[Gmsh] "Ruled" surface mathematical definition

[Christophe Geuzaine]

Philippe Grenard wrote:
> Hi all,
> 
> I would like to understant how the "ruled surfaces" in gmsh are mathematically 
> defined.

Hi Philippe - Ruled surfaces in Gmsh are actually a bit tricky (and 
misnamed): unless they are located on a sphere, in which case they are 
actual spherical patches, ruled surfaces are obtained through 
transfinite interpolation.

Ch.

> I mean, let's say I have 4 lines (curved, spline or anything)
> These can be discretized by 4 sets of points  P(i,j) :
> P(i=0            , j=1,..,,N-1)
> P(i=1,...,M-1 , j=0)
> P(i=M           , j=1,..,,N-1)
> P(i=1,...,M-1 , j=N)
> 
> How are the internal points P(i,j) of the surface defined ?
> 
> for example :
> Point(1) = {0, 0, 0, 0.04};
> Point(2) = {0, 1, 0, 0.04};
> Point(3) = {1, 0, 0, 0.04};
> Point(4) = {1, 1, 0, 0.04};
> Point(5) = {1, 1, 1, 0.04};
> Line(1) = {1, 2};
> Line(2) = {1, 3};
> Circle(3) = {5, 4, 3};
> Circle(4) = {5, 4, 2};
> Line Loop(5) = {2, -3, 4, -1};
> Ruled Surface(6) = {5};
> 
> How can I define this surface (as a set of points for example) ?
> 
> Thank you for your help,
> 
> Philippe
> 
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> 


-- 
Prof. Christophe Geuzaine
University of Liege, Electrical Engineering and Computer Science
http://www.montefiore.ulg.ac.be/~geuzaine