Generating a sequence of equidistant points on polygon boundary - r

Question

I am looking for a procedure that allows me to generate a sequence of equidistant points (coordinates) along the sides of an arbitrary polygon.
Imaging a polygon defined by the coordinates of its vertexes:
poly.mat <- matrix(c(0,0,
0,1,
0.5,1.5,
0.5,0,
0,0 # last row included to close the polygon
), byrow = T, ncol = 2)
colnames(poly.mat) <- c("x", "y")
plot(poly.mat, type = "l")
If the length of the sequence I want to generate is n (adjustable), how I can produce a sequence, starting at (0,0), of equidistant coordinates.
I got as far as calculating the perimeter of the shape with the geosphere package (which I believe I need)
library(geosphere)
n <- 50 # sequence of length set to be 50
perim <- perimeter(poly.mat)
perim/n # looks like every section needs to be 8210.768 something in length

Answer 1

You will have to write the code yourself. Sorry, there isn't a library function for every last detail of every last assignment. Assuming that each pair of points defines a line segment, you could just generate N points along each segment, as in
begin = [xbegin, ybegin ];
end = [xend, yend ];
xdist = ( xend - xbegin ) / nintervals;
ydist = ( yend - ybegin ) / nintervals;
then your points are given by [ xbegin + i * xdist, ybegin + i * ydist ]

Answer 2

Here is the solution I came up with.
pointDistance <- function(p1, p2){
sqrt((p2[,1]-p1[,1])^2) + sqrt((p2[,2]-p1[,2])^2)
}
getPos <- function(shp.mat, ll){
greaterLL <- shp.mat$cumdis > ll
if(all(greaterLL == FALSE)) return(poly.mat[nrow(poly.mat), c("x", "y")])
smallRow <- min(which(greaterLL)) # the smallest coordinate that has greater length
p.start <- shp.mat[smallRow-1, c("x","y")]
p.end <- shp.mat[smallRow, c("x","y")]
cumVal <- shp.mat$cumdis[smallRow]
prop <- (ll-shp.mat$cumdis[smallRow-1])/(shp.mat$cumdis[smallRow]-shp.mat$cumdis[smallRow-1])
p.start + (prop)* (p.end-p.start)
}
# shp1
poly.mat <- matrix(c(0,0,
0,1,
0.5,1.5,
0.5,0,
0,0
),byrow = T, ncol = 2)
colnames(poly.mat) <- c("x", "y")
poly.mat <- as.data.frame(poly.mat)
# Main fun
pointsOnPath <- function(shp.mat, n){
dist <- vector(mode = "numeric", length = nrow(shp.mat)-1)
for(i in 2:nrow(shp.mat)){
dist[i] <- pointDistance(p1 = shp.mat[i,], p2 = shp.mat[i-1,])
}
shp.mat$dist <- dist
shp.mat$cumdis <- cumsum(shp.mat$dist)
dis <- matrix(seq(from = 0, to = max(shp.mat$cumdis), length.out = n+1), ncol = 1)
out <- lapply(dis, function(x) getPos(shp.mat = shp.mat, ll = x))
out <- do.call("rbind", out)
out$dis <- dis
out[-nrow(out),]
}
df <- pointsOnPath(shp.mat = poly.mat, 5)
# Plot
plot(poly.mat$x, poly.mat$y, type = "l", xlim = c(0,1.5), ylim = c(0,1.5))
points(df$x, df$y, col = "red", lwd = 2)
There is room for improving the code, but it should return the correct result