$$\sqrt{\left[\frac{R_{\min }^2}{2}\left(1+\frac{\sin \left(\theta _m\right)}{\theta _m}\right)-\overline{p}^2\right]}$$
Function from paper below. Parameter R_min is the radius and p_bar seems like the edge length relative to angle. I would like to know where this function comes from and what the graphic/physical meanings are. Is it about the curvature integral or something?
quote part of the article
we compute the standard deviation of the neighbors’ residuals relatively to the plane defined by the normal in the centroid location. If it is lower than a given threshold , we suppose that the neighborhood does not contain any curvature discontinuity and the iterations can be avoided. is defined as the theoretical standard deviation of all points of the continuous underlying shape with a specific curvature radius . This theoretical standard deviation can then be estimated by integration as: function(10)
https://www.sciencedirect.com/science/article/abs/pii/S0924271620300575