## Sunday, October 14, 2007

### Convert polar coordinates to Cartesian

When I want to calculate the coordinates of a location (e.g., a nest or burrow) based on distance and bearing from a grid point, this function helps me avoid writing down SOH-CAH-TOA every time. Just note that the bearing in this case is from the grid point (known location) to the unknown location.
`polar2cart<-function(x,y,dist,bearing,as.deg=FALSE){  ## Translate Polar coordinates into Cartesian coordinates  ## based on starting location, distance, and bearing  ## as.deg indicates if the bearing is in degrees (T) or radians (F)    if(as.deg){    ##if bearing is in degrees, convert to radians    bearing=bearing*pi/180  }    newx<-x+dist*sin(bearing)  ##X  newy<-y+dist*cos(bearing)  ##Y  return(list("x"=newx,"y"=newy))}##Exampleoldloc=c(0,5) bearing=200 #degreesdist=5newloc<-polar2cart(oldloc[1],oldloc[2],dist,bearing,TRUE)plot(oldloc[1],oldloc[2],xlim=c(-10,10),ylim=c(-10,10))points(newloc\$x,newloc\$y,col="red")`

Etienne said...

It's a bit late, but actually I think you mixed x and y. x = d * cos(theta) and y = d * sin(theta). SOH-CAH-TOA!
Have a look at http://en.wikipedia.org/wiki/Polar_coordinate_system#Converting_between_polar_and_Cartesian_coordinates

Forester said...

Hi Etienne,

Thanks for your comment -- it highlights a common mistake. This function is for use with compass bearings (i.e., where North is 0 degrees, East is 90 degrees, etc.). Try the function out with this in mind and let me know if it clears things up for you.

Etienne said...

Good point! Context here is quite important. Sorry for the confusion and thanks for the clarification.