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Could someone please tell me what does having 2 negative solutions of t signify? I understand that if we have one positive and one negative, the point lies inside the sphere. But what if both are negative? Does it mean that the ray has already pierced the body twice and is out on other side?


Yes, I believe that two negative solutions means that d is pointing away from the sphere---in the picture, it would be if d is pointing in the exact opposite direction.


@Asterix Right, @jzhanson got it: it means that the origin is outside the sphere, and the ray is pointing away from the sphere.