Generate a star polygon string art pattern

ststar() generates a classical star polygon {n/k} by placing n pegs on a circle and connecting each peg to the peg k positions ahead.

Usage

ststar(
  n = 5,
  k = 2,
  col = "blue",
  lwd = 1,
  plot = TRUE,
  show_points = TRUE,
  show_labels = FALSE,
  verbose = FALSE,
  radius = 1,
  rotate = pi/2,
  show_strings = TRUE,
  template = FALSE,
  draw_polygon = TRUE,
  border_col = "grey50",
  border_lwd = 1,
  point_col = "black",
  point_cex = 0.8,
  point_pch = 19,
  point_bg = "white",
  label_cex = 0.7,
  label_col = "black",
  bg = "white",
  main = NULL
)

Arguments

n: Integer. Number of pegs on the circle. Must be at least 3.
k: Integer. Star step. Must satisfy 1 <= k <= n - 1.
col: String color passed to graphics::segments().
lwd: Positive number. Line width used to draw the star.
plot: Logical. If TRUE, draws the figure.
show_points: Logical. If TRUE, draws the pegs.
show_labels: Logical. If TRUE, draws peg labels.
verbose: Logical. If TRUE, prints a short audit to the console.
radius: Positive number. Circle radius.
rotate: Numeric. Rotation angle in radians applied to the star.
show_strings: Logical. If TRUE, draws the star connections.
template: Logical. If TRUE, draws only the peg template, without star connections. This is equivalent to setting show_strings = FALSE and show_points = TRUE.
draw_polygon: Logical. If TRUE, draws the underlying regular polygon.
border_col: Polygon border color.
border_lwd: Positive number. Border line width.
point_col: Peg color.
point_cex: Positive number. Peg size.
point_pch: Plotting symbol used for pegs.
point_bg: Peg background color when applicable.
label_cex: Positive number. Label size.
label_col: Label color.
bg: Plot background color.
main: Optional plot title. If NULL, no title is displayed.

Value

Invisibly returns a list of class stringart_result with:

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: A character vector with audit information.
meta: A list with construction metadata.

Details

The star polygon uses the additive modular rule

to = ((from + k - 1) %% n) + 1.

The greatest common divisor gcd(n, k) determines the number of cycles. If gcd(n, k) = 1, the star is a single cycle. Otherwise, the construction decomposes into several independent cycles.

Examples

ststar()

ststar(n = 5, k = 2)
ststar(n = 7, k = 2)

ststar(n = 8, k = 3)

ststar(template = TRUE)