Generate a triangular string art pattern — sttriangle • stringArt

sttriangle() generates a string art pattern on the boundary of an equilateral triangle. Pegs are distributed uniformly along the triangle perimeter and connected using an additive modular rule.

Usage

sttriangle(
  n = 30,
  k = 7,
  col = "blue",
  lwd = 1,
  plot = TRUE,
  show_points = TRUE,
  show_labels = FALSE,
  verbose = FALSE,
  side = 2,
  rotate = 0,
  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,
  bg = "white",
  main = NULL
)

Arguments

n: Integer. Number of pegs placed along the triangle boundary. Must be at least 3.
k: Integer. Additive modular step used in the connection rule. Must satisfy 1 <= k <= n - 1.
col: String color passed to graphics::segments().
lwd: Positive number. Line width used to draw the strings.
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.
side: Positive number. Side length of the equilateral triangle.
rotate: Numeric. Rotation angle in radians applied to the whole figure.
show_strings: Logical. If TRUE, draws the string connections.
template: Logical. If TRUE, draws only the peg template, without string connections. This is equivalent to setting show_strings = FALSE and show_points = TRUE.
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.
border_col: Triangle border color.
border_lwd: Positive number. Triangle border line width.
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, including the triangle vertices.

Details

The triangle is centered at the origin using its centroid. The pegs are placed uniformly along the perimeter in counterclockwise order.

The additive modular connection rule is:

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

When gcd(n, k) = 1, the modular rule forms a single cycle through all pegs. When gcd(n, k) > 1, the construction decomposes into independent cycles.

Examples

sttriangle()


res <- sttriangle(plot = FALSE)
head(res$pegs)
#>   index    x          y
#> 1     1 -1.0 -0.5773503
#> 2     2 -0.8 -0.5773503
#> 3     3 -0.6 -0.5773503
#> 4     4 -0.4 -0.5773503
#> 5     5 -0.2 -0.5773503
#> 6     6  0.0 -0.5773503
head(res$connections)
#>   connection_index from to x_from     y_from x_to       y_to    length
#> 1                1    1  8   -1.0 -0.5773503  0.4 -0.5773503 1.4000000
#> 2                2    2  9   -0.8 -0.5773503  0.6 -0.5773503 1.4000000
#> 3                3    3 10   -0.6 -0.5773503  0.8 -0.5773503 1.4000000
#> 4                4    4 11   -0.4 -0.5773503  1.0 -0.5773503 1.4000000
#> 5                5    5 12   -0.2 -0.5773503  0.9 -0.4041452 1.1135529
#> 6                6    6 13    0.0 -0.5773503  0.8 -0.2309401 0.8717798
res$total_length
#> [1] 33.03866

sttriangle(n = 30, k = 7, side = 2, col = "blue", lwd = 1)
sttriangle(n = 18, k = 5, show_points = TRUE, show_labels = TRUE)

sttriangle(template = TRUE)