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The eigenvectors represent the rotation matrix of the ellipsoid in the space while the eigenvalues represent the scale of the sphere through the rotation frame axes. Here http://geus.wordpress.com/2011/09/15/how-to-represent-a-3d-normal-function-with-ros-rviz/ you can see a blog post with a more detailed code and a video with the results.

Here you can see a chunk of python code about how to solve the problem (thanks to hersh and dornhege for the suggestions):

enter code here
(eigValues,eigVectors) = numpy.linalg.eig (covMat)
eigx_n=PyKDL.Vector(eigVectors[0,0],eigVectors[0,1],eigVectors[0,2])
eigy_n=-PyKDL.Vector(eigVectors[1,0],eigVectors[1,1],eigVectors[1,2])
eigz_n=PyKDL.Vector(eigVectors[2,0],eigVectors[2,1],eigVectors[2,2])
eigx_n.Normalize()
eigy_n.Normalize()
eigz_n.Normalize()
rot = PyKDL.Rotation (eigx_n,eigy_n,eigz_n)
quat = rot.GetQuaternion ()

#painting the Gaussian Ellipsoid Marker
marker.pose.orientation.x =quat[0]
marker.pose.orientation.y = quat[1]
marker.pose.orientation.z = quat[2]
marker.pose.orientation.w = quat[3]
marker.scale.x = eigValues[0]
marker.scale.y = eigValues[1]
marker.scale.z =eigValues[2]

The eigenvectors represent the rotation matrix of the ellipsoid in the space while the eigenvalues represent the scale of the sphere through the rotation frame axes. Here http://geus.wordpress.com/2011/09/15/how-to-represent-a-3d-normal-function-with-ros-rviz/ you can see a blog post with a more detailed code and a video with the results.

Here you can see a chunk of python code about how to solve the problem (thanks to hersh and dornhege for the suggestions):

enter code here
(eigValues,eigVectors) = numpy.linalg.eig (covMat)
eigx_n=PyKDL.Vector(eigVectors[0,0],eigVectors[0,1],eigVectors[0,2])
eigy_n=-PyKDL.Vector(eigVectors[1,0],eigVectors[1,1],eigVectors[1,2])
eigz_n=PyKDL.Vector(eigVectors[2,0],eigVectors[2,1],eigVectors[2,2])
eigx_n.Normalize()
eigy_n.Normalize()
eigz_n.Normalize()
rot = PyKDL.Rotation (eigx_n,eigy_n,eigz_n)
quat = rot.GetQuaternion ()

#painting the Gaussian Ellipsoid Marker
marker.pose.orientation.x =quat[0]
marker.pose.orientation.y = quat[1]
marker.pose.orientation.z = quat[2]
marker.pose.orientation.w = quat[3]
marker.scale.x = eigValues[0]
marker.scale.y = eigValues[1]
marker.scale.z =eigValues[2]
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fixing an error in the code...

The eigenvectors represent the rotation matrix of the ellipsoid while the eigenvalues represent the scale of the sphere through the rotation frame axes. Here http://geus.wordpress.com/2011/09/15/how-to-represent-a-3d-normal-function-with-ros-rviz/ you can see a blog post with a more detailed code and a video with the results.

Here you can see a chunk of python code about how to solve the problem (thanks to hersh and dornhege for the suggestions):

enter code here
(eigValues,eigVectors) = numpy.linalg.eig (covMat)
eigx_n=PyKDL.Vector(eigVectors[0,0],eigVectors[0,1],eigVectors[0,2])
eigy_n=-PyKDL.Vector(eigVectors[1,0],eigVectors[1,1],eigVectors[1,2])
eigz_n=PyKDL.Vector(eigVectors[2,0],eigVectors[2,1],eigVectors[2,2])
eigx_n.Normalize()
eigy_n.Normalize()
eigz_n.Normalize()

eigx_n=-PyKDL.Vector(eigVectors[0,0],eigVectors[1,0],eigVectors[2,0])
eigy_n=-PyKDL.Vector(eigVectors[0,1],eigVectors[1,1],eigVectors[2,1])
eigz_n=-PyKDL.Vector(eigVectors[0,2],eigVectors[1,2],eigVectors[2,2])

rot = PyKDL.Rotation (eigx_n,eigy_n,eigz_n)
quat = rot.GetQuaternion ()

#painting the Gaussian Ellipsoid Marker
marker.pose.orientation.x =quat[0]
marker.pose.orientation.y = quat[1]
marker.pose.orientation.z = quat[2]
marker.pose.orientation.w = quat[3]
marker.scale.x = eigValues[0]
marker.scale.y = eigValues[1]
marker.scale.z =eigValues[2]