I'm not sure this is what I am looking for, if it is, then I missed it. I have an implicit function f(x,y,z)=0 (it is actually a model with adjustable parameters). I have an experimental data point (Xexp, Yexp, Zexp). You can probably see where I am heading with this. I want to know where a line, orthogonal/perpendicular to the surface, will intersect the surface. I'm calling this point of intersection Xcalc, Ycalc, Zcalc. How do I proceed? Based on other videos I watched, it looks like the first step is to linearize the surface using Taylor series. So, now I have a plane (in terms of partial derivatives and (Xcalc, Ycalc, Zcalc) which is still unknown. I want to know the point of intersection (Xcalc, Ycalc, Zcalc) of the orthogonal line from Xexp, Yexp, Zexp. At first, I thought is it a trial an error iterative procedure (I have to guess Xcalc, Ycalc, Zcalc) so I programmed that, but the answers I am getting do not seem to be correct. I'm also beginning to suspect that the solution can be direct, not iterative. Any thoughts?
