R实现重叠矩形的并集

Question

I am trying to solve a problem where I have multiple overlapping rectangles and I need to find the combined area of the rectangles. Intersecting portion of the rectangles need to looked at just once. I searched online and I found that Line sweep algorithm will work perfectly for me, as explained here : What is an Efficient algorithm to find Area of Overlapping Rectangles

My question is, Does R have something similar already implemented? I could not find anything similar in R. I do not want to reinvent the wheel if it already exists.

Answer 1

Interesting question. Suppose we've four rectangle coordinates as shown below:

require(data.table) # v1.9.7+
dt = data.table(x0 = c(7,17,5,1),  x1 = c(14,27,11,10), 
                y0 = c(1,55,6,14), y1 = c(10,70,20,34))
dt[, id := .I] # add row numbers
#    x0 x1 y0 y1 id
# 1:  7 14  1 10  1
# 2: 17 27 55 70  2
# 3:  5 11  6 20  3
# 4:  1 10 14 34  4

To see if rectangle i intersects with j , the condition, IIUC is:

x0_i <= x1_j, x1_i >= x0_j, y0_i <= y1_j, y1_i >= y0_j, where

x0_i < x1_i, x0_j < x1_j, y0_i < y1_i, y0_j < y1_j

This can be achieved with a conditional join, which was recently implemented in the current development version of data.table, v1.9.7. See installation instructions here .

ans = dt[dt, 
        .(id1 = pmin(i.id, x.id), id2 = pmax(i.id, x.id), 
           x0 = pmax(x.x0, i.x0),  x1 = pmin(x.x1, i.x1), 
           y0 = pmax(x.y0, i.y0),  y1 = pmin(x.y1, i.y1)), 
        on = .(x0 <= x1, x1 >= x0, y0 <= y1, y1 >= y0)
      ][id1 != id2]
ans = unique(ans)
#    id1 id2 x0 x1 y0 y1
# 1:   1   3  7 11  6 10
# 2:   3   4  5 10 14 20

Basically this performs a self-join . For each row in dt , it finds all matching indices with itself based on the condition provided to the on= argument, and based on the matching rows it extracts indices of the two rectangles and their intersecting portions. The id1 != id2 filters out self-overlaps..

Then we make sure that are no duplicates. The result shows which rectangle id1 overlaps with which ones id2 , and their intersecting region x0, x1, y0, y1 .

Is this more or less what you were looking for?