A family of plane, oriented and continuous paths depending on a fixed real positive number is considered. For any point on the path, the previous points lie out of any disk with same radius, having interior normal in a suitable tangent cone to the path. These paths are locally descent curves of a nested family sets of same positive reach. Avoiding any smoothness requirements, we get angle estimate and not intersection property. Afterwards, we are able to estimate the length and detour of this curve.

中文翻译：

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平面路径和下降曲线的整流特性

考虑依赖于固定实正数的平面、定向和连续路径族。对于路径上的任何点，先前的点位于具有相同半径的任何圆盘之外，并在路径的合适切锥中具有内部法线。这些路径是具有相同正范围的嵌套族集的局部下降曲线。避免任何平滑要求，我们得到角度估计而不是相交属性。之后，我们可以估计这条曲线的长度和绕行。