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[wen <>]

Hi, Sylvain

Thank you for your instrutction. I will learn the code and the references, although the Delaunay hierarchy is a little difficult to understand.

Best regards!

------------------ 原始邮件 ------------------

发件人: "Sylvain Pion-3 [via cgal-discuss]";<[hidden email]>;

发送时间: 2016年7月27日(星期三) 晚上11:49

收件人: "王雯"<[hidden email]>;

主题: Re: The exact algorithm and references of CGAL's 3DDelaunayfunction

There is also this nice article by Liu and Snoeyink which gives details on several important aspects of implementations of 3D Delaunay triangulations, including the one of CGAL (at the time of 2005 at least) : http://library.msri.org/books/Book52/files/23liu.pdf

Also, for people who want to study the code of CGAL, the "modular view" in git is more organized than the "flat view" that is presented in the releases, so for 3D Delaunay, you can go here : https://github.com/CGAL/cgal/tree/master/Triangulation_3

2016-07-26 7:58 GMT-07:00 Monique Teillaud <[hidden email]>:

See http://doc.cgal.org/latest/Triangulation_3/classCGAL_1_1Delaunay__triangulation__3.html

The first line shows: #include <CGAL/Delaunay_triangulation_3.h> 

--

Monique Teillaud 
https://members.loria.fr/Monique.Teillaud/
INRIA Nancy - Grand Est, LORIA 
Institut National de Recherche en Informatique et Automatique 

On 26 Jul 2016, at 12:15, 王雯 <[hidden email]> wrote:

 Hi Monique,
Thank you for your kind advice.

 I will learn delaunay of CGAL with the references as you mentioned. For CGAL code, I just searched in the CGAL directory about delaunay and find many related files with .h extension. So, can you recommend the target program files that contain the detail of the algorithm implementation of 3d delaunay. 

Best wishes! 

------------------ Original ------------------

From:  "Monique Teillaud";<[hidden email]>;

Date:  Tue, Jul 26, 2016 02:43 PM

To:  "cgal-discuss"<[hidden email]>;

Subject:  Re: [cgal-discuss] The exact algorithm and references of CGAL's 3DDelaunay function

Hi,

Thank you for your nice email.

Though the basic incremental algorithm used is very standard (see e.g., Bowyer 1981), the 3d Delaunay triangulation of CGAL is the result of quite a long research process, in particular on robustness issues. You can find a few references here https://members.loria.fr/Monique.Teillaud/biblio/Keyword/CGAL_.html but they are not the only ones.

If you want to know more about the details of the implementation, well, the CGAL source code is public…

Best regards,

--

Monique Teillaud 
https://members.loria.fr/Monique.Teillaud/
INRIA Nancy - Grand Est, LORIA 
Institut National de Recherche en Informatique et Automatique

On 26 Jul 2016, at 04:56, wen <[hidden email]> wrote:

Hi,
I am learning geometric modelling and I want to do some research on 3D
Delaunay. I just tried 3d delaunay function  provided by CGAL and was
impressed by its high efficiency. I implemented 3D delaunay myself with
Incremental  Insertion Algorithms, but the efficiency was much less than
CGAL.
In addition, it needs to add eight auxiliary bounding points before point
insertion during 3D Delaunay  triangulation. In my program, the coordinates
of the eight points was configured with the rules that the bounding  box
formed by the eight points can contain the whole point set. But the
triangulation result is a bit different on  surface compared with 3D
delaunay of CGAL.

So, I wonder how to find the exact algorithm and references of CGAL's 3D
delaunay function.

Thanks for any help.



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