This article focuses on the classical problem of the control of information loss during the digitization step. The properties proposed in the literature rely on smoothness hypotheses that are not satisfied by the curves including angular points. The notion of turn introduced by Milnor in the article On the Total Curvature of Knots generalizes the notion of integral curvature to continuous curves. Thanks to the turn, we are able to define the local turn-boundedness. This promising property of curves does not require smoothness hypotheses and shares several properties with the par(r)-regularity, in particular well-composed digitizations. Besides, the local turn-boundedness enables to constrain spatially the continuous curve as a function of its digitization.

中文翻译：

---

局部转弯有界度：连续曲线的曲率控制及其在数字化中的应用

本文重点讨论数字化步骤中信息丢失控制的经典问题。文献中提出的特性依赖于包括角点的曲线不满足的平滑度假设。Milnor在“结的总曲率”一文中引入的转弯概念将积分曲率的概念推广到连续曲线。多亏了转弯，我们能够定义局部转弯边界。曲线的这种有希望的特性不需要平滑性假设，并且具有与par（r）正则性相同的多个特性，尤其是精心组合的数字化。此外，局部转弯边界能够根据其数字化在空间上限制连续曲线。