Question

I have a 2-dimmensional unit grid, and a bunch of line segments that start and end at any rational number. I need an efficient way to calculate which grid cells the line passes through. For example, the line:

From (2.1, 3.9) to (3.8, 4.8) passes through the grid cells with lower left points (2, 3), (2, 4), and (3, 4).

Is there a quick, efficient way to calculate these quadrants from the line’s endpoints?

I’ll be working in R, but an answer in Python or pseudocode would work too. Thanks!

Answer 1

Folks who work with spatial data deal with this kind of question all the time, so it may be worth piggy-backing on their efforts. Here’s a solution that uses R’s raster package (and functions from the sp package on which it depends):

library(raster)

## Create a SpatialLines object
a <- c(2.1, 3.9) 
b <- c(3.8, 4.8)
## Method #1 -- Uses functions from the sp package.
SL <- SpatialLines(list(Lines(list(Line(rbind(a,b))), "ab")))
## Method #2 -- Uses readWKT() from the rgeos package. Easier to read.
# library(rgeos)
# string <- paste0("LINESTRING(", paste(a, b, collapse=", "), ")")
# SL <- readWKT(string)

## Create a raster object
m <- 10
n <- 10
mat <- matrix(seq_len(m*n), nrow = m, ncol = n)
r <- raster(mat, xmn = 0, xmx = n, ymn = 0, ymx = m) 

## Find which cells are intersected & get coordinates of their lower-left corners
ii <- extract(r, SL, cellnumbers=TRUE)[[1]][, "cell"]
floor(xyFromCell(r, ii))
#      x y
# [1,] 2 4
# [2,] 3 4
# [3,] 2 3

## Confirm that this is correct with a plot
image(r)
plot(as(rasterize(SL, r), "SpatialPolygons"), 
     border = "darkgrey", lwd = 2, add = TRUE)
lines(SL)