I have a 3x3 kernel in which I am interested to find the directional derivative of a scalar field($\phi$) at point P along the normal $\hat{n}$. I know the value of $\phi$ at Points P,1,2,3,4,5,6. I am interested in capturing the influence of the values at all these points. The orange and white are two different materials and I am interested to find the gradient of $\phi$ in the white material.
What I am doing right now is to calculate gradients at P w.r.t individual points. I then project them over the normal($\hat{n}$). Further, I am averaging them with inverse distance weighting. Can we average directional derivatives like this?
Thanks
