Pixels to 3D coordinates

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Indeed indeed... (moment of clarity came to me) There still must be a plane or an object you are pointing at. Otherwise you'll just have a vector of infinate length. Now I see why there's no math solution available. There's no need for one. Only if you are using a 3rd party graphics engine that doesn't have picking, then the math solution is needed.

I was always afraid of making objects pickable, like they had an effect on performance like mesh intersects do. Mesh picking is just something that comes for free when calculating z-buffer, isn't it?