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How to simulate an orthographic projection while looking through a perspective camera?

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I want to simulate the appearance of an orthographic projection, for selected geometry, while looking through a perspective camera.

The attached file is as far as I could get with my limited knowledge of mathematics. It seems to come close, but isn't correct -- parallel edges on the cube don't remain so when viewed through the camera. The approach also feels pretty hacky.

What is the right way to do this?



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