\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D and Surface Function Interpolation

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InterpolationTraits Concept Reference
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 point type on which the function is defined and interpolated.
typedef unspecified_type | Vector_d
| The corresponding vector type.
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...
| InterpolationTraits ()
| default constructor.

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

typedef unspecified_type InterpolationTraits::Compute_squared_distance_d

Constructor object for `FT`.

Provides the operator:

`FT operator() (Point_d a, Point_d b)` returning the squared distance between `a` and `b`.

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`.

typedef unspecified_type InterpolationTraits::Construct_vector_d

A constructor object for `Vector_d`.

Provides :

`Vector_d operator() (Point_d a, Point_d b)` which produces the vector `b - a` and

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