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Extracting frustum planes without matrices

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Hello everyone,

I'm making a raytracer with a bunch of friends and I'm currently in the process of implementing a view frustum so we can cull objects for the primary ray. The thing is that we are not working with matrices at all, so we are only using the right, up and look vector for all our calculation.

I would like to know how to extract the 6 frustum planes with only those 3 vectors and the screen ratio, camera position, etc. but without any view*projection matrix.

Thanks in advance for your answer.

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