In this way VCG Lib provides a way to check if a mesh is manifold on a specific edge because the FF adjacency relation is mutual, i.e. the face f0 points to the face f1 which points to the face f0, if and only if the mesh is manifold over the corresponding edge.
A very nice property is that given a pos c, there is only another neighbor pos c' that can be obtained from c changing only one of the elements of the triple.
We call the operation of passing from a pos to one of its neighbors Flip and write FlipV, FlipE and FlipF to indicate that the flipped element is the vertex, the edge or the face respectively.
For example consider c1: there is only another pos which is the same as c0 except for the vertex component of the triple, and it is c2. For brevity, we write c2 = FlipV(c1).
In the left of the table some other examples are shown just to make this point clear.
Note that concatenating two flips: FlipF and FlipE we obtain a transition from a pos to the next in counterclockwise or in clockwise sense, depending if the starting pos is on the CCW edge of the face with respect to the vertex or not. Also note that, thanks to how FF adjacency is defined, when a pos is on the border, it bounces back. This pair of flip are widely used in the VCG Lib to run over the one ring neighborhood of manifold vertices.
The following code snippet shows how to use the pos to iterate around a vertex:
#include <vcg/simplex/face/pos.h> // include the definition of pos
...includes to define your mesh type
class MyVertex: ...
class MyFace: public vcg::FaceSimp2<MyVertex,MyEdge,MyFace, vcg::face::VertexRef, vcg::face::FFAdj>{};
void OneRingNeighborhood( MyFace * f)
{
MyVertex * v = f->V(0);
MyFace* start = f;
vcg::face::Pos<MyFace> p(f,0,v);// constructor that takes face, edge and vertex
do
{
p.FlipF();
p.FlipE();
}while(p.f!=start);
}
Two important notes:
We arbitrarily picked f->V(0) as pivot vertex. In general one may want to start knowing the vertex. This is done by including the attribute vcg::vertex::VFAdj which basically associates to each vertex pointer to one of the faces incident on it. See the VF Adjacency for details.
This implementation does not work if the vertex is on the border. Just try with the example: from the pos c4 it would find c5,c6,c3 which is in the same face as c4. Of course this does not happen if you use the pos itself as a guard and not just the face. However, even in this case, you would obtain the sequence of pos: c5,c6,c3,c1,c0,c4 corresponding to the faces f2,f2,f1,f0,f0,f1 which probably is not what you want. VCG Lib provides a variation of pos that solves this problem
Jumping Pos
-----------
The Jumping Pos works exactly like the Pos, only it does not bounce when it encounters the border. Instead, it jump around the vertex as if the to border faces sharing the vertex (faces f0 and f2 in the image) were adjacent.
VFIterator is a simple iterator to run over the faces in the one-ring neighborhood of a vertex using the VF Adjacency (it is just like Pos for the FF Adjacency) The following code snippet shows how to use the VFIterator:
Here we make a series of simple statements just to avoid confusion and try to help up choosing the adjacencies the best fit your needs.
If the mesh is manifold, the one-ring neighborhood of a vertex computed by using Pos ( needs FF adjacency) is the same as the one computed by using VFIterator (needs VF adjacency). The order in which the faces are visited can be CW or CCW if using Pos, unspecified by using VIterator
If the mesh is non-manifold, Pos may not find all the faces of the one-ring neighborhood of he vertex, VFIterator always does
Boundary relations and adjacency
--------------------------------
In many algorithms you need to simply the boundary/border condition of a face, e.g. to know if a given face f has one or more adjacent faces on a specified edge e. Using FF adjacency this can be done simply by using the face::IsBorder(f,e) static function that simply checks if the pointer stored in face f on the edge e points to f itself. If you are navigating the mesh using a Pos, you have a Pos member function IsBorder() that reports the boundary condition of the current pos. Similarly, for testing manifoldness of specific places over a mesh, there is a face::IsManifold(f,e) static function and a IsManifold(e) function member of the pos class.
If you are not using FF adjacency evaluating the boundary conditions could be not very efficient, so vcg library provides a technique to cook the current boundary conditions of the mesh into vertex and face flags. Use the members of the UpdateFlags static class to compute flags that reflects the current mesh status and the access these flags using the IsB(e) member function of the face class. Remember that flags based boundary information can become invalid if you change the mesh topology. On the other hand consider that many non-mesh-modifying algorithms do not require explicit FF adjacency but just boundary information (typical examples: most mesh smoothing and curvature computation algorithms).
Please note that the boundary flags are set true also for non manifold conditions.
