# Understanding inequality to equality in the Hartmann & Gribbs frustum planes extraction method

I've been reading this article on how to extract the plane equations from the view and projection matrices. And I can understand most of it. However, the only thing that is unclear to me (and that might be for lack of mathematical knowledge), is the part where they transform their inequality 0 < v * (row4 + row1) into the equality  v * (row4 + row1) = 0 (that is for calculating the plane in the x negative side).

Usually, to convert inequality to equality you use a slack variable, but in their approach, none was used. How can we be sure that  v * (row4 + row1) will always be zero on that frustum plane? All we know is that the resulting value of  v * (row4 + row1) has to be positive to be on the right side of that frustum plane.

I also know how the plane equation is constructed. How we use the dot product of two vectors (any vector in the plane and the normal a,b,c) must be equal to zero: ax + by + cz + d = 0. I can see that the resulting expression from v * (row4 + row1) > 0 results into a identical plane equation. My only doubts are in the conversion from inequality to equality.