Hi everyone,

I have a question and I hope someone can help me to know whether what I've done is correct?
The problem:
I have 300 particles move in 3D space. Their movement is very simple.
They move together one step every second.
*We are not very interested in the deformation of the shape that can be consisted of the particles while they are moving.*

The requirements:
I want to visualize the principal axes of the shape at every timestep.

I used Eigen to calculate the SVD to find the rotation matrix but I don't know how to get the principal axes?
I've done some research and I found that the principal axes are associated with the largest eigenvectors.

The question:
Am I in the right direction ( i.e by computing the SVD and trying to find the eigenvectors).
If yes, how can I get the eigenvectors? how can they be used to visualize the Axes (do they represent the axes directly or do I need to do some calculation on them )?

This topic is the most related one in this forum:
viewtopic.php?f=74&t=109403&hilit=SVD+eigenvector

I hope someone can help.

Nai

Hi,

I've got the answer elsewhere (no URL available).

After calculating the svd:
JacobiSVD<Eigen::Matrix3d> svd(H, Eigen::ComputeFullU | Eigen::ComputeFullV );

we can obtain the U matrix which includes the eigenvectors
U = svd.matrixU();

the eigenvectors can be accessed by using the col property (each eigenvector is stored in a column)
for example:
U.col(0) will return the first eigenvector U.col(1) the second and so on.
You need to figure out the direction of each eigenvector by finding the largest component of that eigenvector.

I hope that helps someone.

Nai