Write a point on/inside the convex hull of a set of vertices

Question

We work over $\mathbb{R}^N$. We consider a convex hull defined by its $L$ vertices.

• How to write a point $\textbf{on}$ (in) the convex hull in function of all the vertices?
• How to write a point $\textbf{inside}$ the convex hull in function of all the vertices?

Thank you!