[petsc-users] orientation semantics for DMPlex

[Geoffrey Irving]

On Fri, Nov 22, 2013 at 10:22 AM, Matthew Knepley <knepley at gmail.com> wrote:
> On Fri, Nov 22, 2013 at 12:11 PM, Geoffrey Irving <irving at naml.us> wrote:
>>
>> On Fri, Nov 22, 2013 at 3:08 AM, Matthew Knepley <knepley at gmail.com>
>> wrote:
>> > On Thu, Nov 21, 2013 at 8:12 PM, Geoffrey Irving <irving at naml.us> wrote:
>> >>
>> >> What are the orientation semantics of DMPlex?  I figured if I listed
>> >> the edges of each triangle in counterclockwise order it would come out
>> >> right, but it appears to be right for some triangles and wrong for
>> >> others.  Do I always have to call DMPlexSetConeOrientation?
>> >>
>> >> Unfortunately, I haven't yet grasped the documentation for
>> >> DMPlexSetConeOrientation.
>> >
>> > This is because I have kept changing my mind. There is the way it is,
>> > and
>> > the way I want it to be now. So, the way it is:
>> >
>> >   All cone arrows have an orientation attached. This indicates the order
>> > in
>> > which the _next_ cone (of that cone point) should be read out. The order
>> > is cyclic. A positive integer p means "start from vertex p instead of
>> > 0". A
>> > negative integer q means "start from -(q+1) and go backward".
>>
>> Can't the order only be meaningfully described as cyclic only if the
>> child element has dimension 2 (triangles) where the element boundary
>> is topologically S^1?  A cyclic order doesn't make any sense for
>> tetrahedra (boundary S^2) or for segments (S^1), both of which have
>> trivial fundamental group.  If I have a triangle (0 1 2) pointing to
>> child segment (0 1), wouldn't orientation values 0 and -1 refer to the
>> same traversal?
>
>
> There is a problem with the word "orientation", since it does not mean what
> is traditional in topology. Rather it means something close to a label for the
> element of the symmetric group associated with the cell. So it really is
> PetscInt.

If that's the case, the documentation should mention the fact that of
the four possible values of the orientation flag for a segment child
of a triangle, there are only two distinct meanings.  And for
tetrahedra children of hypersimplices (not they those are particularly
common) both forward and reversed orders refer to the same topological
orientation, so the data structure doesn't work for that case at all.

Geoffrey

>> Since only one bit is ideally conveyed here, namely the sign of the
>> permutation required to reorient the child to match the parent, would
>> it be better to have orientations be PetscBool?  Is it too late for
>> that kind of API change?
>>
>> > The important thing to remember here is that this is ordering only the
>> > cone
>> > points, and is composed with higher level ordering when reading out the
>> > full closure is 3D. I have considered changing the semantics for
>> > negative
>> > values to start at -(coneSize-q+1) since then negation does what you
>> > think
>> > it should (go backwards from the guy just before), but then all the
>> > routines
>> > needs to know the coneSize which is not great.
>> >
>> > The reason that your example does not work is that triangles on opposite
>> > sides
>> > of an edge must have the opposite orientation for that edge. For
>> > example, an
>> > edge e = {v0, v1} lies between two triangles. Now the cone of e will
>> > always come
>> > out {v0, v1}. In triangle 0 that is fine, but in triangle 1 it needs to
>> > be {v1, v0} if all
>> > triangles are oriented counter-clockwise, so we need orientation -2 for
>> > that edge
>> > in the cone of triangle 1.
>>
>> Thanks, I should be good to go.  It might be useful to have a
>> consistency checking routine for users to run to make sure their
>> custom created DMPlex is valid.
>
>
> I do have DMPlexOrient(). We should probably add DMPlexCheckOrientation()
> which
> does exactly the same thing except mismatches are not corrected.
>
>    Matt
>
>>
>>
>> Geoffrey
>
>
>
>
> --
> 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