\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.13.2 - 2D and Surface Function Interpolation
GradientFittingTraits Concept Reference

Definition

Types

typedef unspecified_type FT
 The number type must follow the model FieldNumberType.
 
typedef unspecified_type Point_d
 The (weightless) point type.
 
typedef unspecified_type Weighted_point_d
 The weighted point type.
 
typedef unspecified_type Vector_d
 The corresponding vector type.
 
typedef unspecified_type Aff_transformation_d
 defines a matrix type. More...
 
typedef unspecified_type Construct_point_d
 A constructor object for Point_d. More...
 
typedef unspecified_type Construct_vector_d
 A constructor object for Vector_d. More...
 
typedef unspecified_type Construct_scaled_vector_d
 Constructor object for Vector_d. More...
 
typedef unspecified_type Compute_squared_distance_d
 Constructor object for FT. More...
 
typedef unspecified_type Construct_null_matrix_d
 Constructor object for Aff_transformation_d. More...
 
typedef unspecified_type Construct_scaling_matrix_d
 Constructor object for Aff_transformation_d. More...
 
typedef unspecified_type Construct_sum_matrix_d
 Constructor object for Aff_transformation_d. More...
 
typedef unspecified_type Construct_outer_product_d
 Constructor object for Aff_transformation_d. More...
 

Creation

 GradientFittingTraits ()
 default constructor.
 

Operations

The following functions that create instances of the above constructor object types must exist.

Construct_vector_d construct_point_d_object ()
 
Construct_vector_d construct_vector_d_object ()
 
Construct_scaled_vector_d construct_scaled_vector_d_object ()
 
Compute_squared_distance_d compute_squared_distance_d_object ()
 
Construct_null_matrix_d construct_null_matrix_d_object ()
 
Construct_scaling_matrix_d construct_scaling_matrix_d_object ()
 
Construct_sum_matrix_d construct_sum_matrix_d_object ()
 
Construct_outer_product_d construct_outer_product_d_object ()
 

Member Typedef Documentation

◆ Aff_transformation_d

defines a matrix type.

Must provide the following member functions :

Aff_transformation tr.inverse (), which gives the inverse transformation, and

Aff_transformation tr.transform(Vector v), which returns the multiplication of tr with v.

◆ Compute_squared_distance_d

Constructor object for FT.

Provides the operator:

FT operator() (Point_d p, Point_d q), which returns the squared distance between p and q.

◆ Construct_null_matrix_d

Constructor object for Aff_transformation_d.

Provides :

Aff_transformation_d operator()(), which introduces an affine transformation whose matrix has only zero entries.

◆ Construct_outer_product_d

Constructor object for Aff_transformation_d.

Provides :

Aff_transformation_d operator()(Vector v), which returns the outer product, i.e. the quadratic matrix v \( ^t\)v.

◆ Construct_point_d

A constructor object for Point_d.

Provides :

Point_d operator() (Point_d p), which simply returns p

Point_d operator() (Weighted_point_d wp), which returns the bare point contained in wp.

◆ Construct_scaled_vector_d

Constructor object for Vector_d.

Provides :

Vector_d operator() (Vector_d v, FT scale), which produces the vector v scaled by a factor scale.

◆ Construct_scaling_matrix_d

Constructor object for Aff_transformation_d.

Provides :

Aff_transformation_d operator()(FT scale), which introduces a scaling by a scale factor scale.

◆ Construct_sum_matrix_d

Constructor object for Aff_transformation_d.

Provides :

Aff_transformation_d operator()(Aff_transformation_d tr1, Aff_transformation_d tr2), which returns the sum of the two matrices representing tr1 and tr2.

◆ Construct_vector_d

A constructor object for Vector_d.

Provides :

Vector_d operator() (Point_d p, Point_d q), which produces the vector q - p and

Vector_d operator() (Null_vector NULL_VECTOR), which introduces the null vector.