split polygon art

Intro

• Documenting my attempt at recreating the art I saw in this tweet with R.
• Then trying to further develop the idea
• This code is not written for speed or efficiency - using spatial libraries is certainly overkill, but it’s the first way I prototyped the code and I haven’t felt the need to go back and change it!

library(tidyverse)
library(sf)
library(lwgeom)
library(wesanderson)

Function

• Psuedo code for function
  • Compute the (x,y) vertices of a regular polygon by rotating a line of length radius through equal angle steps about the point (ox, oy)
  • Convert the vertices to an {sf} POLYGON
  • Compute a random point inside the polygon if px and py is not provided
  • Create an {sf} MULTILINESTRING containing a line from the point (px, py) to each vertex of the regular polygon
  • Use the MULTILINESTRINGS to plit the regular polygon into sub polygons

#' Return the {sf} polygons
#'
#' @param n_sides number of sides of regular polygon
#' @param offset_degrees offset angle for orientation of regular polygon
#' @param ox origin of regular polygon x coordinate
#' @param oy origin of regular polygon y coordinate
#' @param radius radius of or regular polygon (distance from origin to polygon vertices)
#' @param px origin point for the splitting lines x coordinate
#' @param py origin point for the splitting lines y coordinate
split_poly <- function(n_sides, offset_degrees, ox, oy, radius, px = NULL, py = NULL){

    # Create polygon angles and vertex xy coords
    a_step <- (2*pi)/n_sides
    a <- seq(pi/2 + offset_degrees*(pi/180), by = a_step, l = n_sides)
    x <- ox + cos(a) * radius
    y <- oy + sin(a) * radius
    
    # Create POLYGON
    # Close polygon by making the last point the same as the first point
    shape_polygon <- st_polygon(x = list(matrix(c(c(x, x[1]), c(y, y[1])), ncol = 2)))

    # Compute a random point inside the polygon if no px or py is provided
    if(is.null(px) || is.null(py)){
        p_xy <- st_coordinates(st_sample(shape_polygon, 1))
        px <- p_xy[1,1]
        py <- p_xy[1,2]}

    # Create MULTILINESTRING from each polygon vertex to the random point
    lines <-
        st_multilinestring(
            lapply(
                X = seq_along(a), 
                FUN = function(b) matrix(c(c(x[b], px), c(y[b], py)), ncol = 2)))
    
    # Split the polygon based on the MULTILINESTRING
    lwgeom::st_split(shape_polygon, lines) |> st_collection_extract("POLYGON")}

Explore some different setups

• Create uniform square grid of x and y coordinates for the regular polygon centers
• Add values for the regular polygon number of sides, offset and radius against each grid point
• Run split_poly() on each point
• Assign a colour to each if the sub polygons created from each regular polygon
  • Use the wesanderson palette Zissou1
• Plot the result

set.seed(1)
crossing(ox = 1:5, oy = 1:5) |> 
    mutate(
        n_sides = 4,
        offset_degrees = 45,
        radius = 0.55,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy, 
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(col = sample(wes_palettes$Zissou1, size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = NA)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))

• Choose colours from any of the wesanderson palettes

set.seed(4)
crossing(ox = 1:5, oy = 1:5) |> 
    mutate(
        n_sides = 4,
        offset_degrees = 45,
        radius = 0.55,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy, 
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(col = sample(unlist(wes_palettes), size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = NA)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))

• Larger grid and vary the regular polygon radius value based on position

set.seed(2)
crossing(ox = 1:10, oy = 1:10) |> 
    mutate(
        n_sides = 4,
        offset_degrees = 45,
        radius = scales::rescale(sqrt(abs(ox - 5.5)^2 + abs(oy - 5.5)^2), c(0.5, 0.3)),
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy, 
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(col = sample(wes_palettes$Darjeeling2, size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = 1)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = sample(unlist(wes_palettes), 1)))

• Gradually change the offset angle across the image

set.seed(1)
crossing(ox = 1:5, oy = 1:5) |> 
    mutate(
        n_sides = 3,
        offset_degrees = seq(0, 180, l = n()),
        radius = 0.5,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy, 
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(
        a = st_area(g),
        col = sample(wes_palettes$Rushmore, size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = 1)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))

• Random integer (3:5) number of sides for regular polygons

set.seed(1)
crossing(oy = 1:15, ox = 1:15) |> 
    mutate(
        n_sides = sample(3:5, size = n(), replace = TRUE), 
        offset_degrees = runif(n(), 0, 360),
        radius = scales::rescale(sqrt(abs(ox - 4)^2 + abs(oy - 4)^2), c(0.5, 0.1)),
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy, 
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(
        a = st_area(g),
        col = sample(wes_palettes$Moonrise3, size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = 1)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))

• Use non integer number of sides

set.seed(1)
crossing(oy = 1:7, ox = 1:7) |> 
    mutate(
        n_sides = seq(3, 4, l = n()), 
        offset_degrees = seq(0, 90, l = n()),
        radius = 0.45,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy, 
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(
        a = st_area(g),
        col = sample(unlist(wes_palettes), size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = 1)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))

• All shapes using the same px/py point

set.seed(1)
crossing(oy = 1:19, ox = 1:19) |> 
    mutate(
        n_sides = 4, 
        offset_degrees = 45,
        radius = 0.45,
        px = 10,
        py = 10,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy,
                    px = px,
                    py = py,
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(
        a = st_area(g),
        col = sample(unlist(wes_palettes), size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = NA)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))

set.seed(1)
crossing(oy = 1:19, ox = 1:19) |> 
    mutate(
        n_sides = 4, 
        offset_degrees = seq(0, 90, l=n()),
        radius = 0.45,
        px = 10,
        py = 10,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy,
                    px = px,
                    py = py,
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(
        a = st_area(g),
        col = sample(unlist(wes_palettes), size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = NA)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))

set.seed(1)
crossing(oy = 1:7, ox = 1:7) |> 
    mutate(
        n_sides = 4, 
        offset_degrees = 45,
        radius = 0.45,
        px = 3,
        py = 3.2,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy,
                    px = px,
                    py = py,
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(
        a = st_area(g),
        col = sample(unlist(wes_palettes), size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = 1)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))

• Vary the px/py point across the shapes

set.seed(1)
crossing(oy = 1:7, ox = 1:7) |> 
    mutate(
        n_sides = 4, 
        offset_degrees = 45,
        radius = 0.45,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy,
                    px = ox + scales::rescale(ox, to = c(-0.2, 0.2)),
                    py = oy + scales::rescale(oy, to = c(-0.2, 0.2)),
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(
        a = st_area(g),
        col = sample(wes_palettes$Zissou1, size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = 1)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))

crossing(oy = 1:10, ox = 1:10) |> 
    mutate(
        n_sides = 4, 
        offset_degrees = 45,
        radius = 0.45,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy,
                    px = 5.5 + cos(seq(0, 2*pi, l= n()))*2,
                    py = 5.5 + sin(seq(0, 2*pi, l= n()))*2,
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(
        a = st_area(g),
        col = sample(wes_palettes$Zissou1, size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = 1)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))+
    theme_bw()

• Approximate circles with high number of regular polygon sides
• Move the px/py point and colour the sub polygons by their area

set.seed(1)
crossing(oy = 1:7, ox = 1:7) |> 
    mutate(
        n_sides = 100, 
        offset_degrees = 0,
        radius = 0.45,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy,
                    px = ox + scales::rescale(ox, to = c(-0.2, 0.2)),
                    py = oy + scales::rescale(oy, to = c(-0.2, 0.2)),
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(a = st_area(g)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = a), col = NA)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    scale_fill_viridis_c(option = "mako")+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey5"))

• A nasty look at hexagons using st_make_grid()

set.seed(1)

nx <- 10
ny <- 10

hex_centers <-
    sf::st_make_grid(
    x = st_polygon(list(matrix(c(0, 0, nx, nx, 0, 0, ny, ny, 0, 0), ncol = 2))),
    n = c(nx, ny), 
    what = "centers",
    square = FALSE, 
    flat_topped = FALSE) |>
    st_coordinates() |> 
    as_tibble() |> 
    rename(ox = X, oy = Y)

hex_polys <-
    sf::st_make_grid(
    x = st_polygon(list(matrix(c(0, 0, nx, nx, 0, 0, ny, ny, 0, 0), ncol = 2))),
    n = c(nx, ny),
    square = FALSE, 
    flat_topped = FALSE)

f <- 1
hex_centers |>
    mutate(
        n_sides = 6,
        offset_degrees = 0,
        radius = (1/sqrt(3))*f,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy, 
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(col = sample(wes_palettes |> unlist(), size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = NA) +
    # geom_sf(data = hex_polys, fill = NA, col = 1) +
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))

f <- 0.85
hex_centers |>
    mutate(
        n_sides = 6,
        offset_degrees = seq(0, 45, l=n()),
        radius = (1/sqrt(3))*f,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy, 
                    px = 2, 
                    py = 2,
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(col = sample(wes_palettes |> unlist(), size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = NA) +
    # geom_sf(data = hex_polys, fill = NA, col = 1) +
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))

• Some additonal experimentation with triangles

set.seed(4)
crossing(ox = 1:9, oy = 1:9) |> 
    mutate(
        n_sides = 3,
        offset_degrees = rep(c(0, 180), length.out = n()),
        radius = 0.45,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy, 
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(col = sample(unlist(wes_palettes), size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = 1)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))

set.seed(4)
crossing(ox = 1:9, oy = 1:9) |> 
    mutate(
        n_sides = 3,
        offset_degrees = rep(c(0, 90, 180, 270), length.out = n()),
        radius = 0.45,
        g = pmap(
            .l =
                list(
                    ox = ox, 
                    oy = oy, 
                    n_sides = n_sides, 
                    offset_degrees = offset_degrees,
                    radius = radius),
            .f = split_poly)) |> 
    unnest(cols = g) |>
    group_by(ox, oy) |> 
    mutate(col = sample(unlist(wes_palettes), size = n(), replace = FALSE)) |> 
    st_as_sf() |> 
    ggplot()+
    geom_sf(aes(fill = I(col)), col = 1)+
    scale_x_continuous(expand = expansion(add = c(1,1)))+
    scale_y_continuous(expand = expansion(add = c(1,1)))+
    theme_void()+
    theme(
        legend.position = "",
        panel.background = element_rect(color = NA, fill = "grey95"))