I have an unanswered [question](https://stackoverflow.com/questions/42248202/how-to-get-the-projection-of-a-point-on-the-closest-edge-of-a-convex-hull-with-s) on Stack Overflow that might more related to mathematics than programming. So the part where I am having a problem is described below.

EDIT: I reformulated the whole problem hoping that will be clearer.

Let $\mathcal{A}$ be a set of $m$ points:
$$
\mathcal{A} = \{P\_i \in \mathbb{R}^6, i \in [1,\ldots, m]\}.
$$

From this set of points, a convex hull $\mathcal{C}$ (the smallest convex set that contains the points ${P\_i}$) can be defined such that:
$$ 
\mathcal{A} \subseteq \mathcal{C}
$$

Let's define $Q \in \mathbb{R}^6$ such that:
$$
Q \not\in \mathcal{C}
$$

How do I find $Q^{\prime} \in \mathbb{R}^6$, the closest point from $Q$ belonging to the convex hull $\mathcal{C}$:
$$ 
Q^{\prime} \in \mathcal{C}, \forall r \in \mathcal{C}\quad ||Q^{\prime}-Q|| \leq ||r-Q|| 
$$

I am looking for any algorithm or mathematic method to solve such problem so that I can implement it in my code.

For information: I am using the python scipy implementation of the qhull library for finding the convex hull from $\mathcal{A}$.