SegmentDelaunayGraphSite_2 Concept Reference

Definition

The concept SegmentDelaunayGraphSite_2 provides the requirements for the sites of a segment Delaunay graph.

Refines:

DefaultConstructible

CopyConstructible

Assignable

Has Models:

CGAL::Segment_Delaunay_graph_site_2<K>

See also

SegmentDelaunayGraphTraits_2

CGAL::Segment_Delaunay_graph_site_2<K>

CGAL::Segment_Delaunay_graph_traits_2<K,MTag>

CGAL::Segment_Delaunay_graph_traits_without_intersections_2<K,MTag>

CGAL::Segment_Delaunay_graph_filtered_traits_2<CK,CM,EK,EM,FK,FM>

CGAL::Segment_Delaunay_graph_filtered_traits_without_intersections_2<CK,CM,EK,EM,FK,FM>

Types
typedef unspecified_type	Point_2
	The point type. More...
typedef unspecified_type	Segment_2
	The segment type. More...
typedef unspecified_type	FT
	The field number type. More...
typedef unspecified_type	RT
	The ring number type. More...

Creation
In addition to the default and copy constructors the following static methods are available for constructing sites:
static SegmentDelaunayGraphSite_2	construct_site_2 (Point_2 p)
	Constructs a site from a point: the site represents the point p. More...
static SegmentDelaunayGraphSite_2	construct_site_2 (Point_2 p1, Point_2 p2)
	Constructs a site from two points: the site represents the (open) segment (p1,p2). More...
static SegmentDelaunayGraphSite_2	construct_site_2 (Point_2 p1, Point_2 p2, Point_2 q1, Point_2 q2)
	Constructs a site from four points: the site represents the point of intersection of the segments (p1,p2) and (q1,q2). More...
static SegmentDelaunayGraphSite_2	construct_site_2 (Point_2 p1, Point_2 p2, Point_2 q1, Point_2 q2, bool b)
	Constructs a site from four points and a boolean: the site represents a segment. More...
static SegmentDelaunayGraphSite_2	construct_site_2 (Point_2 p1, Point_2 p2, Point_2 q1, Point_2 q2, Point_2 r1, Point_2 r2)
	Constructs a site from six points: the site represents the segment with endpoints the points of intersection of the pairs of segments (p1,p2),(q1,q2) and (p1,p2),(r1,r2). More...

Predicates
bool	is_defined ()
	Returns true if the site represents a valid point or segment. More...
bool	is_point ()
	Returns true if the site represents a point. More...
bool	is_segment ()
	Returns true if the site represents a segment. More...
bool	is_input ()
	Returns true if the site represents an input point or a segment defined by two input points. More...
bool	is_input (unsigned int i)
	Returns true if the i-th endpoint of the site is an input point. More...

Access Functions
Point_2	point () const
	Returns the point represented by the site s. More...
Segment_2	segment () const
	Returns the segment represented by the site s. More...
Point_2	source () const
	Returns the source endpoint of the segment. More...
Point_2	target () const
	Returns the target endpoint of the segment. More...
SegmentDelaunayGraphSite_2	supporting_site ()
	Returns a segment site object representing the segment that supports the segment represented by the site. More...
SegmentDelaunayGraphSite_2	supporting_site (unsigned int i)
	Returns a segment site object representing the i-th segment that supports the point of intersection represented by the site. More...
SegmentDelaunayGraphSite_2	crossing_site (unsigned int i)
	Returns a segment site object representing the i-th segment that supports the \( i\)-th endpoint of the site which is not the supporting segment of the site. More...
SegmentDelaunayGraphSite_2	source_site ()
	Returns a point site object representing the source point of the site. More...
SegmentDelaunayGraphSite_2	target_site ()
	Returns a point site object representing the target point of the site. More...
Point_2	source_of_supporting_site ()
	Returns the source point of the supporting site of the this site. More...
Point_2	target_of_supporting_site ()
	Returns the target point of the supporting site of the this site. More...
Point_2	source_of_supporting_site (unsigned int i)
	Returns the source point of the i-th supporting site of the this site. More...
Point_2	target_of_supporting_site (unsigned int i)
	Returns the target point of the i-th supporting site of the this site. More...
Point_2	source_of_crossing_site (unsigned int i)
	Returns the source point of the i-th crossing site of the this site. More...
Point_2	target_of_crossing_site (unsigned int i)
	Returns the target point of the i-th supporting site of the this site. More...

Member Typedef Documentation

typedef unspecified_type SegmentDelaunayGraphSite_2::FT

The field number type.

typedef unspecified_type SegmentDelaunayGraphSite_2::Point_2

The point type.

typedef unspecified_type SegmentDelaunayGraphSite_2::RT

The ring number type.

typedef unspecified_type SegmentDelaunayGraphSite_2::Segment_2

The segment type.

Member Function Documentation

static SegmentDelaunayGraphSite_2 SegmentDelaunayGraphSite_2::construct_site_2 ( Point_2  p )

static

Constructs a site from a point: the site represents the point p.

static SegmentDelaunayGraphSite_2 SegmentDelaunayGraphSite_2::construct_site_2 ( Point_2  p1, Point_2  p2  )

static

Constructs a site from two points: the site represents the (open) segment (p1,p2).

static SegmentDelaunayGraphSite_2 SegmentDelaunayGraphSite_2::construct_site_2 ( Point_2  p1, Point_2  p2, Point_2  q1, Point_2  q2  )

static

Constructs a site from four points: the site represents the point of intersection of the segments (p1,p2) and (q1,q2).

static SegmentDelaunayGraphSite_2 SegmentDelaunayGraphSite_2::construct_site_2 ( Point_2  p1, Point_2  p2, Point_2  q1, Point_2  q2, bool  b  )

static

Constructs a site from four points and a boolean: the site represents a segment.

If b is true the endpoints are p1 and \( p_\times\), otherwise \( p_\times\) and p2. \( p_\times\) is the point of intersection of the segments (p1,p2),(q1,q2).

static SegmentDelaunayGraphSite_2 SegmentDelaunayGraphSite_2::construct_site_2 ( Point_2  p1, Point_2  p2, Point_2  q1, Point_2  q2, Point_2  r1, Point_2  r2  )

static

Constructs a site from six points: the site represents the segment with endpoints the points of intersection of the pairs of segments (p1,p2),(q1,q2) and (p1,p2),(r1,r2).

SegmentDelaunayGraphSite_2 SegmentDelaunayGraphSite_2::crossing_site

(

unsigned int

i

)

Returns a segment site object representing the i-th segment that supports the \( i\)-th endpoint of the site which is not the supporting segment of the site.

Both endpoints of the returned site are input points.

Precondition

i must be at most \( 1\), s.is_segment() must be true and s.is_input(i) must be false.

bool SegmentDelaunayGraphSite_2::is_defined

(

)

Returns true if the site represents a valid point or segment.

bool SegmentDelaunayGraphSite_2::is_input

(

)

Returns true if the site represents an input point or a segment defined by two input points.

Returns false if it represents a point of intersection of two segments, or if it represents a segment, at least one endpoint of which is a point of intersection of two segments.

bool SegmentDelaunayGraphSite_2::is_input

(

unsigned int

i

)

Returns true if the i-th endpoint of the site is an input point.

Returns false if the i-th endpoint of the site is the intersection of two segments.

Precondition

i must be at most \( 1\), and s.is_segment() must be true.

bool SegmentDelaunayGraphSite_2::is_point

(

)

Returns true if the site represents a point.

bool SegmentDelaunayGraphSite_2::is_segment

(

)

Returns true if the site represents a segment.

Point_2 SegmentDelaunayGraphSite_2::point

(

)

const

Returns the point represented by the site s.

Precondition

s.is_point() must be true.

Segment_2 SegmentDelaunayGraphSite_2::segment

(

)

const

Returns the segment represented by the site s.

Precondition

s.is_segment() must be true.

Point_2 SegmentDelaunayGraphSite_2::source

(

)

const

Returns the source endpoint of the segment.

Note that this method can construct an inexact point if the number type used is inexact.

Precondition

s.is_segment() must be true.

Point_2 SegmentDelaunayGraphSite_2::source_of_crossing_site

(

unsigned int

i

)

Returns the source point of the i-th crossing site of the this site.

Precondition

is_segment() must be true, is_input(i) must be false and i must either be 0 or 1.

Point_2 SegmentDelaunayGraphSite_2::source_of_supporting_site

(

)

Returns the source point of the supporting site of the this site.

Precondition

is_segment() must be true.

Point_2 SegmentDelaunayGraphSite_2::source_of_supporting_site

(

unsigned int

i

)

Returns the source point of the i-th supporting site of the this site.

Precondition

is_point() must be true, is_input() must be false and i must either be 0 or 1.

SegmentDelaunayGraphSite_2 SegmentDelaunayGraphSite_2::source_site

(

)

Returns a point site object representing the source point of the site.

Precondition

s.is_segment() must be true.

SegmentDelaunayGraphSite_2 SegmentDelaunayGraphSite_2::supporting_site

(

)

Returns a segment site object representing the segment that supports the segment represented by the site.

Both endpoints of the returned site are input points.

Precondition

s.is_segment() must be true.

SegmentDelaunayGraphSite_2 SegmentDelaunayGraphSite_2::supporting_site

(

unsigned int

i

)

Returns a segment site object representing the i-th segment that supports the point of intersection represented by the site.

Both endpoints of the returned site are input points.

Precondition

i must be at most \( 1\), s.is_point() must be true and s.is_input() must be false.

Point_2 SegmentDelaunayGraphSite_2::target

(

)

const

Returns the target endpoint of the segment.

Note that this method can construct an inexact point if the number type used is inexact.

Precondition

s.is_segment() must be true.

Point_2 SegmentDelaunayGraphSite_2::target_of_crossing_site

(

unsigned int

i

)

Returns the target point of the i-th supporting site of the this site.

Precondition

is_segment() must be true, is_input(i) must be false and i must either be 0 or 1.

Point_2 SegmentDelaunayGraphSite_2::target_of_supporting_site

(

)

Returns the target point of the supporting site of the this site.

Precondition

is_segment() must be true.

Point_2 SegmentDelaunayGraphSite_2::target_of_supporting_site

(

unsigned int

i

)

Returns the target point of the i-th supporting site of the this site.

Precondition

is_point() must be true, is_input() must be false and i must either be 0 or 1.

SegmentDelaunayGraphSite_2 SegmentDelaunayGraphSite_2::target_site

(

)

Returns a point site object representing the target point of the site.

Precondition

s.is_segment() must be true.