## CGAL::HalfedgeDS_const_decorator<HDS>

### Definition

The classes CGAL::HalfedgeDS_items_decorator<HDS>, CGAL::HalfedgeDS_decorator<HDS>, and CGAL::HalfedgeDS_const_decorator<HDS> provide additional functions to examine and to modify a halfedge data structure HDS. The class CGAL::HalfedgeDS_items_decorator<HDS> provides additional functions for vertices, halfedges, and faces of a halfedge data structure without knowing the containing halfedge data structure. The class CGAL::HalfedgeDS_decorator<HDS> stores a reference to the halfedge data structure and provides functions that modify the halfedge data structure, for example Euler-operators. The class CGAL::HalfedgeDS_const_decorator<HDS> stores a const reference to the halfedge data structure. It contains non-modifying functions, for example the test for validness of the data structure.

All these additional functions take care of the different capabilities a halfedge data structure may have or may not have. The functions evaluate the type tags of the halfedge data structure to decide on the actions. If a particular feature is not supported nothing is done. Note that for example the creation of new halfedges is mandatory for all halfedge data structures and will not appear here again.

#include <CGAL/HalfedgeDS_const_decorator.h>

### Inherits From

CGAL::HalfedgeDS_items_decorator<HDS>

### Creation

HalfedgeDS_const_decorator<HDS> D ( const HDS& hds);
| keeps internally a const reference to hds.

### Validness Checks

A halfedge data structure has no definition of validness of its own, but a useful set of tests is defined with the following levels:

Level 0
  The number of halfedges is even. All pointers except the vertex pointer and the face pointer for border halfedges are unequal to their respective default construction value. For all halfedges h: The opposite halfedge is different from h and the opposite of the opposite is equal to h. The next of the previous halfedge is equal to h. For all vertices v: the incident vertex of the incident halfedge of v is equal to v. The halfedges around v starting with the incident halfedge of v form a cycle. For all faces f: the incident face of the incident halfedge of f is equal to f. The halfedges around f starting with the incident halfedge of f form a cycle. Redundancies among internal variables are tested, e.g., that iterators enumerate as many items as the related size value indicates.
Level 1
  All tests of level 0. For all halfedges h: The incident vertex of h exists and is equal to the incident vertex of the opposite of the next halfedge. The incident face (or hole) of h is equal to the incident face (or hole) of the next halfedge.
Level 2
  All tests of level 1. The sum of all halfedges that can be reached through the vertices must be equal to the number of all halfedges, i.e., all halfedges incident to a vertex must form a single cycle.
Level 3
  All tests of level 2. The sum of all halfedges that can be reached through the faces must be equal to the number of all halfedges, i.e., all halfedges surrounding a face must form a single cycle (no holes in faces).
Level 4
  All tests of level 3 and normalized_border_is_valid.

bool | D.is_valid ( bool verbose = false, int level = 0)
|  | returns true if the halfedge data structure hds is valid with respect to the level value as defined above. If verbose is true, statistics are written to cerr.
bool | D.normalized_border_is_valid ( bool verbose = false)

returns true if the border halfedges are in normalized representation, which is when enumerating all halfedges with the halfedge iterator the following holds: The non-border edges precede the border edges. For border edges, the second halfedge is a border halfedge. (The first halfedge may or may not be a border halfedge.) The halfedge iterator border_halfedges_begin() denotes the first border edge. If verbose is true, statistics are written to cerr.

### See Also

CGAL::HalfedgeDS_items_decorator<HDS>
CGAL::HalfedgeDS_decorator<HDS>

### Example

The following program fragment illustrates the implementation of a is_valid() member function for a simplified polyhedron class. We assume here that the level three check is the appropriate default for polyhedral surfaces.

    namespace CGAL {
        template <class Traits>
        class Polyhedron {
            typedef HalfedgeDS_default<Traits> HDS;
            HDS hds;
        public:
            // ...
            bool is_valid( bool verb = false, int level = 0) const {
                Verbose_ostream verr(verb);
                verr << "begin Polyhedron::is_valid( verb=true, level = " << level
                     << "):" << std::endl;
                HalfedgeDS_const_decorator<HDS> decorator(hds);
                bool valid = decorator.is_valid( verb, level + 3);
                // further checks ...
            }
        };
    }