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/** \page mesh_navigation How to navigate on a mesh

\section nav_overview Overview

\li \ref nav_intro
\li \ref nav_he
\li \ref nav_bound
\li \ref nav_io
\li \ref nav_opposite
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\li \ref nav_to_from
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\section nav_intro Introduction

In this tutorial you will learn how to navigate on a mesh using
the %OpenMesh library. In the previous chapter (see \ref mesh_iterators) you have learned
how to iterate over vertices, edges, halfedges and faces as well as
circulate over certain structures such as 1-rings and many more.
So in this tutorial we will focus on efficiently using the
halfedge data structure and some very useful attributes such as
the boundary flag. We assume that you already made yourself familiar with the halfedge
structure which is used in %OpenMesh. Further information on this topic
can be found in \ref mesh_hds.

\section nav_he Navigating over halfedges

So let's start with navigating over halfedges of a mesh.
Assume we have the following mesh topology:

\image html mesh.normal.png

We can now select an arbitrary halfedge of this mesh which then offers
either one of two possible navigations:

\li If the chosen halfedge lies at a boundary or in other
words is not adjacent to a face, we can now navigate
along the boundary (or hole) of our mesh by using \c next_halfedge_handle()
or \c prev_halfedge_handle():

\image html mesh.outer.png

\li If the chosen halfedge is adjacent to a face, we can then navigate
along all halfedges that are adjacent to this face. In other words we circulate
around the inner halfedges of one face:

\image html mesh.inner.png

In both cases the code would look something like the following example.
Depending on whether the initial halfedge is adjacent to a face or not,
we will either navigate on the boundary halfedges of our mesh or along
the inner halfedges of a face:

References:<br />
OpenMesh::Concepts::KernelT< FinalMeshItems >::next_halfedge_handle()<br />
OpenMesh::Concepts::KernelT< FinalMeshItems >::prev_halfedge_handle()

\section nav_bound Mesh boundaries

As you have seen in the previous section, navigating along boundaries
is very simple. In general %OpenMesh also offers a boundary attribute
for edges, vertices and faces. So testing i.e. whether a face is a boundary
face is quite simple using OpenMesh::PolyConnectivity::is_boundary().<br />

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\note You can iterate along boundaries by using the next_halfedge_handle(). If you are on a boundary, the next halfedge is guaranteed to be also a boundary halfedge.

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So for each type we can make use of one of the following functions:


\section nav_io Using incoming and outgoing halfedges

%OpenMesh offers quite a lot of iterators and circulators to easily iterate
over the structures of a mesh. A very helpful iterator is the
OpenMesh::PolyConnectivity::VertexIHalfedgeIter or the OpenMesh::PolyConnectivity::VertexOHalfedgeIter which are used to iterate
over all incoming/outgoing halfedges of a vertex.
So, sticking to the illustration below, a OpenMesh::PolyConnectivity:V:ertexIHalfedgeIter for the
lower most vertex would iterate over all incoming halfedges (blue),
whereas the OpenMesh::PolyConnectivity::OpenMesh::PolyConnectivity::VertexOHalfedgeIter would iterate over all outgoing halfedges (red):

\image html mesh.inout.png

A schematic code example of how to use the halfedge iterators as described above:

\section nav_opposite Using opposite halfedges

The halfedge structure splits every edge into two directional parts by creating two
directed edges out of one undirected edge. So for every halfedge there exists its
counterpart pointing in the opposite direction. %OpenMesh allows to easily navigate
through opposing halfedges via the function OpenMesh::Concepts::KernelT< FinalMeshItems >::opposite_halfedge_handle().
So in the illustration below \c opposite_halfedge_handle() for the blue halfedge would
return the red halfedge:

\image html mesh.opp.png

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Use this function as described in the example below:


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There are also a few more functions that offer easy access to opposing structures:


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\section nav_to_from Getting the to and from vertices

\image  html

If you have an halfedge, you can get the to and the from handles of the adjacent vertices.
\note The halfedges have a direction. Therefore the to vertex is the from vertex of the opposite halfedge and vice versa.