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How to make screen warp like in nether portal and how to connect this screen warp to my custom effect?

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This effect is hardcoded for the Nether portal only. If you wanted to recreate the effect, I think you could perform similar operations on the projection matrix before rendering, which would be done in the EntityViewRenderEvent.CameraSetup. Unfortunately, this event is fired after the projection matrix is already loaded into RenderSystem, and with no reference to the general-purpose new MatrixStack that is passed around for rendering. In order to modify it, then, you would use RenderSystem#multMatrix() with your effect matrix. This method is marked as deprecated, which means it's not supposed to be called in general. I don't know what the consequences of doing so are.

Fancy 3D Graphing Calculator mod, with many different coordinate systems.

Lightweight 3D/2D position/vector transformations library, also with support for different coordinate systems.

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