plot_apollonius: Plot Apollonius Diagram

In transport: Computation of Optimal Transport Plans and Wasserstein Distances

Plot Apollonius Diagram

Description

Plots the Apollonius diagram, a.k.a. (additively) weighted Voronoi diagram, based on a matrix of points (centers) in 2d and their weights.

Usage

plot_apollonius(
  points,
  weights,
  show_points = TRUE,
  show_weights = TRUE,
  add_to_weights = 0,
  add = FALSE,
  col = 4,
  lwd = 1.5,
  ...
)

Arguments

points	A two-column matrix containing the 2d points.
weights	A vector of weights for the points.
show_points	Logical. Should the points be displayed in the plot? Defaults to TRUE.
show_weights	Logical. Should the weights be displayed in the plot? Defaults to TRUE.
add_to_weights	A value added to the weights to make the plot more informative.
add	Logical. Should the plot be added to the current device? Defaults to FALSE.
col	The colour for the cell boundaries.
lwd	The line width for the cell boundaries.
...	Further parameters to the base plot if add is FALSE.

Details

For points x_1, \ldots, x_n with weights w_1, \ldots, w_n The $i$-th cell of the Apollonius diagram contains all the points x that satisfy

\|x-x_i\|-w_i < \|x-x_j\|-w_j

for all j \neq i. Its boundaries are hyperbola segments.

If show_weights is TRUE, grey circles of radii weights + add_to_weights are plotted around the points. Negative radii are set to zero.

Note

This function requires the Computational Geometry Algorithms Library (CGAL), available at https://www.cgal.org. Adapt the file src/Makevars according to the instructions given there and re-install from source.

Author(s)

Valentin Hartmann [e-mail] (most of the code)
Dominic Schuhmacher [e-mail] (R-port)

References

Menelaos Karavelas and Mariette Yvinec. 2D Apollonius Graphs (Delaunay Graphs of Disks). In CGAL User and Reference Manual. CGAL Editorial Board, 4.12 edition, 2018

Examples

## Not run: 
w <- c(0.731, 0.0372, 0.618, 0.113, 0.395, 0.222, 0.124, 0.101, 0.328, 0)
points <- matrix(runif(20), 10, 2)
plot_apollonius(points, w, add_to_weights = -0.1)
## End(Not run)

transport documentation built on Sept. 17, 2024, 1:08 a.m.