HCR - Algorithm for Minimum Distance from Surface

Given $x_h$ haptic point (same as $x_a$ just a different name):

$$x_h=<x_{hx},x_{hy},x_{hz}>$$

the minimum distance from the place $\Sigma$ ($ax+by+cz+d=0)$ can be computed as the distance of $x_h$ from $x_p$ ($p$: proxy) where $x_p$ is defined as the projection of $x_h$ onto $\Sigma$.