
/*!
\ingroup PkgInterpolation2Concepts
\cgalConcept

\ref PkgInterpolationSibsonGradientFitting are parameterized by a
traits class that defines the primitives used by the algorithm. The
concept `GradientFittingTraits` defines this common set of requirements.

\cgalHasModelsBegin
\cgalHasModels{CGAL::Interpolation_gradient_fitting_traits_2<K>}
\cgalHasModelsEnd

\sa `InterpolationTraits`
\sa `CGAL::Interpolation_traits_2<K>`
\sa \ref PkgInterpolationSibsonGradientFitting
\sa `CGAL::sibson_c1_interpolation()`
\sa `CGAL::farin_c1_interpolation()`
\sa `CGAL::quadratic_interpolation()`
*/
class GradientFittingTraits
{
public:

/// \name Types
/// @{

/*!
The number type must follow the model `FieldNumberType`.
*/
typedef unspecified_type FT;

/*!
The (weightless) point type.
*/
typedef unspecified_type Point_d;

/*!
The weighted point type.
*/
typedef unspecified_type Weighted_point_d;

/*!
The corresponding vector type.
*/
typedef unspecified_type Vector_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`.

*/
typedef unspecified_type Aff_transformation_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`.
*/
typedef unspecified_type Construct_point_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.
*/
typedef unspecified_type Construct_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 Construct_scaled_vector_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`.
*/
typedef unspecified_type Compute_squared_distance_d;

/*!
Constructor object for `Aff_transformation_d`. Provides :

`Aff_transformation_d operator()()`, which introduces an affine transformation
whose matrix has only zero entries.
*/
typedef unspecified_type Construct_null_matrix_d;

/*!
Constructor object for `Aff_transformation_d`. Provides :

`Aff_transformation_d operator()(FT scale)`, which introduces a scaling by a scale factor `scale`.
*/
typedef unspecified_type Construct_scaling_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`.
*/
typedef unspecified_type Construct_sum_matrix_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`\f$ ^t\f$`v`.
*/
typedef unspecified_type Construct_outer_product_d;

/// @}

/// \name Creation
/// @{

/*!
default constructor.
*/
GradientFittingTraits();

/// @}

/// \name 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();

/// @}

}; /* end GradientFittingTraits */

