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))

}

##Example

oldloc=c(0,5)

bearing=200 #degrees

dist=5

newloc<-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")

## 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.

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## 3 comments:

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

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.

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

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