Being given an implicit surface of the form f(x,y,z)=0
And assuming we know the gradient G=(xi,yi,zi) at a known point P (x0,y0,z0) on the surface, how do you compute the tangent plane to that surface at P ?
You don't know f, only it's gradient.
To my understanding the gradient is perpendicular to the tangent plane at point P, so it suffices to say that (P-X).G=0 where X is an arbitrary point which should lead to an implicit linear equation of the form:
ax+by+cz+d = 0
and then if one wished to express this as a function of 2 variables the final solution would be for example:
(-a/c)x+(-b/c)y-d/c = z
However it seems this is wrong, and I don't understand why