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True Portal Effect

So I did a small portal project from this tutorial: https://www.youtube.com/watch?v=sK9Qf8ElFHo Only problem I had is that the use of render texture is not as realistic as Portal. I am not looking to make it as realistic as Portal in terms of texture (but if you know how than that is much better). Basically in Portal when you move closer or further from a portal, you see more or less. When you move around, what you see through the portal is different depending on the direction between you and the portal. I get that the camera rotates and change its field of view to create the realism, but I just don't really get the math behind it, like how much rotation around what axis and how much field of view increment/reduction is needed.

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