Efficient method to determine location on a grid(array)

Question

I am representing a grid with a 2D list in python. I would like to pick a point (x,y) in the list and determine it's location...right edge, top left corner, somewhere in the middle...

Currently I am checking like so:

         # left column, not a corner
         if x == 0 and y != 0 and y != self.dim_y - 1:
             pass
         # right column, not a corner
         elif x == self.dim_x - 1 and y != 0 and y != self.dim_y - 1:
             pass
         # top row, not a corner
         elif y == 0 and x != 0 and x != self.dim_x - 1:
             pass
         # bottom row, not a corner
         elif y == self.dim_y - 1 and x != 0 and x != self.dim_x - 1:
             pass
         # top left corner
         elif x == 0 and y == 0:
             pass
         # top right corner
         elif x == self.dim_x - 1 and y == 0:
             pass
         # bottom left corner
         elif x == 0 and y == self.dim_y - 1:
             pass
         # bottom right corner
         elif x == self.dim_x - 1 and y == self.dim_y - 1:
             pass
         # somewhere in middle; not an edge
         else:
             pass

Where I have some function do something after the location is determined

dim_x and dim_y are the dimensions of the list.

Is there a better way of doing this without so many if-else statements? Something efficient would be good since this part of the logic is being called a couple million times...it's for simulated annealing.

Thanks in advance. Also, what would be a better way of wording the title?

Answer 1

def location(x,y,dim_x,dim_y):
    index = 1*(y==0) + 2*(y==dim_y-1) + 3*(x==0) + 6*(x==dim_x-1)
    return ["interior","top","bottom","left","top-left",
            "bottom-left","right","top-right","bottom-right"][index]