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First of all, it is a newbie question and I am a noob so ya.

I am working on Unity with low level network API. I am able to connect multiple client's to the server and they spawn on clients. All the clients get the information about the location of the other connected player, that is transform.position (ie. x, y and z coordinates) Position of all players is updated on all clients, that is, their transform.position gets updated with new available coordinates.

The question: How do I simulate walking animation (of connected players) on client's screens? (I use Unity's Horizontal and Vertical input)

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Welcome to the world of multiplayer online game development, you will find that a lot of stuff is a mix of cheating and interpolation. For example you want to be able to know when to play a walk animation on remote client's screens? Then get the old position aof the object to animate and the new position just received and compute its velocity using the difference in the time stamp of those (yes, you should start using time stamps on your messages).

I cannot be more percise because the argument is very huge. I can suggest you some very useful and informative read that will guide you in this magical word. First of all this important series of articles from Gabriel Gambetta, and then this very useful website with articles about physics in 3d and how to network it.

Hope you are satisfied with my answer, good luck with your learning.

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