[petsc-users] Input arguments of DMPlexCreateFromDAG

[Cedric Doucet]

Thank you for your answer. 
I understand well the reason why coneSize begins with faces of cells and vertices first. 
However, I am not sure to understand how cone points are numbered in the definition of <start>. 
For example, in CreateSimplex2D in ex5.c (two triangles sharing an edge), we have: 

PetscInt numPoints[3] = {4, 5, 2}; 
PetscInt coneSize[11] = {3, 3, 0, 0, 0, 0, 2, 2, 2, 2, 2}; 
PetscInt cones[16] = {6, 7, 8, 9, 7, 10, 2, 3, 3, 4, 4, 2, 5, 4, 3, 5}; 
PetscInt coneOrientations[16] = {0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}; 
PetscScalar vertexCoords[8] = {-0.5, 0.5, 0.0, 0.0, 0.0, 1.0, 0.5, 0.5}; 

The fact that coneOrientations[4] equals -2 means that edge cones[4]=7 must be oriented in reverse order starting at vertex 1. 
However, edge 7 is defined by vertices (3,4). Does it mean that a local numbering is used here: (3,4)~(v0,v1)? 

In algebraic topology, a convenient way to orient simplices is to number their vertices in ascendant order. 
For example, an edge (i,j) is oriented so that i<j, a face (i,j,k) is oriented so that i<j<k, etc. 
Can we adopt the same convention here and does it simplify something? 

Best regards, 

Cédric Doucet 

----- Mail original -----

> De: "Matthew Knepley" <knepley at gmail.com>
> À: "Cedric Doucet" <cedric.doucet at inria.fr>
> Cc: petsc-users at mcs.anl.gov
> Envoyé: Jeudi 30 Janvier 2014 19:26:36
> Objet: Re: [petsc-users] Input arguments of DMPlexCreateFromDAG

> On Thu, Jan 30, 2014 at 12:19 PM, Cedric Doucet <
> cedric.doucet at inria.fr > wrote:

> > Hello,
> 
> > I tried to use DMPlexCreateFromDAG function to create a DM
> > structure
> > from a hybrid mesh.
> 
> > To understand how it works, I look at ex5.c file.
> 
> > Unfortunately, there are some things that I do not understand.
> 
> > 1. Why does coneSize lists faces of cells first, then faces of
> > vertices and finally faces of edges (in 2D)? Listing faces of
> > vertices, then faces of edges and finally faces of cells is not
> > simpler?
> 

> This is really about what order you number points. I wanted to
> support meshes with just cells and vertices, as well as
> those with face and edges. I also wanted to be able to convert
> between them. Thus it made sense to leave the cell
> and vertex numbers invariant under this change. I still think this is
> the best pragmatic alternative.

> > 2 What does coneOrientations contain? For two counterclockwise
> > oriented triangles sharing an edge e={v0,v1}, I understand that
> > {v0,v1} is the right oriented edge for the second triangle (and e
> > for the first one) but what is the meaning of value -2? I read that
> > it is -(o+1) with o=1 but why does o equal 1 in this case?
> 
> Right now, orientation o = <sign><start> means:

> <sign>: + means traverse in cone order
> - means traverse in the reverse of cone order

> <start>: cone point to start iteration on
> if <sign> is -, then start on point -(<start>+1)

> Thus -2 means start on point 1 and go in reverse order, so
> for an edge that would be {1, 0} which is what you want.

> What we should really have is <start> identify a group element from
> the symmetry
> group of the point, and <sign> indicate inversion. However, that will
> be a big rewrite
> and needs to be motivated by applications.

> Matt

> > Thank you very much for your help!
> 
> > Best regards,
> 
> > Cédric Doucet
> 

> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which
> their experiments lead.
> -- Norbert Wiener
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