transport (version 0.15-4)

plot_apollonius: 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.

Author

Valentin Hartmann (most of the code)
Dominic Schuhmacher (R-port)

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.

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

if (FALSE) {
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)}