CGAL 6.2 - Advancing Front Surface Reconstruction: AdvancingFrontSurfaceReconstructionTraits_3 Concept Reference

CGAL 6.2 - Advancing Front Surface Reconstruction

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AdvancingFrontSurfaceReconstructionTraits_3 Concept Reference
Reference Manual

## Definition

The concept `AdvancingFrontSurfaceReconstructionTraits_3` describes the requirements for 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`.