How to render .obj files in a non-euclidean way?

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Apologies in advance if this question is misguided or foolish; I'm learning. My goal is to write a non-euclidean renderer in the Rust programming language, and I'm wondering if anyone could tell me if this would theoretically work. I want to be able to import a scene of objects and render them in curved space. In the paper I'm reading, Jeff Weeks defines that, for rotation and translation,

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As I understand, a 4D Hypersphere is defined by the formula

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Does this imply I can render spherical space by replacing the w?

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