# Calculate turning angles and step lengths from location data

May 16, 2007
By

(This article was first published on Quantitative Ecology, and kindly contributed to R-bloggers)

```anglefun <- function(xx,yy,bearing=TRUE,as.deg=FALSE){  ## calculates the compass bearing of the line between two points  ## xx and yy are the differences in x and y coordinates between two points  ## Options:  ## bearing = FALSE returns +/- pi instead of 0:2*pi  ## as.deg = TRUE returns degrees instead of radians  c = 1  if (as.deg){    c = 180/pi  }    b<-sign(xx)  b[b==0]<-1  #corrects for the fact that sign(0) == 0  tempangle = b*(yy<0)*pi+atan(xx/yy)  if(bearing){    #return a compass bearing 0 to 2pi    #if bearing==FALSE then a heading (+/- pi) is returned    tempangle[tempangle<0]<-tempangle[tempangle<0]+2*pi  }  return(tempangle*c)}bearing.ta <- function(loc1,loc2,loc3,as.deg=FALSE){  ## calculates the bearing and length of the two lines  ##    formed by three points  ## the turning angle from the first bearing to the  ##    second bearing is also calculated  ## locations are assumed to be in (X,Y) format.  ## Options:  ## as.deg = TRUE returns degrees instead of radians  if (length(loc1) != 2 | length(loc2) != 2 | length(loc3) !=2){    print("Locations must consist of either three vectors, length == 2,or three two-column dataframes")    return(NaN)  }  c = 1  if (as.deg){    c = 180/pi  }    locdiff1<-loc2-loc1  locdiff2<-loc3-loc2  bearing1<-anglefun(locdiff1[1],locdiff1[2],bearing=F)  bearing2<-anglefun(locdiff2[1],locdiff2[2],bearing=F)  if(is.data.frame(locdiff1)){    dist1<-sqrt(rowSums(locdiff1^2))    dist2<-sqrt(rowSums(locdiff2^2))  }else{    dist1<-sqrt(sum(locdiff1^2))    dist2<-sqrt(sum(locdiff2^2))  }    ta=(bearing2-bearing1)    ta[ta < -pi] = ta[ta < -pi] + 2*pi  ta[ta > pi] = ta[ta > pi] - 2*pi  return(list(bearing1=unlist(bearing1*c),bearing2=unlist(bearing2*c),  ta=unlist(ta*c),dist1=unlist(dist1),dist2=unlist(dist2)))}

```

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