CGAL users discussion list

["Amir Vaxman" <>]

What I need is any total order on planes, as I have a set of planes, and
want to know efficiently if another input plane is already in the set. The
planes in the set are not parameterized in any assumed fashion, and neither
does the input plane parameterized the same way as the plane in the set it
might fit to, so the only thing given is that the set planes are different.
New entities are no problem, but normalization is, because I use a gmpq
kernel.

Amir.

-----Original Message-----
From: Andreas Fabri 
[mailto:]
 
Sent: Wednesday, March 18, 2009 2:14 PM
To: 

Subject: Re: [cgal-discuss] Sorting Planes Lexicographically

Hi Amir,

Isn't the most important question, what do you want to achieve by orderng
them?

Take the vector which has the same direction as the normal.
That orders them also in the case they have the same normal.

Is the question if they can be ordered based on the a,b,c,d
without computing new entities ?

andreas

Amir Vaxman wrote:
> Yes, but then you have to normalize.. (there is no Direction_3 total 
> order like in Direction_2).
> 
>  
> 
> *From:* 
> 
>  
> [mailto:]
>  *On 
> Behalf Of *Ophir Setter
> *Sent:* Wednesday, March 18, 2009 1:34 PM
> *To:* 
> 
> *Subject:* Re: [cgal-discuss] Sorting Planes Lexicographically
> 
>  
> 
> I am guessing that you could sort the normals to the planes 
> (lexicographically).
> 
> On Mon, Mar 16, 2009 at 3:01 PM, Amir Vaxman 
> <
>  
> <mailto:>>
>  wrote:
> 
> Hello,
> 
>  
> 
> Is there a way to sort planes lexicographically in CGAL, in a similar 
> manner as points are sorted? Of course, I am looking for something 
> invariant of plane parameterization.
> 
>  
> 
> Amir.
> 
>  
> 

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