CGAL 6.1 - 2D and Surface Function Interpolation

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InterpolationTraits Concept Reference
Reference Manual » Concepts

## Definition

Most interpolation functions are parameterized by a traits class that defines the primitives used in the interpolation algorithms. The concept `InterpolationTraits` defines this common set of requirements.

Has models
  `CGAL::Interpolation_traits_2<K>`
  `CGAL::Interpolation_gradient_fitting_traits_2<K>`

See also
  `GradientFittingTraits`
  `CGAL::sibson_c1_interpolation()`
  Sibson Gradient Fitting Functions
  `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 | 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`.
| InterpolationTraits ()
| default constructor.

## Construction objects
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 ()

## Member Typedef Documentation

## ◆ Compute_squared_distance_d

typedef unspecified_type InterpolationTraits::Compute_squared_distance_d

Constructor object for `FT`.

Provides the operator:

`FT operator() (Point_d p, Point_d q)` returning the squared distance between `p` and `q`.

## ◆ Construct_point_d

typedef unspecified_type InterpolationTraits::Construct_point_d

A constructor object for `Point_d`.

Provides :

`Point_d operator() (Point_d p)` which returns the point itself.

`Point_d operator() (Weighted_point_d wp)` which extracts the bare point from the weighted point.

## ◆ Construct_scaled_vector_d

typedef unspecified_type InterpolationTraits::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_vector_d

typedef unspecified_type InterpolationTraits::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.