Embodiment and subjectivity are important research issues for collaborative virtual environments. We claim that the direction and distance of an embodiment are the most important indicatorsof the relation between a user and surrounding objects or other users. In an objective view of a virtual environment, embodiment motion is unambiguous since all users will see all other users and all artifacts in the same positions. However, there are many reasons to present different views of the same basic data set to different users. If objects end up in different positions in different views, we cannot retain a common coordinate system for the embodiments, since directions and distances are distorted. We present an implementation of artifact-centred coordinate mappings by which the positions of the artifacts that the user is interacting with govern how that user is represented to other users of the system.