How to plot the recursive partitioning from the rpart package-CodePudding

I want to plot a partition of a two-dimensional covariate space constructed by recursive binary splitting. To be more precise, I would like to write a function that replicates the following graph (taken from

Displayed above is a two-dimensional covariate space and a partition obtained by recursive binary splitting the space using axis-aligned splits (what is also called a CART algorithm). What I want to implement is a function that takes the output of the rpart function and generates such plot.

It follows some example code:

## Generating data.
set.seed(1975)

n <- 5000
p <- 2

X <- matrix(sample(seq(0, 1, by = 0.01), n * p, replace = TRUE), ncol = p)
Y <- X[, 1]   2 * X[, 2]   rnorm(n)

## Building tree.
tree <- rpart(Y ~ ., data = data.frame(Y, X), method = "anova", control = rpart.control(cp = 0, maxdepth = 2))

Incidentally, this package also contains the function parttree, which returns something very similar to your rpart_splits function:

parttree(tree)
  node         Y                        path  xmin  xmax  ymin  ymax
1    4 0.7556079   X2 < 0.565 --> X2 < 0.265  -Inf 0.265  -Inf   Inf
2    5 1.3087679  X2 < 0.565 --> X2 >= 0.265 0.265 0.565  -Inf   Inf
3    6 1.8681143  X2 >= 0.565 --> X1 < 0.645 0.565   Inf  -Inf 0.645
4    7 2.4993361 X2 >= 0.565 --> X1 >= 0.645 0.565   Inf 0.645   Inf