[Gmsh] making an equilateral mesh.

[Dr Colin J. Cotter]

Dear Gmsh list,
I have been trying to make a mesh of equilateral triangles by
extruding a horizontal line at a 60 degree angle (later I will use
periodic boundary conditions so I have an equilateral mesh on the
torus). I have noticed that if you do this then the extrusion divides
the quadrilaterals in the wrong direction and you don't get a Delaunay
mesh (the equilateral one):

Point(1) = {0,0,0,0.1};
Extrude {1,0,0} {
Point{1}; Layers{5};
}
Extrude {0.5,0.866025403784,0} {
Line{1}; Layers{5};
}

but it works if you extrude at a -60 degree angle instead:

Point(1) = {0,0,0,0.1};
Extrude {1,0,0} {
Point{1}; Layers{5};
}
Extrude {-0.5,0.866025403784,0} {
Line{1}; Layers{5};
}

Is there a way to force Gmsh to produce a Delaunay mesh in the first case?

all the best
--cjc

[David Colignon]

Hi Colin,

what about this ?


Point(1) = {0,0,0,0.1};
Extrude {1,0,0} { Point{1}; }
Extrude {0.5,0.866025403784,0} { Line{1}; }
Transfinite Line { 1 , 2 , 3 , 4 } = 5 ;
Transfinite Surface {5} Left ;


Cheers,

Dave
--
David Colignon, Ph.D.
Collaborateur Logistique du F.R.S.-FNRS
CÉCI - Consortium des Équipements de Calcul Intensif
ACE - Applied & Computational Electromagnetics
Sart-Tilman B28
Université de Liège
4000 Liège - BELGIQUE
Tél: [phone]
Fax: [phone]
WWW: http://hpc.montefiore.ulg.ac.be/
Agenda: http://www.google.com/calendar/embed?src=david.colignon%40gmail.com

Post by Dr Colin J. Cotter
Dear Gmsh list,
I have been trying to make a mesh of equilateral triangles by
extruding a horizontal line at a 60 degree angle (later I will use
periodic boundary conditions so I have an equilateral mesh on the
torus). I have noticed that if you do this then the extrusion divides
the quadrilaterals in the wrong direction and you don't get a Delaunay
Point(1) = {0,0,0,0.1};
Extrude {1,0,0} {
Point{1}; Layers{5};
}
Extrude {0.5,0.866025403784,0} {
Line{1}; Layers{5};
}
Point(1) = {0,0,0,0.1};
Extrude {1,0,0} {
Point{1}; Layers{5};
}
Extrude {-0.5,0.866025403784,0} {
Line{1}; Layers{5};
}
Is there a way to force Gmsh to produce a Delaunay mesh in the first case?
all the best
--cjc
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[Dr Colin J. Cotter]

Dear Dave,
Thanks for your reply. I'm running Gmsh 2.2 which complains about the
"Left" bit (not sure what that does):
Error : 'equilateral3.geo', line 4 : syntax error (Left)

When I run it in command line mode I get a mesh which is not perfectly
regular.

--cjc

Post by David Colignon
Hi Colin,
what about this ?
Point(1) = {0,0,0,0.1};
Extrude {1,0,0} { Point{1}; }
Extrude {0.5,0.866025403784,0} { Line{1}; }
Transfinite Line { 1 , 2 , 3 , 4 } = 5 ;
Transfinite Surface {5} Left ;
Cheers,
Dave

[David Colignon]

Post by Dr Colin J. Cotter
Dear Dave,
Thanks for your reply. I'm running Gmsh 2.2

you should upgrade to the latest 2.4.2 version :-)

Post by Dr Colin J. Cotter
which complains about the

see "Transfinite Surface" in http://www.geuz.org/gmsh/doc/texinfo/gmsh.html#Structured-grids

Post by Dr Colin J. Cotter
Error : 'equilateral3.geo', line 4 : syntax error (Left)

you can replace

Transfinite Surface {5} Left ;

by

Transfinite Surface {5} = {1,2,4,3} ;

Post by Dr Colin J. Cotter
When I run it in command line mode I get a mesh which is not perfectly
regular.

What do you mean by "not perfectly regular" ?

Dave

Post by Dr Colin J. Cotter
--cjc

Post by David Colignon
Hi Colin,
what about this ?
Point(1) = {0,0,0,0.1};
Extrude {1,0,0} { Point{1}; }
Extrude {0.5,0.866025403784,0} { Line{1}; }
Transfinite Line { 1 , 2 , 3 , 4 } = 5 ;
Transfinite Surface {5} Left ;
Cheers,
Dave

[Christophe Geuzaine]

Post by Dr Colin J. Cotter
Dear Gmsh list,
I have been trying to make a mesh of equilateral triangles by
extruding a horizontal line at a 60 degree angle (later I will use
periodic boundary conditions so I have an equilateral mesh on the
torus). I have noticed that if you do this then the extrusion divides
the quadrilaterals in the wrong direction and you don't get a Delaunay
Point(1) = {0,0,0,0.1};
Extrude {1,0,0} {
Point{1}; Layers{5};
}
Extrude {0.5,0.866025403784,0} {
Line{1}; Layers{5};
}
Point(1) = {0,0,0,0.1};
Extrude {1,0,0} {
Point{1}; Layers{5};
}
Extrude {-0.5,0.866025403784,0} {
Line{1}; Layers{5};
}
Is there a way to force Gmsh to produce a Delaunay mesh in the first case?

there's no option to subdivide in the other direction... but you could
use the following trick:

Point(1) = {1,0,0,0.1};
Extrude {-1,0,0} {
Point{1}; Layers{5};
}
Extrude {0.5,0.866025403784,0} {
Line{1}; Layers{5};
}

Post by Dr Colin J. Cotter
all the best
--cjc
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