The cell of \(x_i\) is the window intersected with the half-planes
\((x_j - x_i) \cdot (u - (x_i + x_j)/2) \le 0\) for every other point,
computed by Sutherland-Hodgman clipping. Returned with the cell areas,
the Voronoi intensity \(1/area\) at each point (Barr and Schoenberg
2010), perimeters, centroids, the Voronoi edges between points (the
Delaunay neighbours) with their lengths, the adjacency matrix, the
neighbour counts and the Voronoi entropy \(-\sum_k P_k \log P_k\) of
their distribution. Areas and neighbours equal deldir::deldir
with digits = 15.
Value
List with areas, cells, intensity,
perimeters, centroids, edges (matrix of 1-based
i, j, length), neighbours, adjacency,
neighbour_counts, entropy.
References
Okabe, A., Boots, B., Sugihara, K. and Chiu, S. N. (2000). Spatial Tessellations, 2nd ed. Wiley.
Barr, C. D. and Schoenberg, F. P. (2010). On the Voronoi estimator for the intensity of an inhomogeneous planar Poisson process. Biometrika 97, 977-984.
Bormashenko, E. et al. (2018). Characterization of self-assembled 2D patterns with Voronoi entropy. Entropy 20, 956.