CGAL 6.1.2 - 2D and Surface Function Interpolation: GradientFittingTraits Concept Reference

CGAL 6.1.2 - 2D and Surface Function Interpolation

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GradientFittingTraits Concept Reference
Reference Manual » Concepts

## Definition

Sibson Gradient Fitting Functions are parameterized by a traits class that defines the primitives used by the algorithm. The concept `GradientFittingTraits` defines this common set of requirements.

Has models
  `CGAL::Interpolation_gradient_fitting_traits_2<K>`

See also
  `InterpolationTraits`
  `CGAL::Interpolation_traits_2<K>`
  Sibson Gradient Fitting Functions
  `CGAL::sibson_c1_interpolation()`
  `CGAL::farin_c1_interpolation()`
  `CGAL::quadratic_interpolation()`

## 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.
typedef unspecified_type | Construct_point_d
| A constructor object for `Point_d`.
typedef unspecified_type | Construct_vector_d
| A constructor object for `Vector_d`.
typedef unspecified_type | Construct_scaled_vector_d
| Constructor object for `Vector_d`.
typedef unspecified_type | Compute_squared_distance_d
| Constructor object for `FT`.
typedef unspecified_type | Construct_null_matrix_d
| Constructor object for `Aff_transformation_d`.
typedef unspecified_type | Construct_scaling_matrix_d
| Constructor object for `Aff_transformation_d`.
typedef unspecified_type | Construct_sum_matrix_d
| Constructor object for `Aff_transformation_d`.
typedef unspecified_type | Construct_outer_product_d
| Constructor object for `Aff_transformation_d`.

## 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

typedef unspecified_type GradientFittingTraits::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

typedef unspecified_type GradientFittingTraits::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

typedef unspecified_type GradientFittingTraits::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

typedef unspecified_type GradientFittingTraits::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

typedef unspecified_type GradientFittingTraits::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

typedef unspecified_type GradientFittingTraits::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

typedef unspecified_type GradientFittingTraits::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

typedef unspecified_type GradientFittingTraits::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

typedef unspecified_type GradientFittingTraits::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.