Understanding inequality to equality in the Hartmann & Gribbs frustum planes extraction method
The volume inside of the frustum is defined by a set of inequalities, and since we are trying to find the boundaries of the frustum, we set the inequalities to equalities. That's really all it is.
To take a 1D example, if we have a &quot;frustum&quot; defined by 0 &lt; x &lt; 5, then of course the bounding points of it are defined by x = 0 and x = 5. Replacing each inequality by an equality, in turn, gives you the most extreme point you can get to in that direction.
Slack variables, BTW, don't really convert inequalities to equalities. They just transform the inequality into a standardized form &quot;x &gt; 0&quot; (or &quot;x ≥ 0&quot;) for some slack variable x.