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The first assignment to P here sets the X coordinate to seven, leaving the Y coordinate unchanged; the second then sets the Y coordinate to five, leaving the X coordinate unchanged. The final result is thus that P contains the point with coordinates (7.0,5.0), as desired. Note carefully that, in contrast with the analogous example in the body of the chapter, we do not have to collect together the two constituent assignments in order to achieve the desired result. Why not Well, in order to answer this question, it helps to examine a more complex example: CREATE TYPE ELLIPSE AS ( A INTEGER, B INTEGER, CTR POINT ) ; DECLARE E ELLIPSE ; SET ( E.A, E.B ) = ROW ( 7, 3 ) ; For brevity, let s combine the two expansions this time. The overall result looks like this: BEGIN DECLARE TEMP ROW ( F1 SET TEMP = ROW ( 7, 3 SET E = E.A ( TEMP.F1 SET E = E.B ( TEMP.F2 END ; ..., F2 ... ) ; ) ; ) ; ) ;

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If you need to, you can update the generated classes by adding, deleting, and modifying existing entries. The automated process generates these classes:

Now suppose the previous value of E had a = 10 and b = 8. Then the first assignment to E yields an ellipse with a = 7 and b = 8 in other words, an ellipse with a < b. However, this state of affairs does not cause a run-time error (and the second assignment to E thus goes on to yield an ellipse with a = 7 and b = 3, as required). Why is there no run-time error Because SQL is unaware of the type constraint to the effect that a must be greater than or equal to b (observe that the definition of type ELLIPSE included no such constraint); in fact, SQL doesn t support the concept of type constraints at all (we can t even state them). In our opinion, this lack of type constraint support on SQL s part constitutes a very serious flaw. While it does make it easier to support multiple assignment, as we ve just seen,21 it also means there are many real world types that can t be properly specified in SQL! For example, suppose we want to define a type called LENGTH (with the obvious meaning). Then we might specify, say, integers as the associated representation, and of course that specification does impose an a priori constraint on the values that go to make up the type. Considered as type constraints, however, such a priori constraints are extremely weak. In the case at hand, for example, there s no

Even with today s digital inking and painting software, the animation process often relies on individual artists hand-drawing or correcting each frame, as you ve seen with KToon. If you re trying to produce animation by yourself or in a small team, you may find the process prohibitively time-consuming or too boring. It can be done, but some animators have spent years on one short film particularly when they were just starting out and had no one to help them. Commercial animation studios have often worked around this problem by having the lead artist draw the key frames of the action and then outsourcing the drawing of the in-between frames to less well-paid animators, often in countries where pay rates and labor laws are much less demanding. If the key frames are drawn as a series of vectors, then it becomes possible to use the computer s number-crunching power to fill the gaps in time and space automatically using a process known as tweening, as in in-betweening. Essentially, this is an extension of the same vector techniques you looked at in 4. Letting the computer do the time-consuming, boring work potentially makes goodquality animation much more practical for individual artists and small teams.

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