R - Plotting Hexagon Tessellations

Question

I'd like to generate some square plots that have arrays of hexagons inside of them, like drawn here. I'd like to plot both regular (geometrically regular) and abnormal hexagon tessellations, so I don't think tools from the "sp" package will work.

Below is my attempt at a regular hexagon tesselation using owin and plot.

---

library(maptools)
library(spatstat)

twid <- 20
theight <-  20
sideL <- 2
rp1 <- (sideL/2)*sqrt(3)
rp2 <- 2*(sideL/2)*sqrt(3)
rp3 <- 3*sideL

    bx <- c(1:floor(twid/rp3))
    by <- c(1:floor(theight/rp3))
    hex_array1 <- list(bx)
    hex_array2 <- list(by)

    for(i in 1:ceiling(twid/rp3)){
        bx[i] <- list(x=c(0+rp3*i,1+rp3*i,3+rp3*i,4+rp3*i,3+rp3*i,1+rp3*i)) 
        by[i] <- list(y=c(rp1,rp2,rp2,rp1,0,0))
            hex_array1[i] <- bx[i]
            hex_array2[i] <- by[i]
    }

    har1 <- list(x=c(0,1,3,4,3,1), y=c(rp1,rp2,rp2,rp1,0,0))

    har2 <- list(x=hex_array1,y=hex_array2)


hexig <- owin(poly=list(list(x=c(0,twid,twid,0), y=c(0,0,theight,theight)),
                        har1, har2
                        )
                )
    plot(hexig)

However, the above seems to error out because har2 isn't formatted as a list of lists correctly.

The above is obviously only for a single row of hexagons but I figured once I got the first row I'd just wrap the single row in a for loop that added a set x and y distances for each row. I just can't figure out how to format har2 so that I can directly plug it into owin's poly function.

I'm open to completely changing the way I've done the above, I'm still relatively new to R so I definitely still don't know how to do things the most efficient/elegant way. I'm currently running R version 3.3.2 on Win 10 x64 running RStudio V0.99.903

Any help is appreciated.

Thank you!

Dock

Possibly the dggridR package could also help. "dggridR builds discrete global grids which partition the surface of the Earth into hexagonal, triangular, or diamond cells, all of which have the same size." – Kensell

I know this is an older post, but the link up top is broken so your example no longer works. Do you have an alternative? – Aspergillum

Answer 1

I think spatstat has just the functions you are looking for: hextess and affine.tess.

Take a look at the examples for affine.tess. Here is an example of what you can do (add trim = FALSE to avoid the bounding box):

library(spatstat)
H <- hextess(square(5), 0.2)
plot(H)

shear <- matrix(c(1,0,0.6,1), 2, 2)
sH <- affine(H, shear)
plot(sH)

Oxpecker

Compared with my ggplot hack, this directly creates the desired tesselation pattern and is much more flexible in terms of transformations. Hopefully, the OP will return and select this as the best answer. Also, it would be helpful if you got rid of all the #> and #> affn.t> and just provided the bare code so that people can copy and paste without having to edit out the cursor characters. – Bakelite

Thanks for the positive feedback @eipi10. I have updated my answer to make it easier to copy and paste. – Oxpecker

Answer 2

It might be easier to just do a hexbin plot and then override the coloring (not that it wouldn't be an interesting programming exercise to plot the hexagon tesselation lines directly). For example, using ggplot2:

library(ggplot2)

dat = data.frame(x=runif(5000, 0,10), y=runif(5000,0,10))

# Basic plot
p = ggplot(dat, aes(x,y)) + 
  geom_hex(colour="black", fill="white", bins=10) +
  theme_minimal() + 
  guides(fill=FALSE) +
  scale_y_continuous(limits=c(-0.4,10.6)) +
  scale_x_continuous(limits=c(-0.4,10.6)) +
  theme(axis.text=element_blank(),
        axis.title=element_blank())

# Regular hexagons
p + coord_equal(ratio=1)

# 2:1 aspect ratio
p + coord_equal(ratio=2)

geom_hex only works with Cartesian coordinates, so this method can only produce hexagons with varying aspect ratios, but not shears or other distortions.

Bakelite

Wow, thanks so much. This is exactly what I was hoping for. Do you know of a way to easily tessellate other combinations of shapes. For example, tesselate squares, hexagons and triangles together? I'm thinking of something like what you can see at the below link. principlesofnature.com/references/…. – Dock

Answer 3

scale = 1

scale = 2

I wrote a hexagon() function that is a base graphics::polygon() approach. Just had to figure out a little bit of the geometry of hexagons and map it to an indexing that made sense. This is what I came up with:

• The index_i = 1, index_j=1 hexagon is the lower left hexagon. It has its leftmost vertex at cartesian coordinate (0,opp). It will be flush on the y=0 line (x-axis).

• The index_i = 2, index_j=1 hexagon will be adjacent to the right from the index_i = 1, index_j=1 hexagon (lower left). It'll be slightly elevated.

• The index_i=1, index_j=2 will be right on top of the index_i = 1, index_j=1 hexagon (lower left).

• In this way incrementing index_i references hexagons to the right (think of index_i as the x-coordinate position) and incrementing index_j references hexagons above (think of index_j as the y-coordinate position).

• scale makes them bigger or smaller

• pass colors to each hexagon with fill_color

• Use a double for-loop to tessellate

library(RColorBrewer)
mypalette<-brewer.pal(5,"PuOr")[c(-1,-3)]
lwd.in<-1

hexagon<-function(index_i=1, index_j=1, scale=1, fill_color=sample(rev(mypalette)[2],1)){
  
  opp=tan(pi/3)*scale; 
  adj=1*scale;

  side_length <- sqrt(adj^2+opp^2)

vertex_a <- c(  0                ,   opp)
vertex_b <- c(adj                , 2*opp)
vertex_c <- c(adj+side_length    , 2*opp)
vertex_d <- c(adj+adj+side_length,   opp)
vertex_e <- c(  adj+side_length  , 0)
vertex_f <- c(adj                , 0)

cpoint <- c(adj+0.5*side_length,opp)


if( index_i %% 2 == 1){
  
  odds_up_to_index_i <- seq(1,index_i,by=2)
  
  key <- data.frame(      i = seq(from=0, by=3, length.out = length(odds_up_to_index_i)),
                    index_i = odds_up_to_index_i)
  
  i <- key$i[key$index_i == index_i]
  j <- 2*(index_j - 1)
  
  return_hex <-
    polygon(x = c(vertex_a[1],vertex_b[1],vertex_c[1],vertex_d[1],vertex_e[1],vertex_f[1]) + cpoint[1]*i,
            y = c(vertex_a[2],vertex_b[2],vertex_c[2],vertex_d[2],vertex_e[2],vertex_f[2]) + cpoint[2]*j,
            col=fill_color,
            lwd=lwd.in,
            border=sample(c("white","black")[1],1)
            
            
    )
}

if( index_i %% 2 == 0){
  
  i <- index_i - 1
  j <- 2*(index_j - 1)
  
  return_hex <-
    polygon(x = c(vertex_a[1],vertex_b[1],vertex_c[1],vertex_d[1],vertex_e[1],vertex_f[1]) + (cpoint[1]+0.5*side_length)*(i),
            y = c(vertex_a[2],vertex_b[2],vertex_c[2],vertex_d[2],vertex_e[2],vertex_f[2]) + cpoint[2]*(j+1),
            col=fill_color,
            lwd=lwd.in,
            border=sample(c("white","black")[1],1)
    )
  }
}

par(pty="s", mai=c(0,0,0,0)+0.1)
plot(NA,NA,xlim=c(0,200),ylim=c(0,200), axes = FALSE, xlab="", ylab="") ## if you adjust `opp` and `adj` from (7,4)
#box()
abline(v=0)
abline(h=0)

for(i in 1:100){
  for(j in 1:100){
    hexagon(index_i = i, index_j = j)
  }
}

hexagon(index_i = 1, index_j = 1)
hexagon(index_i = 1, index_j = 2)
hexagon(index_i = 1, index_j = 3)
hexagon(index_i = 1, index_j = 4)
hexagon(index_i = 1, index_j = 5)

hexagon(index_i = 2, index_j = 1)
hexagon(index_i = 2, index_j = 2)
hexagon(index_i = 2, index_j = 3)
hexagon(index_i = 2, index_j = 4)
hexagon(index_i = 2, index_j = 5)

hexagon(index_i = 3, index_j = 1)
hexagon(index_i = 3, index_j = 2)
hexagon(index_i = 3, index_j = 3)
hexagon(index_i = 3, index_j = 4)
hexagon(index_i = 3, index_j = 5)

hexagon(index_i = 4, index_j = 1)
hexagon(index_i = 4, index_j = 2)
hexagon(index_i = 4, index_j = 3)
hexagon(index_i = 4, index_j = 4)
hexagon(index_i = 4, index_j = 5)

hexagon(index_i = 5, index_j = 1)
hexagon(index_i = 5, index_j = 5)
hexagon(index_i = 6, index_j = 1)
hexagon(index_i = 6, index_j = 4)
hexagon(index_i = 7, index_j = 2)
hexagon(index_i = 7, index_j = 3)
hexagon(index_i = 7, index_j = 4)

## Infected: color, white border
hexagon(index_i = 5, index_j = 3, fill_color=rev(mypalette)[3])
## Vaccinated:  deeper color, black border (nah, just white)
hexagon(index_i = 5, index_j = 2, fill_color=rev(mypalette)[1])
hexagon(index_i = 6, index_j = 3, fill_color=rev(mypalette)[1])
hexagon(index_i = 6, index_j = 2, fill_color=rev(mypalette)[1])
hexagon(index_i = 5, index_j = 4, fill_color=rev(mypalette)[1])
hexagon(index_i = 4, index_j = 2, fill_color=rev(mypalette)[1])
hexagon(index_i = 4, index_j = 3, fill_color=rev(mypalette)[1])



## Infected: color, white border
hexagon(index_i = 20, index_j = 20, fill_color=rev(mypalette)[3])
## Vaccinated:  deeper color, black border (nah, just white)
hexagon(index_i = 20, index_j = 19, fill_color=rev(mypalette)[1])
hexagon(index_i = 20, index_j = 21, fill_color=rev(mypalette)[1])

hexagon(index_i = 19, index_j = 20, fill_color=rev(mypalette)[1])
hexagon(index_i = 19, index_j = 21, fill_color=rev(mypalette)[1])

hexagon(index_i = 21, index_j = 20, fill_color=rev(mypalette)[1])
hexagon(index_i = 21, index_j = 21, fill_color=rev(mypalette)[1])



par(pty="s", mai=c(0,0,0,0)+0.1)
plot(NA,NA,xlim=c(0,200),ylim=c(0,200), axes = FALSE, xlab="", ylab="") ## if you adjust `opp` and `adj` from (7,4)
#box()
abline(v=0)
abline(h=0)

scale.in <- 2

for(i in 1:100){
  for(j in 1:100){
    hexagon(index_i = i, index_j = j, scale=scale.in)
  }
}

hexagon(index_i = 1, index_j = 1, scale=scale.in)
hexagon(index_i = 1, index_j = 2, scale=scale.in)
hexagon(index_i = 1, index_j = 3, scale=scale.in)
hexagon(index_i = 1, index_j = 4, scale=scale.in)
hexagon(index_i = 1, index_j = 5, scale=scale.in)

hexagon(index_i = 2, index_j = 1, scale=scale.in)
hexagon(index_i = 2, index_j = 2, scale=scale.in)
hexagon(index_i = 2, index_j = 3, scale=scale.in)
hexagon(index_i = 2, index_j = 4, scale=scale.in)
hexagon(index_i = 2, index_j = 5, scale=scale.in)

hexagon(index_i = 3, index_j = 1, scale=scale.in)
hexagon(index_i = 3, index_j = 2, scale=scale.in)
hexagon(index_i = 3, index_j = 3, scale=scale.in)
hexagon(index_i = 3, index_j = 4, scale=scale.in)
hexagon(index_i = 3, index_j = 5, scale=scale.in)

hexagon(index_i = 4, index_j = 1, scale=scale.in)
hexagon(index_i = 4, index_j = 2, scale=scale.in)
hexagon(index_i = 4, index_j = 3, scale=scale.in)
hexagon(index_i = 4, index_j = 4, scale=scale.in)
hexagon(index_i = 4, index_j = 5, scale=scale.in)

hexagon(index_i = 5, index_j = 1, scale=scale.in)
hexagon(index_i = 5, index_j = 5, scale=scale.in)
hexagon(index_i = 6, index_j = 1, scale=scale.in)
hexagon(index_i = 6, index_j = 4, scale=scale.in)
hexagon(index_i = 7, index_j = 2, scale=scale.in)
hexagon(index_i = 7, index_j = 3, scale=scale.in)
hexagon(index_i = 7, index_j = 4, scale=scale.in)

## Infected: color, white border
hexagon(index_i = 5, index_j = 3, scale=scale.in, fill_color=rev(mypalette)[3])
## Vaccinated:  deeper color, black border (nah, just white)
hexagon(index_i = 5, index_j = 2, scale=scale.in, fill_color=rev(mypalette)[1])
hexagon(index_i = 6, index_j = 3, scale=scale.in, fill_color=rev(mypalette)[1])
hexagon(index_i = 6, index_j = 2, scale=scale.in, fill_color=rev(mypalette)[1])
hexagon(index_i = 5, index_j = 4, scale=scale.in, fill_color=rev(mypalette)[1])
hexagon(index_i = 4, index_j = 2, scale=scale.in, fill_color=rev(mypalette)[1])
hexagon(index_i = 4, index_j = 3, scale=scale.in, fill_color=rev(mypalette)[1])



## Infected: color, white border
hexagon(index_i = 20, index_j = 20, scale=scale.in, fill_color=rev(mypalette)[3])
## Vaccinated:  deeper color, black border (nah, just white)
hexagon(index_i = 20, index_j = 19, scale=scale.in, fill_color=rev(mypalette)[1])
hexagon(index_i = 20, index_j = 21, scale=scale.in, fill_color=rev(mypalette)[1])

hexagon(index_i = 19, index_j = 20, scale=scale.in, fill_color=rev(mypalette)[1])
hexagon(index_i = 19, index_j = 21, scale=scale.in, fill_color=rev(mypalette)[1])

hexagon(index_i = 21, index_j = 20, scale=scale.in, fill_color=rev(mypalette)[1])
hexagon(index_i = 21, index_j = 21, scale=scale.in, fill_color=rev(mypalette)[1])

Companionway

Any idea this can be extended to triangles (not hexagons) with the boundary be a regular hexagon and not a square. – Semiyearly