For use in [[Perspective Projection]] / [[Clip Coordinates]], perspective division is when you map a homogenous point $\tilde{P}$ where $\tilde P_w$ is not one to its [[../Math/Homogeneous Equivalence|Homogeneous Equivalent]] [[../Math/Point|Point]] $\tilde P'$.
$\huge
\mat{
x\\y\\z\\w
}
\stackrel{\div w}
\mapsto
\frac{1}{w}
\mat{ x\\y\\z }
$