floting-point camerazoom distortion

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I'm making an fps/tps but ran into a problem a while ago.

When in third person mode, to get an adequate view of your surroundings, the camera must be placed outside of the characters collision radius. But this allowed the camera to go through objects. To correct this problem I moved the camera inside the radius and gave the camerazoom a value of 0.2. However, this results in severe distortion of the image somewhat like looking at a strongly concave mirror. I finally corrected this problem by putting the camera's image on a convex square and watching the square through another camera. This works, but takes up significant system resources. To make it worse, this is a multiplayer game, and this technique will have to be used on all the players to make it look good

Could you use a simple mathematical formula to correct the problem?