Package 'Apollonius'

Apollonius diagram and Apollonius graph

Description

Computation of the Apollonius diagram and the Apollonius graph of some weighted 2D points. The Apollonius graph is the dual of the Apollonius diagram. It is also called the additively weighted Voronoï diagram.

Usage

Apollonius(sites, radii, tmax = 30, nsegs = 100L, nrays = 300L)

Arguments

sites	the 2D points, a numeric matrix with two columns (one point per row)
radii	the weights, a numeric vector of length equal to the number of points (i.e. the number of rows of sites)
tmax	a positive number passed to gyroray, controlling the length of the infinite edges (i.e. the hyperbolic rays) of the Apollonius graph
nsegs	a positive integer, the desired number of points of each finite edge of the Apollonius graph
nrays	a positive integer, the desired number of points of each infinite edge of the Apollonius graph

Details

See the CGAL documentation.

Value

A list with two fields diagram and graph. The diagram field is a list providing the sites and the faces of the Apollonius diagram. The graph field is a list providing the sites and the edges of the Apollonius graph.

Examples

library(Apollonius)
sites <- rbind(
  c(0, 0),
  c(4, 1),
  c(2, 4),
  c(7, 4),
  c(8, 0),
  c(5, -2),
  c(-4, 4),
  c(-2, -1),
  c(11, 4),
  c(11, 0)
)
radii <- c(1, 1.5, 1.25, 2, 1.75, 0.5, 0.4, 0.6, 0.7, 0.3)
apo <- Apollonius(sites, radii)
opar <- par(mar = c(4, 4, 1, 1))
plotApolloniusGraph(apo, xlab = "x", ylab = "y")
par(opar)

# Example of a non-valid graph ####
library(Apollonius)
sites <- rbind(
  c(-1, -1),
  c(-1, 1),
  c(1, 1),
  c(1, -1),
  c(0, 0)
)
angle_ <- seq(0, 2*pi, length.out = 13L)[-1L]
circle <- cbind(2 * cos(angle_), 2 * sin(angle_))
sites <- rbind(sites, circle)
radii <- c(rep(2, 5), rep(1, 12))
## Not run: apo <- Apollonius(sites, radii)

---

Plot Apollonius graph

Description

Plot an Apollonius graph.

Usage

plotApolloniusGraph(
  apo,
  limits = NULL,
  circles = TRUE,
  fill = TRUE,
  centers = TRUE,
  colors = "distinct",
  distinctArgs = list(seedcolors = c("#ff0000", "#00ff00", "#0000ff")),
  randomArgs = list(hue = "random", luminosity = "dark"),
  ...
)

Arguments

apo	an output of Apollonius
limits	either NULL or a vector of length two passed to the arguments xlim and ylim of plot; if NULL, automatic limits are calculated
circles	Boolean, whether to plot the original sites as circles with the given radii
fill	Boolean, whether to fill the circles if circles=TRUE or to plot only their border
centers	when circles=TRUE and fill=FALSE, whether to plot the centers of the circles
colors	a character string controlling the colors of the sites; "random" to get multiple colors with randomColor, "distinct" to get multiple colors with createPalette, or a color name or a hexadecimal color code
distinctArgs	if colors = "distinct", a list of arguments passed to createPalette
randomArgs	if colors = "random", a list of arguments passed to randomColor
...	arguments passed to plot, such as xlab and ylab

Value

No returned value, called for plotting.

Examples

library(Apollonius)
sites <- rbind(
  c(0, 0),
  c(4, 1),
  c(2, 4),
  c(7, 4),
  c(8, 0),
  c(5, -2),
  c(-4, 4),
  c(-2, -1),
  c(11, 4),
  c(11, 0)
)
radii <- c(1, 1.5, 1.25, 2, 1.75, 0.5, 0.4, 0.6, 0.7, 0.3)
apo <- Apollonius(sites, radii)
opar <- par(mar = c(3, 3, 1, 1))
plotApolloniusGraph(
  apo, fill = FALSE, colors = "random", xlab = NA, ylab = NA
)
par(opar)

---