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Documenting an idea I had recently (probably in a dream).
- Visualise a wall of analogue clocks showing random times.
- Where the clock hands meet, join them together and differentiate them from the others, probably by colour
- Does it make cool connected patterns across the wall of clocks?
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I’m no longer developing this - but wanted to document where I got to and share it for any potential future use!
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As per usual, start by adding
{tidyverse}and{sf}to the search path
library(tidyverse)
library(sf)- A function that returns a LINESTRING representation of the hands of a clock given the hour and minutes
#' Return hour and minute hands as a LINESTRING
#'
#' @param h Hour (1-12)
#' @param m Minute (1-60)
#' @param x0 x-origin of clock (default = 0)
#' @param y0 y-origin of clock (default = 0)
#' @param h_length Multiplicative factor for hour hand length (default = 0.5)
#' @param m_length Multiplicative factor for minute hand length (default = 0.5)
clock_hands <- function(h, m, x0=0, y0=0, h_length=0.5, m_length=0.5){
# Compute angle (fraction of 2*pi) for h and m
# Minute angle is 90 degrees minus the minutes/60 proportion of 2pi
m_a <- (pi/2) - ((m/60) * (2*pi))
# Hour angle is 90 degrees minus the hour/12 proportion of 2pi, minus the minutes/60 proportion of 2pi/12
h_a <- (pi/2) - ((h/12) * (2*pi)) - ((m/60)*((2*pi)/12))
# Construct LINESTRING from the three coordinates
# End of hour hand - clock origin - end of minute hand
st_linestring(matrix(c(x0 + h_length*cos(h_a), y0 + h_length*sin(h_a),
x0, y0,
x0 + m_length*cos(m_a), y0 + m_length*sin(m_a)),
ncol=2, byrow = TRUE)) %>%
st_geometry()
}- Run some visual tests on the
clock_hands()code
map2(sample(1:12, 9),
sample(1:60, 9),
~clock_hands(.x, .y, h_length = 0.6, m_length = 0.9) %>%
ggplot() +
geom_polygon(data = tibble(x = cos(seq(0,2*pi,l=100)),
y = sin(seq(0,2*pi,l=100))),
aes(x, y), fill=NA, col=1)+
geom_point(data = tibble(x = cos(seq(0,2*pi,l=13)),
y = sin(seq(0,2*pi,l=13))),
aes(x, y), fill=NA, col=1)+
geom_sf() +
labs(subtitle = paste0(.x,":",.y))+
theme_void()) %>%
patchwork::wrap_plots()
- Create a grid of random clock faces using
clock_hands()
nx <- 20
ny <- 20
set.seed(1234)
clocks <-
crossing(x=1:nx, y=1:ny) %>%
mutate(h = sample(1:12, size = nrow(.), replace = TRUE),
m = sample(1:60, size = nrow(.), replace = TRUE)) %>%
mutate(g = pmap(list(x=x, y=y, h=h, m=m), clock_hands)) %>%
unnest(g) %>%
st_as_sf()- Buffer the clock hands and wrangle to individual polygons
my_buffer <- 0.02
clock_polys <-
clocks %>%
st_buffer(my_buffer, endCapStyle = "ROUND") %>%
st_union() %>%
st_cast("POLYGON") %>%
st_as_sf() %>%
mutate(a = st_area(x))- Create clock face circles to add to the visualisation.
- I make them as buffered LINESTRING so that they always render at the same size as the clock hands
a <- seq(0, 2*pi, l=200)
circles <-
clocks %>%
as_tibble() %>%
select(x, y) %>%
mutate(circle = map2(x, y,
~st_linestring(matrix(c(.x + cos(a)*0.5,
.y + sin(a)*0.5),
ncol = 2)) %>%
st_geometry())) %>%
unnest(circle) %>%
st_as_sf() %>%
st_buffer(my_buffer)- Visualise
ggplot() +
geom_sf(data = circles, fill=1, col=NA)+
geom_sf(data = clock_polys, aes(fill = a), col=NA)+
scale_fill_viridis_c(option = "plasma")+
theme_void()+
theme(legend.position = "",
panel.background = element_rect(fill="grey20", color=NA))
- Same idea but on a hexagonal grid rather than square
set.seed(1234)
# Hexagon size (centre to point)
s <- 0.5/cos(pi/6)
# Width and height
w <- sqrt(3) * s
h <- 2 * s
# Distance on grid
vd <- h*(3/4)
hd <- w
clocks <-
crossing(x = seq(from = 1, by = hd, l = nx),
y = seq(from = 1, by = vd, l = ny)) %>%
mutate(shove = rep(c(TRUE, FALSE), length.out = nrow(.)),
x = case_when(shove ~ x+(hd/2), TRUE ~ x)) %>%
mutate(h = sample(1:12, size = nrow(.), replace = TRUE),
m = sample(1:59, size = nrow(.), replace = TRUE)) %>%
mutate(g = pmap(list(x=x, y=y, h=h, m=m), clock_hands)) %>%
unnest(g) %>%
st_as_sf()
my_buffer <- 0.02
clock_polys <-
clocks %>%
st_buffer(my_buffer, endCapStyle = "ROUND") %>%
st_union() %>%
st_cast("POLYGON") %>%
st_as_sf() %>%
mutate(a = st_area(x))
a <- seq(0, 2*pi, l=200)
circles <-
clocks %>%
as_tibble() %>%
select(x, y) %>%
mutate(circle = map2(x, y,
~st_linestring(matrix(c(.x + cos(a)*0.5,
.y + sin(a)*0.5),
ncol = 2)) %>%
st_geometry())) %>%
unnest(circle) %>%
st_as_sf()
ggplot() +
geom_sf(data = circles %>% st_buffer(my_buffer), fill=1, col=NA)+
geom_sf(data = clock_polys, aes(fill = a), col=NA)+
scale_fill_viridis_c(option = "plasma")+
theme_void()+
theme(legend.position = "",
panel.background = element_rect(fill="grey20", color=NA))
- Animation using the hexagonal grid approach
- All clocks start at 12:00 and run at random rates
- Code not run in this .Rmd file. The individual images are saved and animated outside of the R session with ImageJ
nx <- 8
ny <- 8
my_buffer <- 0.04
baseline_area <-
clock_hands(12,30) %>%
st_buffer(my_buffer, endCapStyle = "ROUND") %>%
st_area()
# Hexagon size (centre to point)
s <- 0.5/cos(pi/6)
# Width and height
w <- sqrt(3) * s
h <- 2 * s
# Distance on grid
vd <- h*(3/4)
hd <- w
oclocks <-
crossing(x = seq(from = 1, by = hd, l = nx),
y = seq(from = 1, by = vd, l = ny)) %>%
mutate(shove = rep(c(TRUE, FALSE), length.out = nrow(.)),
x = case_when(shove ~ x+(hd/2), TRUE ~ x)) %>%
# Define original starting time of each clock
# and its rate and direction (negative is back in time!)
mutate(
om = 0,
rate = runif(nrow(.), min = 0.0001, 2)
) %>%
mutate(h = floor(om/60),
m = om - (h*60)) %>%
mutate(g = pmap(list(x=x, y=y, h=h, m=m), clock_hands)) %>%
unnest(g) %>%
st_as_sf()
a <- seq(0, 2*pi, l=200)
circles <-
oclocks %>%
as_tibble() %>%
select(x, y) %>%
mutate(circle = map2(x, y,
~st_linestring(matrix(c(.x + cos(a)*0.5,
.y + sin(a)*0.5),
ncol = 2)) %>%
st_geometry())) %>%
unnest(circle) %>%
st_as_sf() %>%
st_buffer(my_buffer/2)
for(i in 1:(60*8)){
clocks <-
oclocks %>%
mutate(om = om + ((i-1)*rate)) %>%
mutate(h = floor(om/60),
m = om - (h*60)) %>%
mutate(g = pmap(list(x=x, y=y, h=h, m=m), clock_hands)) %>%
unnest(g) %>%
st_as_sf()
clock_polys <-
clocks %>%
st_buffer(my_buffer, endCapStyle = "ROUND") %>%
st_union() %>%
st_cast("POLYGON") %>%
st_as_sf() %>%
mutate(a = st_area(x))
ggplot() +
geom_sf(data = circles, fill=1, col=NA)+
geom_sf(data = clock_polys, aes(fill = a), col=NA)+
scale_fill_viridis_c(option = "plasma",
begin = 0.1,
limits=c(0, baseline_area*5),
na.value = "green")+
scale_x_continuous(limits = c(0, 9.5))+
scale_y_continuous(limits = c(0, 8.06))+
theme_void()+
theme(legend.position = "",
panel.background = element_rect(fill="grey20", color=NA))
ggsave(paste0("animation/", i, ".png"), width=2.5, height=2.5, bg = "grey20")
}
- Animation using the hexagonal grid approach
- All clocks start at a random time and run at random rates
- Stop clocks when they intersect with another clock
- Code not run in this .Rmd file. The individual images are saved and animated outside of the R session with ImageJ
nx <- 8
ny <- 8
my_buffer <- 0.04
baseline_area <-
clock_hands(12,30) %>%
st_buffer(my_buffer, endCapStyle = "ROUND") %>%
st_area()
# Hexagon size (centre to point)
s <- 0.5/cos(pi/6)
# Width and height
w <- sqrt(3) * s
h <- 2 * s
# Distance on grid
vd <- h*(3/4)
hd <- w
oclocks <-
crossing(x = seq(from = 1, by = hd, l = nx),
y = seq(from = 1, by = vd, l = ny)) %>%
mutate(shove = rep(c(TRUE, FALSE), length.out = nrow(.)),
x = case_when(shove ~ x+(hd/2), TRUE ~ x)) %>%
# Define original starting time of each clock
# and its rate and direction (negative is back in time!)
mutate(
om = runif(nrow(.), 0, 60*12),
rate = runif(nrow(.), min = 0.0001, 2)
) %>%
mutate(h = floor(om/60),
m = om - (h*60)) %>%
mutate(g = pmap(list(x=x, y=y, h=h, m=m), clock_hands)) %>%
unnest(g) %>%
st_as_sf()
a <- seq(0, 2*pi, l=200)
circles <-
oclocks %>%
as_tibble() %>%
select(x, y) %>%
mutate(circle = map2(x, y,
~st_linestring(matrix(c(.x + cos(a)*0.5,
.y + sin(a)*0.5),
ncol = 2)) %>%
st_geometry())) %>%
unnest(circle) %>%
st_as_sf() %>%
st_buffer(my_buffer/2)
for(i in 1:(60*8)){
clocks <-
oclocks %>%
mutate(om = om + (ifelse(i==1, 0, 1)*rate)) %>%
mutate(h = floor(om/60),
m = om - (h*60)) %>%
mutate(g = pmap(list(x=x, y=y, h=h, m=m), clock_hands)) %>%
unnest(g) %>%
st_as_sf()
clock_polys <-
clocks %>%
st_buffer(my_buffer, endCapStyle = "ROUND")
# For clock hands that intersect - set their rate to 0
oclocks$rate[(clock_polys %>% st_intersects() %>% lengths()) > 1] <- 0
# Update original minutes(om) with the time when they intersected
oclocks$om <- (clocks$h*60) + clocks$m
clock_polys <-
clock_polys %>%
st_union() %>%
st_cast("POLYGON") %>%
st_as_sf() %>%
mutate(a = st_area(x))
ggplot() +
geom_sf(data = circles, fill=1, col=NA)+
geom_sf(data = clock_polys, aes(fill = a), col=NA)+
scale_fill_viridis_c(option = "plasma",
begin = 0.1,
limits=c(0, baseline_area*7),
na.value = "green")+
scale_x_continuous(limits = c(0, 9.5))+
scale_y_continuous(limits = c(0, 8.06))+
theme_void()+
theme(legend.position = "",
panel.background = element_rect(fill="grey20", color=NA))
ggsave(paste0("animation2/", i, ".png"), width=2.5, height=2.5, bg="grey20")
}