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I am unsure of what you mean by perspective and parallell projection. I am relatively new to Java3D and am unfamiliar with these terms.
I think I am trying to solve a similar problem to you so maybe we can help each other as I suspect both our answers relate to [Transform3D|http://download.oracle.com/docs/cd/E17802_01/j2se/javase/technologies/desktop/java3d/forDevelopers/J3D_1_3_API/j3dapi/index.html].
In my case, I am simply trying to move a point in the scene. I am able to get this to work when in top down view and the default zoom. However, when the scene is rotated or scaled the coordinates do not match up. Is this the same issue you are dealing with?
The Transform3D has a 4x4 matrix that I believe stores the current views "translations, rotations, and scaling and shear effects". If we are able to understand this matrix then we should be able to perform some math to match up the coordinates.
If this isn't the issue you are dealing with, I apologise for the response but things seem to move slowly on this forum.