A geometric interpretation of weighted normal vectors and its improvements

The weighted normal vector method was applied to estimate the curvatures on a surface in the 1990s. However, this estimation method still causes serious problems, such as when two adjacent triangles are of coplanarity. In this paper, our main goals are to provide a geometric interpretation of weighted normal vectors and then give an improvement to handle this problem. In 2004, we pointed out that the normal vector estimation with area weights cannot distinguish the difference between contributions when two different triangles have the same area. To deal with this drawback, we presented the centroid weight to improve the estimation of normal vectors. Here, we give a particular interpretation of centroid weight and extend this idea to introduce a new weight, the gravitational weight.