I have a rectangular cuboid-shaped 3D "cell" with scalar values at each vertex $(v_1,\ldots,v_8)$. Within this cuboid I do tri-linear interpolation. What I want is the maximum value of that function intersected with a sphere.
I reckon this is an optimization problem, or at least wikipedia tells me that it is. How would I go about finding the maximum value? I'm not interested in where this maximum occurs exactly, in case that makes things easier.