CGAL 5.6.1 - Surface Mesh
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#include <CGAL/Surface_mesh/Surface_mesh.h>
This class is a data structure that can be used as halfedge data structure or polyhedral surface.
It is an alternative to the classes HalfedgeDS
and Polyhedron_3
defined in the packages Halfedge Data Structures and 3D Polyhedral Surface. The main difference is that it is indexed based and not pointer based, and that the mechanism for adding information to vertices, halfedges, edges, and faces is much simpler and done at runtime and not at compile time. When elements are removed, they are only marked as removed, and a garbage collection function must be called to really remove them.
P | The type of the point property of a vertex. There is no requirement on P , besides being default constructible and assignable. In typical use cases it will be a 2D or 3D point type. |
Classes | |
class | Edge_index |
This class represents an edge. More... | |
class | Face_index |
This class represents a face. More... | |
class | Halfedge_index |
This class represents a halfedge. More... | |
class | Vertex_index |
This class represents a vertex. More... | |
Related Functions | |
(Note that these are not member functions.) | |
template<typename P > | |
Surface_mesh< P > & | operator+= (Surface_mesh< P > &sm, const Surface_mesh< P > &other) |
template<typename P > | |
std::ostream & | operator<< (std::ostream &os, const Surface_mesh< P > &sm) |
template<typename P > | |
std::istream & | operator>> (std::istream &is, Surface_mesh< P > &sm) |
Basic Types | |
typedef P | Point |
The point type. | |
typedef boost::uint32_t | size_type |
The type used to represent an index. | |
Range Types | |
Each range | |
typedef unspecified_type | Vertex_range |
The range over all vertex indices. More... | |
typedef unspecified_type | Halfedge_range |
The range over all halfedge indices. More... | |
typedef unspecified_type | Edge_range |
The range over all edge indices. More... | |
typedef unspecified_type | Face_range |
The range over all face indices. More... | |
Vertex_range | vertices () const |
returns the iterator range of the vertices of the mesh. | |
Halfedge_range | halfedges () const |
returns the iterator range of the halfedges of the mesh. | |
Edge_range | edges () const |
returns the iterator range of the edges of the mesh. | |
Face_range | faces () const |
returns the iterator range of the faces of the mesh. | |
Construction, Destruction, Assignment | |
Copy constructors as well as assignment do also copy simplices marked as removed. | |
Surface_mesh () | |
Default constructor. | |
Surface_mesh (const Surface_mesh &rhs) | |
Copy constructor: copies rhs to *this . Performs a deep copy of all properties. | |
Surface_mesh (Surface_mesh &&sm) | |
Move constructor. | |
Surface_mesh & | operator= (const Surface_mesh &rhs) |
assigns rhs to *this . Performs a deep copy of all properties. | |
Surface_mesh & | operator= (Surface_mesh &&sm) |
move assignment | |
Surface_mesh & | assign (const Surface_mesh &rhs) |
assigns rhs to *this . Does not copy custom properties. | |
Adding Vertices, Edges, and Faces | |
Vertex_index | add_vertex () |
adds a new vertex, and resizes vertex properties if necessary. | |
Vertex_index | add_vertex (const Point &p) |
adds a new vertex, resizes vertex properties if necessary, and sets the point property to p . More... | |
Halfedge_index | add_edge () |
adds a new edge, and resizes edge and halfedge properties if necessary. | |
Halfedge_index | add_edge (Vertex_index v0, Vertex_index v1) |
adds two opposite halfedges, and resizes edge and halfedge properties if necessary. More... | |
Face_index | add_face () |
adds a new face, and resizes face properties if necessary. | |
template<typename Range > | |
Face_index | add_face (const Range &vertices) |
if possible, adds a new face with vertices from a range with value type Vertex_index . More... | |
Face_index | add_face (Vertex_index v0, Vertex_index v1, Vertex_index v2) |
adds a new triangle connecting vertices v0 , v1 , v2 . More... | |
Face_index | add_face (Vertex_index v0, Vertex_index v1, Vertex_index v2, Vertex_index v3) |
adds a new quad connecting vertices v0 , v1 , v2 , v3 . More... | |
Low-Level Removal Functions | |
Although the elements are only marked as removed their connectivity and properties should not be used.
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void | remove_vertex (Vertex_index v) |
removes vertex v from the halfedge data structure without adjusting anything. More... | |
void | remove_edge (Edge_index e) |
removes the two halfedges corresponding to e from the halfedge data structure without adjusting anything. More... | |
void | remove_face (Face_index f) |
removes face f from the halfedge data structure without adjusting anything. More... | |
Memory Management | |
Functions to check the number of elements, the amount of space allocated for elements, and to clear the structure. | |
size_type | number_of_vertices () const |
returns the number of vertices in the mesh. | |
size_type | number_of_halfedges () const |
returns the number of halfedges in the mesh. | |
size_type | number_of_edges () const |
returns the number of edges in the mesh. | |
size_type | number_of_faces () const |
returns the number of faces in the mesh. | |
bool | is_empty () const |
returns true iff the mesh is empty, i.e., has no vertices, halfedges and faces. | |
void | clear_without_removing_property_maps () |
removes all vertices, halfedge, edges and faces. Collects garbage but keeps all property maps. | |
void | clear () |
removes all vertices, halfedge, edges and faces. More... | |
void | reserve (size_type nvertices, size_type nedges, size_type nfaces) |
reserves space for vertices, halfedges, edges, faces, and their currently associated properties. More... | |
void | resize (size_type nvertices, size_type nedges, size_type nfaces) |
bool | join (const Surface_mesh &other) |
copies the simplices from other , and copies values of properties that already exist under the same name in *this . More... | |
Garbage Collection | |
While removing elements only marks them as removed garbage collection really removes them. The API in this section allows to check whether an element is removed, to get the number of removed elements, and to collect garbage. The number of elements together with the number of removed elements is an upperbound on the index, and is needed by algorithms that temporarily store a property in a vector of the appropriate size. Note however that by garbage collecting elements get new indices. In case you store indices in an auxiliary data structure or in a property these indices are potentially no longer referring to the right elements. When adding elements, by default elements that are marked as removed are recycled. | |
size_type | number_of_removed_vertices () const |
returns the number of vertices in the mesh which are marked removed. | |
size_type | number_of_removed_halfedges () const |
returns the number of halfedges in the mesh which are marked removed. | |
size_type | number_of_removed_edges () const |
returns the number of edges in the mesh which are marked removed. | |
size_type | number_of_removed_faces () const |
returns the number offaces in the mesh which are marked removed. | |
bool | is_removed (Vertex_index v) const |
returns whether vertex v is marked removed. More... | |
bool | is_removed (Halfedge_index h) const |
returns whether halfedge h is marked removed. More... | |
bool | is_removed (Edge_index e) const |
returns whether edge e is marked removed. More... | |
bool | is_removed (Face_index f) const |
returns whether face f is marked removed. More... | |
bool | has_garbage () const |
checks if any vertices, halfedges, edges, or faces are marked as removed. More... | |
void | collect_garbage () |
really removes vertices, halfedges, edges, and faces which are marked removed. More... | |
template<typename Visitor > | |
void | collect_garbage (Visitor &visitor) |
void | set_recycle_garbage (bool b) |
controls the recycling or not of simplices previously marked as removed upon addition of new elements. More... | |
bool | does_recycle_garbage () const |
Getter. | |
Validity Checks | |
Functions in this group perform checks for structural consistency of a complete surface mesh, or an individual element. They are expensive and should only be used in debug configurations. | |
bool | is_valid (bool verbose=false) const |
perform an expensive validity check on the data structure and print found errors to std::cerr when verbose == true . More... | |
bool | is_valid (Vertex_index v, bool verbose=false) const |
performs a validity check on a single vertex. | |
bool | is_valid (Halfedge_index h, bool verbose=false) const |
performs a validity check on a single halfedge. | |
bool | is_valid (Edge_index e, bool verbose=false) const |
performs a validity check on a single edge. | |
bool | is_valid (Face_index f, bool verbose=false) const |
performs a validity check on a single face. | |
Low-Level Connectivity | |
Vertex_index | target (Halfedge_index h) const |
returns the vertex the halfedge h points to. | |
void | set_target (Halfedge_index h, Vertex_index v) |
sets the vertex the halfedge h points to to v . | |
Face_index | face (Halfedge_index h) const |
returns the face incident to halfedge h . | |
void | set_face (Halfedge_index h, Face_index f) |
sets the incident face to halfedge h to f . | |
Halfedge_index | next (Halfedge_index h) const |
returns the next halfedge within the incident face. | |
Halfedge_index | prev (Halfedge_index h) const |
returns the previous halfedge within the incident face. | |
void | set_next (Halfedge_index h, Halfedge_index nh) |
sets the next halfedge of h within the face to nh and the previous halfedge of nh to h . More... | |
Halfedge_index | halfedge (Vertex_index v) const |
returns an incoming halfedge of vertex v . More... | |
void | set_halfedge (Vertex_index v, Halfedge_index h) |
sets the incoming halfedge of vertex v to h . | |
Halfedge_index | halfedge (Face_index f) const |
returns a halfedge of face f . | |
void | set_halfedge (Face_index f, Halfedge_index h) |
sets the halfedge of face f to h . | |
Halfedge_index | opposite (Halfedge_index h) const |
returns the opposite halfedge of h . Note that there is no function set_opposite() . | |
Low-Level Connectivity Convenience Functions | |
Vertex_index | source (Halfedge_index h) const |
returns the vertex the halfedge h emanates from. | |
Halfedge_index | next_around_target (Halfedge_index h) const |
returns opposite(next(h)) , that is the next halfedge clockwise around the target vertex of h . More... | |
Halfedge_index | prev_around_target (Halfedge_index h) const |
returns prev(opposite(h)) , that is the previous halfedge clockwise around the target vertex of h . More... | |
Halfedge_index | next_around_source (Halfedge_index h) const |
returns next(opposite(h)) , that is the next halfedge clockwise around the source vertex of h . More... | |
Halfedge_index | prev_around_source (Halfedge_index h) const |
returns opposite(prev(h)) , that is the previous halfedge clockwise around the source vertex of h . More... | |
Vertex_index | vertex (Edge_index e, unsigned int i) const |
returns the i'th vertex of edge e , for i=0 or 1 . | |
Halfedge_index | halfedge (Vertex_index source, Vertex_index target) const |
finds a halfedge between two vertices. More... | |
Switching between Halfedges and Edges | |
Edge_index | edge (Halfedge_index h) const |
returns the edge that contains halfedge h as one of its two halfedges. | |
Halfedge_index | halfedge (Edge_index e) const |
returns the halfedge corresponding to the edge e . | |
Halfedge_index | halfedge (Edge_index e, unsigned int i) const |
returns the i'th halfedge of edge e , for i=0 or 1 . | |
Degree Functions | |
size_type | degree (Vertex_index v) const |
returns the number of incident halfedges of vertex v . | |
size_type | degree (Face_index f) const |
returns the number of incident halfedges of face f . | |
Borders | |
A halfedge, or edge is on the border of a surface mesh if it is incident to a A vertex is on a border if it is isolated or incident to a border halfedge. While for a halfedge and edge this is a constant time operation, for a vertex it means to look at all incident halfedges. If algorithms operating on a surface mesh maintain that the halfedge associated to a border vertex is a border halfedge, this is a constant time operation too. This section provides functions to check if an element is on a border and to change the halfedge associated to a border vertex. | |
bool | is_border (Vertex_index v, bool check_all_incident_halfedges=true) const |
returns whether v is a border vertex. More... | |
bool | is_border (Halfedge_index h) const |
returns whether h is a border halfege, that is if its incident face is sm.null_face() . | |
bool | is_border (Edge_index e) const |
returns whether e is a border edge, i.e., if any of its two halfedges is a border halfedge. More... | |
bool | set_vertex_halfedge_to_border_halfedge (Vertex_index v) |
iterates over the incident halfedges and sets the incident halfedge associated to vertex v to a border halfedge and returns true if it exists. More... | |
void | set_vertex_halfedge_to_border_halfedge (Halfedge_index h) |
applies set_vertex_halfedge_to_border_halfedge(Vertex_index) on all vertices around the face associated to h . More... | |
void | set_vertex_halfedge_to_border_halfedge () |
applies set_vertex_halfedge_to_border_halfedge(Vertex_index) on all vertices of the surface mesh. More... | |
bool | is_isolated (Vertex_index v) const |
returns whether v is isolated, i.e., incident to Surface_mesh::null_halfedge() . | |
Property Handling | |
A Properties can be added, and looked up with a string, and they can be removed at runtime. The point property of type | |
template<class I , class T > | |
using | Property_map = unspecified_type |
Model of LvaluePropertyMap with I as key type and T as value type, where I is either a vertex, halfedge, edge, or face index type. More... | |
template<class I , class T > | |
std::pair< Property_map< I, T >, bool > | add_property_map (std::string name=std::string(), const T t=T()) |
adds a property map named name with value type T and default t for index type I . More... | |
template<class I , class T > | |
std::pair< Property_map< I, T >, bool > | property_map (const std::string &name) const |
returns a property map named name with key type I and value type T , and a Boolean that is true if the property exists. More... | |
template<class I , class T > | |
void | remove_property_map (Property_map< I, T > &p) |
removes property map p . More... | |
template<class I > | |
void | remove_property_maps () |
removes all property maps for index type I added by a call to add_property_map<I>() . More... | |
void | remove_all_property_maps () |
removes all property maps for all index types added by a call to add_property_map() . More... | |
template<class I > | |
std::vector< std::string > | properties () const |
returns a vector with all strings that describe properties with the key type I . More... | |
Property_map< Vertex_index, Point > | points () const |
returns the property for the string "v:point". | |
Property_map< Vertex_index, Point > & | points () |
const Point & | point (Vertex_index v) const |
returns the point associated to vertex v . | |
Point & | point (Vertex_index v) |
returns the point associated to vertex v . | |
Null Elements | |
static Vertex_index | null_vertex () |
returns Vertex_index(std::numeric_limits<size_type>::max()) . | |
static Edge_index | null_edge () |
returns Edge_index(std::numeric_limits<size_type>::max()) . | |
static Halfedge_index | null_halfedge () |
returns Halfedge_index(std::numeric_limits<size_type>::max()) . | |
static Face_index | null_face () |
returns Face_index(std::numeric_limits<size_type>::max()) . | |
typedef unspecified_type CGAL::Surface_mesh< P >::Edge_range |
The range over all edge indices.
A model of BidirectionalRange with value type Edge_index
.
edges()
Halfedge_range
, Vertex_range
, Face_range
typedef unspecified_type CGAL::Surface_mesh< P >::Face_range |
The range over all face indices.
A model of BidirectionalRange with value type Face_index
.
faces()
Vertex_range
, Halfedge_range
, Edge_range
typedef unspecified_type CGAL::Surface_mesh< P >::Halfedge_range |
The range over all halfedge indices.
A model of BidirectionalRange with value type Halfedge_index
.
halfedges()
Vertex_range
, Edge_range
, Face_range
using CGAL::Surface_mesh< P >::Property_map = unspecified_type |
Model of LvaluePropertyMap
with I
as key type and T
as value type, where I
is either a vertex, halfedge, edge, or face index type.
typedef unspecified_type CGAL::Surface_mesh< P >::Vertex_range |
The range over all vertex indices.
A model of BidirectionalRange with value type Vertex_index
.
vertices()
Halfedge_range
, Edge_range
, Face_range
Halfedge_index CGAL::Surface_mesh< P >::add_edge | ( | Vertex_index | v0, |
Vertex_index | v1 | ||
) |
adds two opposite halfedges, and resizes edge and halfedge properties if necessary.
Sets the targets of the halfedge to the given vertices, but does not modify the halfedge associated to the vertices.
v1
as target Face_index CGAL::Surface_mesh< P >::add_face | ( | const Range & | vertices | ) |
if possible, adds a new face with vertices from a range with value type Vertex_index
.
The function adds halfedges between successive vertices if they are not yet indicent to halfedges, or updates the connectivity of halfedges already in place. Resizes halfedge, edge, and face properties if necessary.
Surface_mesh::null_face()
if the face could not be added. Face_index CGAL::Surface_mesh< P >::add_face | ( | Vertex_index | v0, |
Vertex_index | v1, | ||
Vertex_index | v2 | ||
) |
adds a new triangle connecting vertices v0
, v1
, v2
.
Surface_mesh::null_face()
if the face could not be added. Face_index CGAL::Surface_mesh< P >::add_face | ( | Vertex_index | v0, |
Vertex_index | v1, | ||
Vertex_index | v2, | ||
Vertex_index | v3 | ||
) |
adds a new quad connecting vertices v0
, v1
, v2
, v3
.
Surface_mesh::null_face()
if the face could not be added. std::pair<Property_map<I, T>, bool> CGAL::Surface_mesh< P >::add_property_map | ( | std::string | name = std::string() , |
const T | t = T() |
||
) |
adds a property map named name
with value type T
and default t
for index type I
.
Returns the property map together with a Boolean that is true
if a new map was created. In case it already exists the existing map together with false
is returned.
Vertex_index CGAL::Surface_mesh< P >::add_vertex | ( | const Point & | p | ) |
adds a new vertex, resizes vertex properties if necessary, and sets the point property to p
.
void CGAL::Surface_mesh< P >::clear | ( | ) |
removes all vertices, halfedge, edges and faces.
Collects garbage and removes all property maps added by a call to add_property_map()
for all simplex types.
After calling this method, the object is the same as a newly constructed object. The additional property maps are also removed and must thus be re-added if needed.
void CGAL::Surface_mesh< P >::collect_garbage | ( | ) |
really removes vertices, halfedges, edges, and faces which are marked removed.
has_garbage()
Halfedge_index CGAL::Surface_mesh< P >::halfedge | ( | Vertex_index | v | ) | const |
returns an incoming halfedge of vertex v
.
If v
is a border vertex this will be a border halfedge.
target(halfedge(v)) == v
Surface_mesh< P >::Halfedge_index CGAL::Surface_mesh< P >::halfedge | ( | Vertex_index | source, |
Vertex_index | target | ||
) | const |
finds a halfedge between two vertices.
Returns a default constructed Halfedge_index
, if source
and target
are not connected.
bool CGAL::Surface_mesh< P >::has_garbage | ( | ) | const |
checks if any vertices, halfedges, edges, or faces are marked as removed.
bool CGAL::Surface_mesh< P >::is_border | ( | Vertex_index | v, |
bool | check_all_incident_halfedges = true |
||
) | const |
returns whether v
is a border vertex.
With the default value for check_all_incident_halfedges
the function iteratates over the incident halfedges. With check_all_incident_halfedges == false
the function returns true
, if the incident halfedge associated to vertex v
is a border halfedge, or if the vertex is isolated.
Surface_mesh
is not a 2-manifold, then this operation is not guaranteed to return the right result. bool CGAL::Surface_mesh< P >::is_border | ( | Edge_index | e | ) | const |
returns whether e
is a border edge, i.e., if any of its two halfedges is a border halfedge.
bool CGAL::Surface_mesh< P >::is_removed | ( | Vertex_index | v | ) | const |
returns whether vertex v
is marked removed.
collect_garbage()
bool CGAL::Surface_mesh< P >::is_removed | ( | Halfedge_index | h | ) | const |
returns whether halfedge h
is marked removed.
collect_garbage()
bool CGAL::Surface_mesh< P >::is_removed | ( | Edge_index | e | ) | const |
returns whether edge e
is marked removed.
collect_garbage()
bool CGAL::Surface_mesh< P >::is_removed | ( | Face_index | f | ) | const |
returns whether face f
is marked removed.
collect_garbage()
bool CGAL::Surface_mesh< P >::is_valid | ( | bool | verbose = false | ) | const |
perform an expensive validity check on the data structure and print found errors to std::cerr
when verbose == true
.
bool CGAL::Surface_mesh< P >::join | ( | const Surface_mesh< P > & | other | ) |
copies the simplices from other
, and copies values of properties that already exist under the same name in *this
.
In case *this
has a property that does not exist in other
the copied simplices get the default value of the property.
Halfedge_index CGAL::Surface_mesh< P >::next_around_source | ( | Halfedge_index | h | ) | const |
returns next(opposite(h))
, that is the next halfedge clockwise around the source vertex of h
.
Halfedge_index CGAL::Surface_mesh< P >::next_around_target | ( | Halfedge_index | h | ) | const |
returns opposite(next(h))
, that is the next halfedge clockwise around the target vertex of h
.
Halfedge_index CGAL::Surface_mesh< P >::prev_around_source | ( | Halfedge_index | h | ) | const |
returns opposite(prev(h))
, that is the previous halfedge clockwise around the source vertex of h
.
Halfedge_index CGAL::Surface_mesh< P >::prev_around_target | ( | Halfedge_index | h | ) | const |
returns prev(opposite(h))
, that is the previous halfedge clockwise around the target vertex of h
.
std::vector<std::string> CGAL::Surface_mesh< P >::properties | ( | ) | const |
returns a vector with all strings that describe properties with the key type I
.
I | The key type of the properties. |
std::pair<Property_map<I, T>,bool> CGAL::Surface_mesh< P >::property_map | ( | const std::string & | name | ) | const |
returns a property map named name
with key type I
and value type T
, and a Boolean that is true
if the property exists.
In case it does not exist the Boolean is false
and the behavior of the property map is undefined.
void CGAL::Surface_mesh< P >::remove_all_property_maps | ( | ) |
removes all property maps for all index types added by a call to add_property_map()
.
The memory allocated for those property maps is freed.
void CGAL::Surface_mesh< P >::remove_edge | ( | Edge_index | e | ) |
removes the two halfedges corresponding to e
from the halfedge data structure without adjusting anything.
void CGAL::Surface_mesh< P >::remove_face | ( | Face_index | f | ) |
removes face f
from the halfedge data structure without adjusting anything.
void CGAL::Surface_mesh< P >::remove_property_map | ( | Property_map< I, T > & | p | ) |
removes property map p
.
The memory allocated for that property map is freed.
removes all property maps for index type I
added by a call to add_property_map<I>()
.
The memory allocated for those property maps is freed.
void CGAL::Surface_mesh< P >::remove_vertex | ( | Vertex_index | v | ) |
removes vertex v
from the halfedge data structure without adjusting anything.
void CGAL::Surface_mesh< P >::reserve | ( | size_type | nvertices, |
size_type | nedges, | ||
size_type | nfaces | ||
) |
reserves space for vertices, halfedges, edges, faces, and their currently associated properties.
void CGAL::Surface_mesh< P >::set_next | ( | Halfedge_index | h, |
Halfedge_index | nh | ||
) |
sets the next halfedge of h
within the face to nh
and the previous halfedge of nh
to h
.
void CGAL::Surface_mesh< P >::set_recycle_garbage | ( | bool | b | ) |
controls the recycling or not of simplices previously marked as removed upon addition of new elements.
When set to true
(default value), new elements are first picked in the garbage (if any) while if set to false
only new elements are created.
bool CGAL::Surface_mesh< P >::set_vertex_halfedge_to_border_halfedge | ( | Vertex_index | v | ) |
iterates over the incident halfedges and sets the incident halfedge associated to vertex v
to a border halfedge and returns true
if it exists.
void CGAL::Surface_mesh< P >::set_vertex_halfedge_to_border_halfedge | ( | Halfedge_index | h | ) |
applies set_vertex_halfedge_to_border_halfedge(Vertex_index)
on all vertices around the face associated to h
.
void CGAL::Surface_mesh< P >::set_vertex_halfedge_to_border_halfedge | ( | ) |
applies set_vertex_halfedge_to_border_halfedge(Vertex_index)
on all vertices of the surface mesh.