Following up on the using an existing library I have found

Qhull, Copyright (c) 1993-2003

The National Science and Technology Research Center for
Computation and Visualization of Geometric Structures
(The Geometry Center)
University of Minnesota

which is available without any requirement to publish source code, unlike CGAL which has the required areas under a Q-Public Licence, requiring all software using it to be published as open-source under the same licence.