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Open Problems in Physics Engine Design

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To contextualise my question, I come from a mathematical physics background with some experience in programming. 


What are the current open problems in the development on physics engines for games? 


I would imagine that there is a general (time-wise) computability issue in any physics simulation that is aiming for greater fidelity. However, there must be specific phenomena that are more desirable than others which people are unable to simulate effectively.


Any insight you might have would be much appreciated.



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