# Plot a Gaussian 3D representation with markers in rviz

Hi people! I'm thinking of plotting a 3D Gaussian Model with a marker defined by a mean vector and a covariance matrix. Is there any rviz plugin to render this? If not, is it possible to do so plotting a marker?

I think it could be possible just plotting a sphere centered in the mean vector and apply to it a linear deformation using the covariance matrix.

## Any idea or suggestion about how to address this problem?

EDITED: after the responses I made a blog entry to illustrate the problem: http://geus.wordpress.com/2011/09/15/how-to-represent-a-3d-normal-function-with-ros-rviz/

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Dornhege's link to the other discussion (ending ultimately with an enhancement request ticket for rviz) is certainly correct.

However to answer the question more specifically: yes you can do this with a Marker. Specify marker type SPHERE, set the marker.scale.x, y, and z values to the length you want each axis of the "sphere" to be. If the scale x, y, and z values are not all equal it will look like an ellipsoid instead of a sphere. Set marker.pose.orientation to give it an orientation and marker.pose.position to the location of the center, and you are all set.

I'm not the one to ask about the math to go from a covariance matrix to a rotated ellipsoid, but I know you can show rotated ellipsoids in rviz.

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You just need eigenvectors and eigenvalues from the covariance matrix.

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[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
marker.pose.orientation.y = quat
marker.pose.orientation.z = quat
marker.pose.orientation.w = quat
marker.scale.x = eigValues
marker.scale.y = eigValues
marker.scale.z =eigValues

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Note: although the eigenvalues are guaranteed to be positive, the eigenvector matrix may either have a determinant of +1 or -1. Check the eigenvectors carefully before treating it as a rotation matrix. By the way, it's customary to use sqrt(eigvalues) for scale. I think this question is relevant here (seem it is not directly supported currently).

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