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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

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    You know what would be awesome? A [reproducible example](http://stackoverflow.com/questions/5963269/how-to-make-a-great-r-reproducible-example) with sample input and desired output. Just asking for package recommendations is considered off-topic for SO. – MrFlick Sep 12 '14 at 15:20
  • Use standard geometry to find the distance from the point to the full line, then if that point is not on a segment, find the closest segment endpoint. This has nothing to to with `R` . – Carl Witthoft Sep 12 '14 at 15:45
  • If you post the formula, you are more likely to get how to put that in code. – rnso Sep 12 '14 at 15:56

1 Answers1

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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,]
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