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Constructing a function that computes the Voronoi cell of a point set in a discrete metric space.

Given the task: Construct a function that computes the Voronoi cell of a point set in a discrete metric space. The function must return True if there exists a Delaunay triangulation of the point set.
I first tried to find such an algorithm which is not based on Voronoi diagrams and failed to find anything.
So, I was wondering: Is there a known algorithm which computes the Voronoi cell of a point set in a discrete metric space?

A:

A k-dimensional Voronoi cell of a point set is a convex polytope.
Every (n-1)-dimensional convex polytope can be described by the intersection of halfspaces.
So, by reducing the problem to the study of the intersection of convex polygons, we can translate the question into the study of the intersection of convex polygons.
A convex polygon in \$\mathbb{R}^2\$ can be described by an alternating concave/convex sequence of rectangles \$R_0R_1R_2R_3\dots\$.

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