Generate a string art net from two rays

stnet() generates a string art net by placing pegs on two rays that share a common vertex and connecting corresponding peg positions. The construction generalizes the classical parabolic string art envelope by allowing the angle between the two supporting rays to vary.

Usage

stnet(
  n = 30,
  k = 1,
  col = "blue",
  lwd = 1,
  plot = TRUE,
  show_points = TRUE,
  show_labels = FALSE,
  verbose = FALSE,
  length1 = 1,
  length2 = 1,
  angle = pi/2,
  rotate = 0,
  show_strings = TRUE,
  template = FALSE,
  show_envelope = FALSE,
  envelope_col = "red",
  envelope_lwd = 1,
  envelope_lty = 2,
  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 on each ray. Must be at least 3.
k: Integer. Number of shifted sweeps used in the construction. Must satisfy 1 <= k <= n - 1. The classical net is obtained with k = 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.
length1: Positive number. Length of the first ray.
length2: Positive number. Length of the second ray.
angle: Numeric. Angle in radians from the first ray to the second ray. Must not be a multiple of pi.
rotate: Numeric. Rotation angle in radians applied to the whole net.
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.
show_envelope: Logical. If TRUE, draws the theoretical envelope of the basic construction.
envelope_col: Color used for the theoretical envelope.
envelope_lwd: Positive number. Line width used for the envelope.
envelope_lty: Line type used for the envelope.
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: Ray color.
border_lwd: Positive number. Ray 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, y, ray, and local_index.
connections: A data.frame with columns connection_index, from, to, x_from, y_from, x_to, y_to, length, sweep, offset, local_from, and local_to.
total_length: Total string length.
audit: A character vector with audit information.
meta: A list with construction metadata.

Details

The construction uses two rays with a common vertex. Pegs are placed uniformly along the first ray from the common vertex to the first endpoint and along the second ray from the second endpoint back to the common vertex.

For k = 1, the peg at local position i on the first ray is connected to the peg at local position i on the second ray. In oblique coordinates determined by the two rays, the theoretical envelope is given by

C(t) = t^2 A + (1 - t)^2 B,

where A and B are the endpoints of the two rays and 0 <= t <= 1.

For k > 1, the function adds shifted sweeps of the same construction, producing denser string art nets.

Examples

stnet()


res <- stnet(plot = FALSE)
head(res$pegs)
#>   index          x y   ray local_index
#> 1     1 0.00000000 0 first           1
#> 2     2 0.03448276 0 first           2
#> 3     3 0.06896552 0 first           3
#> 4     4 0.10344828 0 first           4
#> 5     5 0.13793103 0 first           5
#> 6     6 0.17241379 0 first           6
head(res$connections)
#>   connection_index from to     x_from y_from         x_to      y_to    length
#> 1                1    1 31 0.00000000      0 6.123234e-17 1.0000000 1.0000000
#> 2                2    2 32 0.03448276      0 5.912088e-17 0.9655172 0.9661328
#> 3                3    3 33 0.06896552      0 5.700942e-17 0.9310345 0.9335853
#> 4                4    4 34 0.10344828      0 5.489796e-17 0.8965517 0.9025002
#> 5                5    5 35 0.13793103      0 5.278650e-17 0.8620690 0.8730337
#> 6                6    6 36 0.17241379      0 5.067504e-17 0.8275862 0.8453552
#>   sweep offset local_from local_to
#> 1     1      0          1        1
#> 2     1      0          2        2
#> 3     1      0          3        3
#> 4     1      0          4        4
#> 5     1      0          5        5
#> 6     1      0          6        6
res$total_length
#> [1] 24.54251

stnet(n = 40, k = 1, angle = pi / 2, col = "steelblue")

stnet(n = 40, k = 3, angle = 2 * pi / 3, col = "firebrick", lwd = 0.7)

stnet(show_envelope = TRUE)

stnet(template = TRUE)