Some geometry

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 pointsu0,…,uk∈Rku_0, \ldots, u_k \in \mathbb{R}^ku0​,…,uk​∈Rk
, withu1−u0,…,uk−u0u_1 - u_0, \ldots, u_k - u_0u1​−u0​,…,uk​−u0​
linearly independent, the simplex determined by them is the set of points
C:θ0u0+⋯+θkuk∣θi≥0,0≤i≤k,∑i=0kθi=1C : {\theta_0 u_0 + \cdots + \theta_k u_k | \theta_i \geq 0, 0 \leq i \leq k, \sum_{i=0}^k \theta_i = 1}C:θ0​u0​+⋯+θk​uk​∣θi​≥0,0≤i≤k,i=0∑k​θi​=1
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​

The mathematics appendix - Previous

Mathematical functions

Next - The mathematics appendix

Cross-field concepts

Last modified 2yr ago

Copy link

On this page

Voronoi tasselation

Simplex

References