An Implementation Comment

The implementation described in the preceding sections stores both rectangular and polar coordinates for a vector in the Vector object. However, the public interface doesn’t depend on this fact. All the interface calls for is that both representations can be displayed and that individual values can be returned. The internal implementation could be quite different. As mentioned earlier, the object could store just the x and y components. Then, say, the magval() method, which returns the value of the magnitude of the vector, could calculate the magnitude from the x and y values instead of just looking up the value as stored in the object. Such an approach changes the implementation but leaves the user interface unchanged. This separation of interface from implementation is one of the goals of OOP. It lets you fine-tune an implementation without changing the code in programs that use the class.

Both of these implementations have advantages and disadvantages. Storing the data means that the object occupies more memory and that code has to be careful to update both rectangular and polar representations each time a Vector object is changed. But data look-up is faster. If an application often needs to access both representations of a vector, the implementation used in this example would be preferable; if polar data were needed only infrequently, the other implementation would be better. You could choose to use one implementation in one program and the second implementation in another, yet retain the same user interface for both.