Time Warp rolls back the game state to when the player action occurred on the client, applies the action, then rolls the game state forward to the current time.
The below figure~ depicts an example of time warp. The figure shows the game world for a shooter game on a Client and the Server, with time advancing from top to bottom. The player on the client is shooting at a green avatar that is moving right to left, with the "plus" sign in the middle representing a weapon reticle. At time t0 at the client, the green avatar is to the right of the reticle, moving into the reticle at time t1 where the player pulls the trigger, and that action is sent to the server arriving just after time t2. Meanwhile, on the server, the green avatar moves past the reticle at time t1 and has continued right at time t2$. When the action arrives at the server, the server "warps" time back to when the action occurred at the client at time t1, applying the action to the world representation at that time.
However, resolving an event in the past and rolling it forward may cause already rendered client game states to be inconsistent with the new game state. This is a well-known artifact of some shooting games, and can result in "shot around the corner" as it's known by players, shown in the figure below. At time t1, at the blue avatar's client, the green avatar is in sight and the blue player fires. However, by time t2 when the server receives the update, the green avatar has reached a safe position around the corner from the blue player and cannot be targeted. However, with time warp, the server, upon receiving the blue player's action at time t2, rolls back time to the green avatar's position at time t1 and applies the action. This hits the green avatar. Rolling the game world forward to the present time, with the green avatar hurt or killed, may feel like being "shot around the corner" for the green player.
Time warp is often called, somewhat confusingly, latency compensation or lag compensation in some papers and, more often, in online blogs and player posts. It is also sometimes simply called rollback. Also somewhat confusing, some image warping techniques are called time warp whereas we classify them as latency concealment.
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