Definition

The concept MeshDomainWithFeatures_3 refines the concept MeshDomain_3. While the concept MeshDomain_3 only exposes the 2-dimensional and 3-dimensional features of the domain through different queries, the concept MeshDomainWithFeatures_3 also exposes 0 and 1-dimensional features. The exposed features of the domain are respectively called subdomains, surface patches, curve segments and corners according to their respective dimensions 3,2,1 and 0.

Refines:: MeshDomain_3

Has Models:

CGAL::Mesh_domain_with_polyline_features_3<MeshDomain_3>

CGAL::Polyhedral_mesh_domain_with_features_3<IGT>

See Also: MeshDomain_3

Types
typedef CGAL::Tag_true	Has_features
	A type to distinguish `MeshDomain_3` models from `MeshDomainWithFeatures_3` models.

typedef unspecified_type	FT
	Numerical type.

typedef unspecified_type	Curve_segment_index
	Type of indices for curve segments ( \( 1\)-dimensional features) of the input domain. More...

typedef unspecified_type	Corner_index
	Type of indices for corners (i.e. 0-dimensional features) of the input domain. More...

Operations
Each connected component of a curve segment is assumed to be oriented. The orientation is defined by the ordering of the two incident corners at the origin and endpoint. Therefore it is possible to defined the signed geodesic distance between two ordered points on the same connected component of a curve segment. A cycle is a connected component of a curve segment incident to 0 or 1 corner. Note `construct_point_on_curve segment` is assumed to return a uniquely defined point. Therefore it is not possible to handle as a single curve segment, a singular curve with several branches incident to the same point.
Point_3	construct_point_on_curve_segment (const Point_3 &p, const Curve_segment_index &ci, FT d) const
	Returns a point on the curve segment with index `ci` at signed geodesic distance `d` from point `p`. More...

Queries
FT	geodesic_distance (const Point_3 &p, const Point_3 &q, const Curve_segment_index &ci) const
	Returns the signed geodesic distance between points `p` and `q` along the input curve segment with index `ci`. More...

CGAL::Sign	distance_sign_along_cycle (const Point_3 &p, const Point_3 &q, const Point_3 &r, const Curve_segment_index &ci) const
	Returns `CGAL::POSITIVE` if the signed geodesic distance from `p` to `q` on the way through \( r\) along cycle with index `ci` is positive, `CGAL::NEGATIVE` if the distance is negative, and `CGAL::ZERO` if `(p = q = r)`. More...

bool	is_cycle (const Point_3 &p, const Curve_segment_index &ci) const
	Returns `true` if the connected component of curve segment `ci` including point `p` is a cycle.

Retrieval of the input features and their incidences
template<typename OutputIterator >
OutputIterator	get_corners (OutputIterator corners) const
	Fills `corners` with the corners of the input domain. More...

template<typename OutputIterator >
OutputIterator	get_curve_segments (OutputIterator curves) const
	Fills `curves` with the curve segments of the input domain. More...

bool	are_incident_surface_patch_curve_segment (Surface_patch_index spi, Curve_segment_index csi)
	Returns `true` if the curve segment with index `csi` is incident to the surface patch with index `spi`.

bool	are_incident_surface_patch_corner (Surface_patch_index spi, Corner_index ci)
	Returns `true` if the corner with index `ci` is incident to the surface patch with index `spi`.

Indices converters
Index	index_from_curve_segment_index (const Curve_segment_index &curve_segment_index) const
	Returns the index to be stored at a vertex lying on the curve segment identified by `curve_segment_index`.

Curve_segment_index	curve_segment_index (const Index &index) const
	Returns the `Curve_segment_index` of the curve segment where lies a vertex with dimension 1 and index `index`.

Index	index_from_corner_index (const Corner_index &corner_index) const
	Returns the index to be stored at a vertex lying on the corner identified by `corner_index`.

Corner_index	corner_index (const Index &index) const
	Returns the `Corner_index` of the corner where lies a vertex with dimension 0 and index `index`.

Member Typedef Documentation

typedef unspecified_type MeshDomainWithFeatures_3::Corner_index

Type of indices for corners (i.e. 0-dimensional features) of the input domain.

Must be a model of CopyConstructible, Assignable, DefaultConstructible and LessThanComparable.

typedef unspecified_type MeshDomainWithFeatures_3::Curve_segment_index

Type of indices for curve segments ( \( 1\)-dimensional features) of the input domain.

Must be a model of CopyConstructible, Assignable, DefaultConstructible and LessThanComparable. The default constructed value must be the value of an edge which does not approximate a 1-dimensional feature of the input domain.

Member Function Documentation

Point_3 MeshDomainWithFeatures_3::construct_point_on_curve_segment	(	const Point_3 &	p,
		const Curve_segment_index &	ci,
		FT	d
	)		const

Returns a point on the curve segment with index ci at signed geodesic distance d from point p.

Precondition: Point p is supposed to be on curve segment ci. If d > 0, the signed geodesic distance from p to the endpoint of the connected component of ci including \( p\), should be greater than \( d\). If d < 0, the signed geodesic distance from p to the origin of the connected component should be less than \( d\) from the origin of the connected component.

CGAL::Sign MeshDomainWithFeatures_3::distance_sign_along_cycle	(	const Point_3 &	p,
		const Point_3 &	q,
		const Point_3 &	r,
		const Curve_segment_index &	ci
	)		const

Returns CGAL::POSITIVE if the signed geodesic distance from p to q on the way through \( r\) along cycle with index ci is positive, CGAL::NEGATIVE if the distance is negative, and CGAL::ZERO if (p = q = r).

Precondition: Points p, q and r belongs to the same connected component of curve segment ci and this component is a cycle.

FT MeshDomainWithFeatures_3::geodesic_distance	(	const Point_3 &	p,
		const Point_3 &	q,
		const Curve_segment_index &	ci
	)		const

Returns the signed geodesic distance between points p and q along the input curve segment with index ci.

Precondition: Points p and q belong to the same connected component of the curve segment with index ci.

template<typename OutputIterator >

OutputIterator MeshDomainWithFeatures_3::get_corners ( OutputIterator corners) const

Fills corners with the corners of the input domain.

The value type of corners must be std::pair<Corner_index,Point_3>.

template<typename OutputIterator >

OutputIterator MeshDomainWithFeatures_3::get_curve_segments ( OutputIterator curves) const

Fills curves with the curve segments of the input domain.

curves value type must be CGAL::cpp11::tuple<Curve_segment_index,std::pair<Point_3,Index>,std::pair<Point_3,Index> >. If the curve segment corresponding to an entry in curves is not a cycle, the pair of associated points should belong to two corners incident on the curve segment. If it is a cycle, then the same Point_3 should be given twice and must be any point on the cycle. The Index values associated to the points are their indices w.r.t. their dimension.

Definition

Types

Operations

Queries

Retrieval of the input features and their incidences

Indices converters

Member Typedef Documentation

Member Function Documentation