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You should give more details, since the answer depends on how your torus is defined. Is it smooth ? Is it given by some equation ? Cartesian or parametric ? Then you could think of computing derivative and use some variational principle to find the distance analytically.

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You should give more details, since the answer depends on how your torus is defined. Is it smooth ? Is it given by some equation ? Cartesian or parametric ? Then you could think of computing derivative derivatives and use some variational principle to find the distance analytically.