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Either is fine, though you should make sure that your triangle-triangle intersection works reasonably well, since it prevents confusion when debugging your BVH intersection code. For example, if it says that two triangles extremely far apart actually intersect, then your BVH-optimized version will not detect this. That wouldn't be a bug in your BVH code, but in your triangle-triangle intersection code.
Is it ok to implement an algorithm from a paper for triangle-triangle intersection or should we develop our own simpler approach?
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