I have a segmented line with about 80 points in 2D and a point P (X/Y) which is not on this line.
I need to know where point P' is on this line, which has the shortest distance to P.
Is there an easy way to calculate this?
EDIT:
Input files:
str(coords)
'data.frame': 80 obs. of 2 variables:
$ x: num 2140 2162 2169 2167 2158 ...
$ y: num 1466 1437 1412 1390 1369 ...
str(point)
'data.frame': 1 obs. of 2 variables:
$ x: num 1778
$ y: num 1911
Output files:
point on segmented line
I have the solution now...even though it is not very efficient. Perhaps someone finds this useful. I changed the coordinates of P to get a better result.
distance <- data.frame(dist = NA)
coordinates <- data.frame(x=NA,y=NA)
coords <- data.frame(x=c(2140,2162,2169,2167,2158),y=c(1466,1437,1412,1390,1369))
point <- data.frame(x=2130,y=1400)
for(j in 1:(length(coords[,1]))){
distance[2*j-1,1] <- sqrt((coords[j,1]-point[1,1])^2+(coords[j,2]-point[1,2])^2)
coordinates[2*j-1,] <- coords[j,]
}
Calculate all perpendicular distances from point P and the coordinates of point P' which are lying on the segmented line
for(j in 1:(length(coords[,1])-1)){
d <- abs((coords[j+1,1]-coords[j,1])*(coords[j,2]-point[1,2])-
(coords[j,1]-point[1,1])*(coords[j+1,2]-coords[j,2]))/
sqrt((coords[j+1,1]-coords[j,1])^2+(coords[j+1,2]-coords[j,2])^2)
t <- abs(((point[1,1]-coords[j,1])*(coords[j+1,1]-coords[j,1])+
(point[1,2]-coords[j,2])*(coords[j+1,2]-coords[j,2]))/
((coords[j+1,1]-coords[j,1])^2+(coords[j+1,2]-coords[j,2])^2))
x <- coords[j,1]+t*(coords[j+1,1]-coords[j,1])
y <- coords[j,2]+t*(coords[j+1,2]-coords[j,2])
if(min(coords$x[j],coords$x[j+1]) <= x && x <= max(coords$x[j],coords$x[j+1]) &&
min(coords$y[j],coords$y[j+1]) <= y && y <= max(coords$y[j],coords$y[j+1])){
if(coords[j,] != c(x,y) && coords[j+1,] != c(x,y)){
distance[2*j,1] <- d
coordinates[2*j,] <- c(x,y)
}
}
}
Position of minimal distance:
p <- which(distance==min(distance, na.rm=TRUE))
coordinates[p,]