How can I make a curved contour + quiver?

Hi all,

I have a set of data in 3D cartesian coordinate, and I'd like to make a contour and quiver on a 3D curved surface like the grey one of the attached figure. The curved surface can be a part of cylinder. Can anyone help me to do that?

The data to be on the contour is not an equation format. It's just data in numbers at each (X,Y,Z) point. The quiver is not the normal vectors. For example, if the contour is about velocity fields in Z direction, quivers are about the velocity fields in X and Y direction.

The attached figure is from http://matplotlib.org/mpl_toolkits/mplot3d/tutorial.html

Thanks in advance, Rojo

[Muhammad Usman Saleem]

Please attach some portion of your data set being use