I know the gradient of a function t on a cartesian grid: $\vec{g}(xi,yj,zk)=\nabla t(xi,yj,zk)$.
I know t for the center pillar: $\ t(xc,yc,zk)$.
For each node in the cartesian grid I want to calculate the timeshift: $\ ts(xi,yj,zk) = t(xi,yj,zk) - t(xc,yc,zk)$
According to the gradient theorem: $\ ts(xi,yj,zk) = \int_{(xc,yc,zk)}^{(xi,yj,zk)} \vec{g}(\vec{r})d\vec{r}$
But how do I quck and runtime effective code this (in Matlab)?
I want to avoid summing over n contributions for every node in the grid; O(n^4) :-(.
Thanks in advance for any answers!