The Of Operator.

  The Of operator takes two operands--a direction and a region--and evaluates to a region that is adjacent to the specified region. The relative position of the resulting region is determined by the signs of the components of the direction vector, and the size of the new region is determined by circumscribing a box around the direction as shown in Figure 1.

  
Figure 1: Illustration of ``Of'' Regions.

 
Mathematically, 		if vector v     and

				 region R   ,

		 [v of R] defines an array of size
      ,

				    where    						 if   

								    or

						        if   

    This array is located outside of R and adjacent to R at
      ,

				 where    						 if   ,

						       				 if   

						       and    				 if    

In other words, if , the upper bound of the Of array is the lower bound of the dimension. If , the lower bound of the Of array is the upper bound of the dimension. And if , the new region has the same upper and lower bounds for dimension i.