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How to check if a cuboid of known vertices and a plane of equation $ax + by + cz + d = 0$ intersects?

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    $\begingroup$ A point $P=(x,y,z)$ lies on either side of the given plane according to the sign of $ax+by+cz+d$. And the plane intersects the cuboid iff at least two of its vertices lie on opposite sides. $\endgroup$ Dec 29, 2021 at 15:34

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The simplest is probably to check whether all vertices are on the same side of the plane or not.

The two half-spaces formed by the plane are respectively such that $ax+by+cz+d > 0$ and $<0$. So calculating $ax+by+cz+d$ for each vertex gives you the answer.

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