It is especially convenient to specify planes in so-called Hessian normal form. This is obtained from the general equation of a plane a x + b y + c z + d = 0 by defining the components of the unit normal vector n^^ = (n_x, n_y, n_z), n_x | = | a/sqrt(a^2 + b^2 + c^2) n_y | = | b/sqrt(a^2 + b^2 + c^2) n_z | = | c/sqrt(a^2 + b^2 + c^2) and the constant p = d/sqrt(a^2 + b^2 + c^2).

plane | point-plane distance

Ludwig Otto Hesse