Esoteric discussion follows. You have been warned!

As with many things in Java3D, because the eyepoint is usually fixed, several approaches can have the same effect on a 2D screen.  For those of us using Java3D in real 3D (VR) these differences are the real kicker for application portability.  The ViewingPlatform in our CAVE located at the front screen, but that's just our choice.  As far as I can see (though I may be wrong), attaching the geometry to the camera will have the lines move with the head tracking, but attaching to the PlatformGeometry will make the lines always appear in the same physical place in the VR space (for us, somewhere past the apparent location of the front screen).

The ConfiguredUniverse file example in the Java3D-enabled CAVE whitepaper somewhat explains how the View and the "camera" (equivalent to the head tracker device location) differ:

// ConfiguredUniverse uses a default view attach policy of NOMINAL_SCREEN,
// so the origin of the view platform in coexistence coordinates will be
// mapped to wherever we place this point.  If head tracking is not enabled,
// then the positions of the eyes in coexistence coordinates are also
// defined relative to this point.  The X, Y, and Z directions of the view
// platform are always aligned with that of coexistence coordinates.

Does anybody know what exactly is the difference between PlatformGeometry and custom geometry add to
the same node that also holds the camera (just slightly displaced of course to meet the near clip
plane)?

I used the latter and it worked fine.

  
Another option is to set your geometry into you PlatformGeometry. So it will
move alongside your câmera. Nice for HUD.
See the java3d demo at:
${JAVA_HOME}/demo/java3d/PlatformGeometry/SimpleGeometry.java
    

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