AdvancingFrontSurfaceReconstructionTraits_3 Concept Reference

Definition

The concept AdvancingFrontSurfaceReconstructionTraits_3 describes the requirements for the the geometric traits of the class CGAL::Delaunay_triangulation_3 used in the class CGAL::Advancing_front_surface_reconstruction. It defines the geometric objects (points, segments...) forming the triangulation together with a few geometric predicates and constructions on these objects.

Refines

DelaunayTriangulationTraits_3

Has models

All models of the concept Kernel

Types
typedef unspecified_type	FT
	The coordinate type.
typedef unspecified_type	Vector_3
	The vector type.
typedef unspecified_type	Sphere_3
	The sphere type.
typedef unspecified_type	Construct_vector_3
	A constructor object that must provide the function operator.
typedef unspecified_type	Construct_cross_product_vector_3
	A constructor object that must provide the function operator.
typedef unspecified_type	Compute_scalar_product_3
	A constructor object that must provide the function operator.
typedef unspecified_type	Construct_sphere_3
	A constructor object that must provide the function operator.
typedef unspecified_type	Construct_center_3
	A constructor object that must provide the function operator.
typedef unspecified_type	Compute_squared_radius_3
	A constructor object that must provide the function operators.
typedef unspecified_type	Compute_squared_distance_3
	A constructor object that must provide the function operator.

Operations
The following functions give access to the predicate and construction objects:
Construct_vector_3	construct_vector_3_object ()
	gives access to the Construct_vector_3 construction.
Construct_cross_product_vector_3	construct_cross_product_vector_3_object ()
	gives access to the Construct_cross_product_vector_3 construction.
Compute_scalar_product_3	compute_scalar_product_3_object ()
	gives access to the Compute_scalar_product_3 construction.
Construct_sphere_3	construct_sphere_3_object ()
	gives access to the Construct_sphere_3 construction.
Construct_center_3	construct_center_3_object ()
	gives access to the Construct_center_3 construction.
Compute_squared_radius_3	compute_squared_radius_3_object ()
	gives access to the Compute_squared_radius_3 construction.
Compute_squared_distance_3	compute_squared_distance_3_object ()
	gives access to the Compute_squared_distance_3 construction.

Member Typedef Documentation

Compute_scalar_product_3

typedef unspecified_type AdvancingFrontSurfaceReconstructionTraits_3::Compute_scalar_product_3

A constructor object that must provide the function operator.

FT operator()(Vector_3 v, Vector_3 w),

which returns the scalar (inner) product of v and w.

Compute_squared_distance_3

typedef unspecified_type AdvancingFrontSurfaceReconstructionTraits_3::Compute_squared_distance_3

A constructor object that must provide the function operator.

FT operator()(Point_3 p, Point_3 q),

which returns the squared distance between the points p and q.

Compute_squared_radius_3

typedef unspecified_type AdvancingFrontSurfaceReconstructionTraits_3::Compute_squared_radius_3

A constructor object that must provide the function operators.

FT operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s),

which returns the squared radius of the sphere passing through p, q and r, and whose center is in the plane defined by these three points.

and

FT operator()(Point_3 p, Point_3 q, Point_3 r, Point_3 s),

which returns the squared radius of the sphere passing through p, q, r, and s.

and

FT operator()(Sphere_3 s),

which returns the squared radius of the sphere s.

Construct_center_3

typedef unspecified_type AdvancingFrontSurfaceReconstructionTraits_3::Construct_center_3

A constructor object that must provide the function operator.

Point_3 operator()(Sphere_3 s),

which returns the center of the sphere s.

Construct_cross_product_vector_3

typedef unspecified_type AdvancingFrontSurfaceReconstructionTraits_3::Construct_cross_product_vector_3

A constructor object that must provide the function operator.

Vector_3 operator()(Vector_3 v, Vector_3 w),

which returns the cross product of v and w.

Construct_sphere_3

typedef unspecified_type AdvancingFrontSurfaceReconstructionTraits_3::Construct_sphere_3

A constructor object that must provide the function operator.

Sphere_3 operator()(Point_3 p, Point_3 q, Point_3 r),

which constructs a sphere initialized to the smallest sphere which passes through the points p, q, and r.

Construct_vector_3

typedef unspecified_type AdvancingFrontSurfaceReconstructionTraits_3::Construct_vector_3

A constructor object that must provide the function operator.

Vector_3 operator()(Point_3 p, Point_3 q),

which constructs the vector q-p.