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Re:[cgal-discuss] Difference between Lazy_exact and Filtered_kernel?


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  • From: "Thomas Zangl - Home" <>
  • To: "cgal-discuss" <>
  • Subject: Re:[cgal-discuss] Difference between Lazy_exact and Filtered_kernel?
  • Date: Sun, 10 Aug 2008 18:09:57 +0200


Am Thu, 03 Jul 2008 15:21:43 +0200, schrieb "Andreas Fabri"
<>:

Hi!

>> Sorry, but I did not get yet what the *main* difference between the
>> Lazy_kernel and Filtered_kernel is.
>
>The main difference is that
>The lazy kernel is exact_predicates_exact_constructions
>The Filtered kernel is only exact_predicates

I tried to summarize your explainations about the lazy kernel and the
DAG of the geometric operations:

If geometric and arithmetic operations are carried out using the exact number
type, the lazy kernel stores a DAG (''directed acyclic graph'') for every
operation. Each node of the DAG stores:

* A geometric object or number with intervals of doubles,
* The type of the geometric or arithmetic operation,
* Pointers to the DAG nodes representing the operands of the
geometric/arithmetic operation.

The DAG for each operation is stored in a history-like way. If a
predicate on the lazy kernel fails, the postponed exact computation is
replayed from the information stored in the DAG. The lazy kernel fails
if e.g., a comparison is performed using Interval arithmetic and the
interval overlaps, hence, the filter cannot securely decide.

-----

However, some questions arise:

-> Is a Geometric object something like a point, line, segment, plane,
triangle?
-> The type of geometric or artihmetic operation is: +,-, etc. or
"intersection(x,y)"?

How are the constructions filtered? Can you please give me an example?

Thank you!
--
,yours Thomas Zangl, Bakk.rer.soc.oec. -

-
- Freelancer - IT Consulting & Software Development -
- Student of Software Development-Economy (Master) -
- http://blog.tzis.net -



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