CGAL 5.1.2 - 2D and Surface Function Interpolation
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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.
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. More... | |
typedef unspecified_type | Construct_point_d |
A constructor object for Point_d . More... | |
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... | |
typedef unspecified_type | Construct_null_matrix_d |
Constructor object for Aff_transformation_d . More... | |
typedef unspecified_type | Construct_scaling_matrix_d |
Constructor object for Aff_transformation_d . More... | |
typedef unspecified_type | Construct_sum_matrix_d |
Constructor object for Aff_transformation_d . More... | |
typedef unspecified_type | Construct_outer_product_d |
Constructor object for Aff_transformation_d . More... | |
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 () |
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
.
Constructor object for FT
.
Provides the operator:
FT operator() (Point_d p, Point_d q)
, which returns the squared distance between p
and q
.
Constructor object for Aff_transformation_d
.
Provides :
Aff_transformation_d operator()()
, which introduces an affine transformation whose matrix has only zero entries.
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
.
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
.
Constructor object for Vector_d
.
Provides :
Vector_d operator() (Vector_d v, FT scale)
, which produces the vector v
scaled by a factor scale
.
Constructor object for Aff_transformation_d
.
Provides :
Aff_transformation_d operator()(FT scale)
, which introduces a scaling by a scale factor scale
.
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
.
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.