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I'm wondering how does RViz visualize a quaternion with a frame? Does it convert a quaternion to euler angles and then visualize the frame according to those euler angles?

I don't believe so.

All "visible objects" in RViz apparently derive from rviz::Object of which instances wrap an Ogre::SceneNode. rviz::Object's pose is updated in two ways: either by "inheritance" from another object (ie: multiplying transforms) or by explicitly calling functions like setPosition(..) and setOrientation(..).

The latter accepts an argument of type Ogre::Quaternion (doc, Ogre doc), so no conversion to Euler angles is required when the orientation comes from a TF frame.