purpose is to take a movie from a camera carried by one of the particles from others. How these particle move doesn't really matters, however the movements should be random.
From: Walter Roberson on
Sahra winter wrote:

> If possible the motion should be constrained to a max Euclidean
> magnitude (moving points/sphere should be constraint to a certain
> volume in space)

http://mathworld.wolfram.com/SpherePointPicking.html