I have been reading a scientific paper and they defined Di as the direction cosine vector, [ cos(latitude of point i)cos(longitude of point i) , cos(latitude of point i)sin(longitude of point i), sin(latitude of point i)]'. The same was done for another coordinate j. Next the dot product of those two vectors (Di and Dj) was taken but I'm not sure what this actually represents. I would appreciate any help on what the result of the dot product is.
This is the link of the paper, the part I am referring to is 2.2.1 Spatial weights matrix: W page 21, equation 16 contains di and dj from my question. I am currently trying to use this method but I am unable to obtain 's'. I have used equation 17 to obtain theta (b) but i have used theta as the Angular distance equation from this link but I'm not sure if i should be using the di dot dj rather than the angular distance equation.
Sorry if this is too lengthy and unclear
The direction cosine vectors are normalized to unity, $|\vec D_i|=|\vec D_j|=1$. Then using the formula for dot product: $$\vec D_i\cdot\vec D_j=|\vec D_i||\vec D_j|\cos\alpha_{ij}=\cos\alpha_{ij}$$ Here $\alpha_{ij}$ is the angle between the two vectors.