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Ball respond in 3D space

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Hi guys, I am working on school project that required to simulate responses of a ball hitting around in 3D envinroment. The environment can be in cube, sphere, torus, cylinder and etc. I will provide an initial condition of a ball, and let the ball hits around the environment. The ball must respond correctly when it hit the boundary of the environment as well as I need to detect the collision point accurately. I am searching online quite some while, and often end up with some complicated game engines. So you guys have any idea that any engine suitable for this purpose?

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