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Suppose $\gamma(t)$ for each $t$ is a curve. We may write $\gamma(t)(s) = \gamma_0(s) + d(t,s)N(s)$ where $\gamma_0$ is some fixed curve, $N$ is the unit normal vector and $d$ is a distance from $\gamma_0$ to the curve $\gamma(t)$.

Under what conditions can this be done? I vaguely recall we need $\gamma_0$ to be Lipschitz, but don't know why or how. And for what $t$ can be this done? Appreciate any references or explanation.

Thanks

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    One can always make a [parallel curve](http://mathworld.wolfram.com/ParallelCurves.html) from a given curve...2012-08-13

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