What is the difference between 向かい and 向こう?


I am unable to locate objects and their orientation with respect to myself
when 向こう and 向かい are used.

Consider:

  * 向こう側

  * 向かい側

  * 向こうの店

  * 向かいの店

Where is 向こう側 and 向かい側 with respect to me? Are they the same place?

My current hypothesis is that 向こう and 向かい both may occupy the same place,
except that 向かい necessarily orientates the object to face the subject (either
the first person, or from some place's perspective which the first person
adopts) by either the having a "front side" or by assuming that the object has
a "front side".




  * 向こう requires a reference line (which may be overtly expressed or not expressed). It means A and B are on opposite sides with respect to C.

> 店は川の向こうにある。  
>  A = current location, B = store, C = river

  * 向かい requires a "forward" direction. It means that along a line starting from A and facing the forward direction, there is B.

> 佐藤さんの向かいが山田さんだ。




  * 向こう requires a reference line (which may be overtly expressed or not expressed). It means A and B are on opposite sides with respect to C.

> 店は川の向こうにある。  
>  A = current location, B = store, C = river

  * 向かい requires a "forward" direction. It means that along a line starting from A and facing the forward direction, there is B.

> 佐藤さんの向かいが山田さんだ。

