Awesome
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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$Zissou1, size = n(), replace = FALSE)) |>
st_as_sf() |>
ggplot()+
geom_sf(aes(fill = I(col)), col = NA)+
scale_x_continuous(expand = expansion(add = c(1,1)))+
scale_y_continuous(expand = expansion(add = c(1,1)))+
theme_void()+
theme(
legend.position = "",
panel.background = element_rect(color = NA, fill = "grey95"))
<img src="README_files/figure-gfm/unnamed-chunk-4-1.png" width="65%" />
- Choose colours from any of the
wesanderson palettes
set.seed(4)
crossing(ox = 1:5, oy = 1:5) |>
mutate(
n_sides = 4,
offset_degrees = 45,
radius = 0.55,
g = pmap(
.l =
list(
ox = ox,
oy = oy,
n_sides = n_sides,
offset_degrees = offset_degrees,
radius = radius),
.f = split_poly)) |>
unnest(cols = g) |>
group_by(ox, oy) |>
mutate(col = sample(unlist(wes_palettes), size = n(), replace = FALSE)) |>
st_as_sf() |>
ggplot()+
geom_sf(aes(fill = I(col)), col = NA)+
scale_x_continuous(expand = expansion(add = c(1,1)))+
scale_y_continuous(expand = expansion(add = c(1,1)))+
theme_void()+
theme(
legend.position = "",
panel.background = element_rect(color = NA, fill = "grey95"))
<img src="README_files/figure-gfm/unnamed-chunk-5-1.png" width="65%" />
- Larger grid and vary the regular polygon radius value based on
position
set.seed(2)
crossing(ox = 1:10, oy = 1:10) |>
mutate(
n_sides = 4,
offset_degrees = 45,
radius = scales::rescale(sqrt(abs(ox - 5.5)^2 + abs(oy - 5.5)^2), c(0.5, 0.3)),
g = pmap(
.l =
list(
ox = ox,
oy = oy,
n_sides = n_sides,
offset_degrees = offset_degrees,
radius = radius),
.f = split_poly)) |>
unnest(cols = g) |>
group_by(ox, oy) |>
mutate(col = sample(wes_palettes$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)))
<img src="README_files/figure-gfm/unnamed-chunk-6-1.png" width="65%" />
- 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$Rushmore, size = n(), replace = FALSE)) |>
st_as_sf() |>
ggplot()+
geom_sf(aes(fill = I(col)), col = 1)+
scale_x_continuous(expand = expansion(add = c(1,1)))+
scale_y_continuous(expand = expansion(add = c(1,1)))+
theme_void()+
theme(
legend.position = "",
panel.background = element_rect(color = NA, fill = "grey95"))
<img src="README_files/figure-gfm/unnamed-chunk-7-1.png" width="65%" />
- Random integer (3:5) number of sides for regular polygons
set.seed(1)
crossing(oy = 1:15, ox = 1:15) |>
mutate(
n_sides = sample(3:5, size = n(), replace = TRUE),
offset_degrees = runif(n(), 0, 360),
radius = scales::rescale(sqrt(abs(ox - 4)^2 + abs(oy - 4)^2), c(0.5, 0.1)),
g = pmap(
.l =
list(
ox = ox,
oy = oy,
n_sides = n_sides,
offset_degrees = offset_degrees,
radius = radius),
.f = split_poly)) |>
unnest(cols = g) |>
group_by(ox, oy) |>
mutate(
a = st_area(g),
col = sample(wes_palettes$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"))
<img src="README_files/figure-gfm/unnamed-chunk-8-1.png" width="65%" />
- 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"))
<img src="README_files/figure-gfm/unnamed-chunk-9-1.png" width="65%" />
- 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"))
<img src="README_files/figure-gfm/unnamed-chunk-10-1.png" width="65%" />
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"))
<img src="README_files/figure-gfm/unnamed-chunk-10-2.png" width="65%" />
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"))
<img src="README_files/figure-gfm/unnamed-chunk-10-3.png" width="65%" />
- 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$Zissou1, size = n(), replace = FALSE)) |>
st_as_sf() |>
ggplot()+
geom_sf(aes(fill = I(col)), col = 1)+
scale_x_continuous(expand = expansion(add = c(1,1)))+
scale_y_continuous(expand = expansion(add = c(1,1)))+
theme_void()+
theme(
legend.position = "",
panel.background = element_rect(color = NA, fill = "grey95"))
<img src="README_files/figure-gfm/unnamed-chunk-11-1.png" width="65%" />
crossing(oy = 1:10, ox = 1:10) |>
mutate(
n_sides = 4,
offset_degrees = 45,
radius = 0.45,
g = pmap(
.l =
list(
ox = ox,
oy = oy,
px = 5.5 + cos(seq(0, 2*pi, l= n()))*2,
py = 5.5 + sin(seq(0, 2*pi, l= n()))*2,
n_sides = n_sides,
offset_degrees = offset_degrees,
radius = radius),
.f = split_poly)) |>
unnest(cols = g) |>
group_by(ox, oy) |>
mutate(
a = st_area(g),
col = sample(wes_palettes$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()
<img src="README_files/figure-gfm/unnamed-chunk-11-2.png" width="65%" />
- 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"))
<img src="README_files/figure-gfm/unnamed-chunk-12-1.png" width="65%" />
- 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"))
<img src="README_files/figure-gfm/unnamed-chunk-13-1.png" width="65%" />
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"))
<img src="README_files/figure-gfm/unnamed-chunk-13-2.png" width="65%" />
- 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"))
<img src="README_files/figure-gfm/unnamed-chunk-14-1.png" width="65%" />
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"))
<img src="README_files/figure-gfm/unnamed-chunk-14-2.png" width="65%" />