Given a surface described by an implicit equation $f(x,y,z,s)=0$ and a point $A(x_A, x_B, x_C)$.
$s$ is a shape parameter. For example, in $y=ax+b$, we have $s=(a,b)$
1-I am looking for the best method to calculate (numerically at least) the distance: $d(A,f)$.
2-I need also the expression of the derivative of the distance with respect to $s$.
Thank you in advance.