We deal with a notion of weak binormal and weak principal normal for non-smooth curves of the Euclidean space with finite total curvature and total absolute torsion. By means of piecewise linear methods, we first introduce the analogous notion for polygonal curves, where the polarity property is exploited, and then make use of a density argument. Both our weak binormal and normal are rectifiable curves which naturally live in the projective plane. In particular, the length of the weak binormal agrees with the total absolute torsion of the given curve. Moreover, the weak normal is the vector product of suitable parameterizations of the tangent indicatrix and of the weak binormal. In the case of smooth curves, the weak binormal and normal yield (up to a lifting) the classical notions of binormal and normal. Finally, the torsion force is introduced: similarly as for the curvature force, it is a finite measure obtained by performing the tangential variation of the length of the tangent indicatrix in the Gauss sphere.

我们处理了具有有限的总曲率和总绝对扭转的欧几里德空间的非光滑曲线的弱双法线和弱主法线的概念。通过分段线性方法，我们首先引入多边形曲线的类似概念，在其中利用极性属性，然后利用密度参数。我们的弱双法线和法线都是可校正的曲线，它们自然存在于投影平面中。特别是，弱双法线的长度与给定曲线的总绝对扭转一致。此外，弱法线是切线和弱双法线的适当参数化的向量积。在平滑曲线的情况下，弱的双法线和法线屈服（最多提升）是双法线和法线的经典概念。最后介绍了扭力：