Re: Comments on decoration ill, intersection and union
Nate,
1) The intersect and convexHull return bare intervals in Motion 42.
Do you mean intersectDec and convexHullDec in your email ?
2) Do you agree that set-based and Kaucher/modal flavours may have distinct set of decorations ?
3) Do you suggest to add EIN to set-based or to Kaucher/modal flavour ?
4) I try to make a reference implementation of flavours of P1788.
The set-based flaver is more complete:
http://java.net/projects/jinterval/sources/svn/show/trunk/jinterval/jinterval-interval-java/src/main/java/net/java/jinterval/interval/set?rev=188
The Kaucher falver is less complete, because there are things I don't understand:
http://java.net/projects/jinterval/sources/svn/show/trunk/jinterval/jinterval-interval-java/src/main/java/net/java/jinterval/interval/kaucher?rev=188
Currently both flavours shares the same set of Decorations
http://java.net/projects/jinterval/sources/svn/content/trunk/jinterval/jinterval-interval-java/src/main/java/net/java/jinterval/interval/Decoration.java?rev=188
Now I see that I need to cahnge this.
Do you want that I make implementation of Kaucher flavour (including Kaucher/modal decorations) more complete ? However, I need to ask you a lot of questions in this case.
-Dima
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Отправленные: Пятница, 28 Декабрь 2012 г 18:13:58 GMT +04:00 Абу-Даби, Маскат
Тема: RE: Comments on decoration ill, intersection and union
John Pryce wrote:
> So it seems "max(dx,dy)" for intersectionDec should be "min(dx,dy)"; and
> "min(dx,dy)" for convexHullDec should be "the tightest decoration
containing dx and dy
> in the containment order". (I assume by "weakest" you mean the min,
because you
> say it is like an arithmetic operation.)
Where do you see "weakest"? It says "the tightest decoration" not "the
weakest decoration". This is not the same thing as the min.
Anyhow, applying these rules to Motion 42 still leads to problems:
In the Example 2 in section 8.8.8 for X=[-1,1], it gives:
U = f1(intersect([-1,1],[-oo,-2]))
= f1((Empty,dac)) // (Empty,dac) is contradictory by section
8.8.4
= (Empty,emp)
V = (f1([-1,1]),dac)
W = f1(intersect([-1,1],[2,+oo]))
= f1((Empty,dac)) // (Empty,dac) is contradictory by section
8.8.4
= (Empty,emp)
So there are still the intermediate results (Empty,dac), which by Motion 42
is a contradiction.
Taking convexHull of U, V and W and propagating the "tightest" decoration by
the containment order gives:
(f1([-1,1]),trv)
This at least is not incorrect (since trv decoration is always true), but it
is not useful or informative.
This demonstrates my point further: to remove the contradictions specified
in section 8.8.4, and also to compute the decoration that is both correct
and most informative, one needs to define an ein decoration as I have done
in the previous e-mails in this discussion. Without these changes, Motion 42
simply does not define the correct decoration system to make decorated set
operations useful, informative or free of contradictions.
Nate