This paper aims to study how to gain the consistency of the state in a DVE(Distributed Virtual Environment) with lag, under the condition of P2P (peer-to-peer) protocol. That is, how to reduce the difference in time of the DVE state information between terminals caused by lag and how to control the shared object in real-time online game is studied. Specifically, the mutualprediction protocol is used in P2P type of the DVE. By utilizing this function, each terminal can compute mutually the state of the local avatar predicted by the remote terminals. In addition, we introduce a concept called AtoZ (Allocated Topographical Zone) of an avatar in which a shared object can be accessed and controlled preferentially by each avatar, dynamically changing its geometrical property depending on the relative arrangement among the object and avatars. As an example of the application using this function, a real-time network air hockey is implemented, in order to evaluate the influence on the real-time interactivity by the protocol above is performed.
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