Pfthb

Is there anybody out there having a smart idea how to create n rectangular tiles from an image, each of different size with no overlapping. The solution given below is limited to n = 4.

randomTiles <- function(w, h, n)

 if(sample(c(TRUE, FALSE), 1))
 tl <- c(0, sample(10:w-10, 1), 0, sample(round(h/10):h-round(h/10), 1))
 bl <- c(0, sample(tl[2]:w-round(w/10), 1), tl[4], h)
 tr <- c(tl[2], w, 0, tl[4])
 br <- c(bl[2], w, tl[4], h)
 else
 tl <- c(0, sample(10:w-10, 1), 0, sample(round(h/10):h-round(h/10), 1))
 tr <- c(tl[2], w, 0, sample(tl[4]:h-round(h/10), 1))
 bl <- c(0, tl[2], tl[4], h)
 br <- c(tl[2], w, tr[4], h)
 
 tileFrame <- data.frame(xleft = c(tl[1], bl[1], tr[1], br[1]),
 ybottom = c(tl[3], bl[3], tr[3], br[3]),
 xright = c(tl[2], bl[2], tr[2], br[2]),
 ytop = c(tl[4], bl[4], tr[4], br[4]),
 col = rgb(runif(4), runif(4), runif(4)))
 return(tileFrame)



h <- 100
w <- 120
n <- 4

op <- par(mfrow = c(2,2))
for(i in 1:4)
 plot(h, xlim = c(0, w), ylim = c(h, 0), type = "n", xlab = "WIDTH", ylab = "HIGHT")
 tiles <- randomTiles(w = w, h = h, n = n)
 rect(tiles[,1], tiles[,2], tiles[,3], tiles[,4], col = tiles[,5])

par(op)

Thanks for any hint...

I was a little bored, so I gave it a go. Works pretty well, but I'm very much not an expert on random generators, so it is very possible that there are some hidden biases in the positions of the rectangles that this code generates.

UPDATE: This really grabbed my attention. I think the first version was in fact biased towards making smaller and smaller rectangles. I updated the code so that this doesn't happen anymore, I think.

library(data.tree)
library(tidyverse)

random_rects <- function (x, y, n) 
 rand_leaf <- function (nd) 
 while (data.tree::isNotLeaf(nd)) 
 nd <- if (runif(1) > .5) nd$r else nd$l
 
 nd
 
 split_node <- function (nd) 
 nd$div <- runif(1)
 nd$dir <- ifelse(runif(1) > .5, "h", "v")
 nd$AddChild("l")
 nd$AddChild("r")
 
 set_dims <- function (nd) 
 p <- nd$parent
 nd$x0 = p$x0
 nd$x1 = p$x1
 nd$y0 = p$y0
 nd$y1 = p$y1
 if (p$dir == "h") 
 new_x <- p$x0 + (p$x1 - p$x0)*p$div
 if (nd$name == "l") 
 nd$x1 <- new_x
 else 
 nd$x0 <- new_x
 
 else 
 new_y <- p$y0 + (p$y1 - p$y0)*p$div
 if (nd$name == "l") 
 nd$y1 <- new_y
 else 
 nd$y0 <- new_y
 
 
 
 get_dims <- function (nd) 
 tibble::tibble(x0 = nd$x0, x1 = nd$x1, y0 = nd$y0, y1 = nd$y1)
 
 root <- data.tree::Node$new("home")
 for (i in seq_len(n - 1)) 
 nd <- rand_leaf(root)
 split_node(nd)
 
 root$x0 <- 0
 root$x1 <- x
 root$y0 <- 0
 root$y1 <- y
 root$Do(set_dims, traversal = "pre-order", filterFun = data.tree::isNotRoot)
 dfs <- purrr::map(data.tree::Traverse(root, filterFun = data.tree::isLeaf), get_dims)
 list(tree = root, df = dplyr::bind_rows(dfs))


set.seed(1)

rect_list <- purrr::rerun(10, random_rects(40, 100, 20))

df <- dplyr::bind_rows(purrr::map(rect_list, ~ dplyr::mutate(.x$df, pos = factor(1:n()))), .id = "rep")

ggplot(df, aes(xmin = x0, xmax = x1, ymin = y0, ymax = y1, fill = pos)) +
 geom_rect(alpha = .7) +
 facet_wrap(~rep)

head(df)
#> # A tibble: 6 x 6
#> rep x0 x1 y0 y1 pos 
#> <chr> <dbl> <dbl> <dbl> <dbl> <fct>
#> 1 1 0 15.3 0 3.56 1 
#> 2 1 0 15.3 3.56 5.21 2 
#> 3 1 0 15.3 5.21 5.47 3 
#> 4 1 15.3 40 0 2.70 4 
#> 5 1 15.3 25.3 2.70 5.47 5 
#> 6 1 25.3 40 2.70 5.47 6

^{Created on 2018-11-11 by the reprex package (v0.2.1)}