elbow 求拐点

distancePointLine <- function(x, y, slope, intercept) {
  ## x, y is the point to test.
  ## slope, intercept is the line to check distance.
  ##
  ## Returns distance from the line.
  ##
  ## Returns 9999 on 0 denominator conditions.
  x1 <- x-10
  x2 <- x+10
  y1 <- x1*slope+intercept
  y2 <- x2*slope+intercept
  distancePointSegment(x,y, x1,y1, x2,y2)
}

distancePointSegment <- function(px, py, x1, y1, x2, y2) {
  ## px,py is the point to test.
  ## x1,y1,x2,y2 is the line to check distance.
  ##
  ## Returns distance from the line, or if the intersecting point on the line nearest
  ## the point tested is outside the endpoints of the line, the distance to the
  ## nearest endpoint.
  ##
  ## Returns 9999 on 0 denominator conditions.
  lineMagnitude <- function(x1, y1, x2, y2) sqrt((x2-x1)^2+(y2-y1)^2)
  ans <- NULL
  ix <- iy <- 0   # intersecting point
  lineMag <- lineMagnitude(x1, y1, x2, y2)
  if( lineMag < 0.00000001) {
    warning("short segment")
    return(9999)
  }
  u <- (((px - x1) * (x2 - x1)) + ((py - y1) * (y2 - y1)))
  u <- u / (lineMag * lineMag)
  if((u < 0.00001) || (u > 1)) {
    ## closest point does not fall within the line segment, take the shorter distance
    ## to an endpoint
    ix <- lineMagnitude(px, py, x1, y1)
    iy <- lineMagnitude(px, py, x2, y2)
    if(ix > iy)  ans <- iy
    else ans <- ix
  } else {
    ## Intersecting point is on the line, use the formula
    ix <- x1 + u * (x2 - x1)
    iy <- y1 + u * (y2 - y1)
    ans <- lineMagnitude(px, py, ix, iy)
  }
  ans
}
###############################################
mydata = read.table('clipboard',header = T)
##########################
#mydata=cbind(c(1:15),wss)
#########################
datanumber = nrow(mydata)
mydist = c()
for(i in c(1:datanumber)){
  d = as.numeric(c(mydata[i,],mydata[1,],mydata[datanumber,]))
  mydist[i] = distancePointSegment(d[1],d[2],d[3],d[4],d[5],d[6])
 
}
mydist
max(mydist)
###############
#filternew = filter(mydist,filter = c(rep(1/datanumber,3)))
#plot(filternew)
################
elbowpoints = which(mydist==max(mydist))
plot(mydist)
abline(v=elbowpoints,lty=2,col='red')
plot(x=mydata[,1],y=mydata[,2],type='l')
elbowp = mydata[elbowpoints,1]
elbowp
abline(v=elbowp,lty=2,col='red')