Voronoi tasselation

The Voronoi tasselation consists in partitioning the plane into regions based on the distance to points in a specific subset of the plane.

For each point, there is a region of all points closer to it than any other one (Voronoi cells).

Simplex

A simplex is the generalisation of a triangle/tetrahedron to an arbitrary number of dimensions. The k simplex is a k-dimensional polytope, the convex hull of its k+1 vertices.

Given points$u_0, \ldots, u_k \in \mathbb{R}^k$, with$u_1 - u_0, \ldots, u_k - u_0$linearly independent, the simplex determined by them is the set of points

• the 2-simplex is a triangle;

• the 3-simplex is a tetrahedron;

• the 4-simplex is a 5-cell

References

1. Wikipedia about the Voronoi diagram​