GradientFittingTraits Concept Reference

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.