in one physics problem, there is a cube. A computationally expensive function can be calculated inside the cube. But one needs to do the calculation faster and to know for a given point inside the cube, an approxmated value, which depends on the 8 vertices. For that I tried linear interpolation in 3D and it works more or less. Now I woule like to try the same idea but with parabolic, polynomic or other better interpolation option (in terms of accuracy), always in 3D. What do you suggest?
PS: Of course, for doing more than linear interpolation you need more points. Forgot to say that this cube is surrounded by lots of other cubes of the same dimensions, where the function has also been calculated.