Circular String Art

stcircle() creates a circular String Art figure by placing equally spaced pegs on a circle and connecting each peg to another peg using an additive modular step.

Usage

stcircle(
  n = 30,
  k = 5,
  col = "blue",
  lwd = 1,
  plot = TRUE,
  show_points = TRUE,
  show_labels = FALSE,
  verbose = FALSE,
  r = 1,
  show_strings = TRUE,
  template = FALSE,
  point_col = "black",
  point_cex = 0.8,
  point_pch = 19,
  point_bg = "white",
  label_cex = 0.7,
  label_col = "black",
  border_col = "grey50",
  border_lwd = 1,
  main = NULL
)

Arguments

n

Integer. Number of pegs on the circle. Defaults to 30.

k

Integer. Additive modular step used to define the connections. Defaults to 5.

col

String color used to draw the segments. Defaults to "blue".

lwd

Positive number. Line width of the string segments. Defaults to 1.

plot

Logical. If TRUE, the figure is drawn using base R graphics.

show_points

Logical. If TRUE, the pegs are shown.

show_labels

Logical. If TRUE, peg labels are shown.

verbose

Logical. If TRUE, an audit summary is printed to the console.

r

Positive number. Radius of the circle. Defaults to 1.

show_strings

Logical. If TRUE, string segments are drawn.

template

Logical. If TRUE, only the peg template is drawn. This sets show_strings = FALSE and show_points = TRUE internally.

point_col

Color of the pegs.

point_cex

Positive number. Size of the pegs.

point_pch

Plotting symbol used for the pegs.

point_bg

Background color of the pegs when the plotting symbol allows filling.

label_cex

Positive number. Size of the peg labels.

label_col

Color of the peg labels.

border_col

Color of the circular border.

border_lwd

Positive number. Line width of the circular border.

main

Character string. Plot title. If NULL, a default title is used.

Value

Invisibly returns a list with the following elements:

pegs

A data frame with columns index, x, and y.

connections

A data frame with columns connection_index, from, to, x_from, y_from, x_to, y_to, and length.

total_length

Total string length.

audit

Character vector with an audit summary.

meta

List with metadata about the construction.

Details

Pegs are numbered from 1 to n counterclockwise, starting at (r, 0). For each peg i, the connected peg is defined by

$$j = ((i + k - 1) \bmod n) + 1.$$

When gcd(n, k) = 1, the rule creates a single cycle passing through all pegs. When gcd(n, k) > 1, the figure is decomposed into independent cycles.

Examples

stcircle()


res <- stcircle(plot = FALSE)
res$total_length
#> [1] 30
head(res$connections)
#>   connection_index from to    x_from    y_from       x_to      y_to length
#> 1                1    1  6 1.0000000 0.0000000  0.5000000 0.8660254      1
#> 2                2    2  7 0.9781476 0.2079117  0.3090170 0.9510565      1
#> 3                3    3  8 0.9135455 0.4067366  0.1045285 0.9945219      1
#> 4                4    4  9 0.8090170 0.5877853 -0.1045285 0.9945219      1
#> 5                5    5 10 0.6691306 0.7431448 -0.3090170 0.9510565      1
#> 6                6    6 11 0.5000000 0.8660254 -0.5000000 0.8660254      1

stcircle(n = 24, k = 7, col = "firebrick", lwd = 1.2,
         show_points = TRUE, show_labels = TRUE)


stcircle(n = 24, k = 7, template = TRUE)