[petsc-users] orientation semantics for DMPlex

[Geoffrey Irving]

On Fri, Nov 22, 2013 at 10:29 AM, Geoffrey Irving <irving at naml.us> wrote:
> 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.

Sorry, it does work, it's just that the sign doesn't matter.  Shifting
by one is an odd permutation on four indices.  Sorry for the noise.

Geoffrey