CGAL 5.4 - Advancing Front Surface Reconstruction

## 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 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. More...

typedef unspecified_type Construct_cross_product_vector_3
A constructor object that must provide the function operator. More...

typedef unspecified_type Compute_scalar_product_3
A constructor object that must provide the function operator. More...

typedef unspecified_type Construct_sphere_3
A constructor object that must provide the function operator. More...

typedef unspecified_type Construct_center_3
A constructor object that must provide the function operator. More...

A constructor object that must provide the function operators. More...

typedef unspecified_type Compute_squared_distance_3
A constructor object that must provide the function operator. More...

## Operations

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.

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.

## ◆ 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

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.

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

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

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

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

A constructor object that must provide the function operator.

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

which constructs the vector q-p.