When linking Curvature into Cutout Opacity, and the 3D mesh does not have its pivot in the center of the scene (XYZ zero), the Curvature shows errors on some mesh faces. When the mesh moves, this faces even start to flicker. The attached images shows the problem. The upper three spheres showing the sphere who rest in the XYZ center correctly displayed (left), while the other two spheres in the middle and right sowing errors. In the lower part, all spheres are in a Connect object and display correctly.
The Curvatures in connection with transparency is very useful to create x-ray or ink like effects. It took some time to narrow down the problem. Would be great if there is a solution other than using the connect object. Attached the C4D scene: curvature-problem-1.zip