Curvature of cubic 3D curve

I want to calculate the curvature of a surface defined by a set of $(x,y,z)$ coordinates. So I fitted this formula to the set of points and obtained values of $a, \dots,k$ with $R^2 \sim 0.98$:

$$z = a + bx + cy + dx^2 + fy^2 + gx^3 + hy^3 + ixy + jx^2y + kxy^2.$$

Now I am wondering how to calculate the curvature of the surface from this equation.

-