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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.

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.